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Ambruş VE, Bazzanini L, Gabbana A, Simeoni D, Succi S, Tripiccione R. Fast kinetic simulator for relativistic matter. NATURE COMPUTATIONAL SCIENCE 2022; 2:641-654. [PMID: 38177272 DOI: 10.1038/s43588-022-00333-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2022] [Accepted: 09/08/2022] [Indexed: 01/06/2024]
Abstract
Relativistic kinetic theory is ubiquitous to several fields of modern physics, finding application at large scales in systems in astrophysical contexts, all of the way down to subnuclear scales and into the realm of quark-gluon plasmas. This motivates the quest for powerful and efficient computational methods that are able to accurately study fluid dynamics in the relativistic regime as well as the transition to beyond hydrodynamics-in principle all of the way down to ballistic regimes. We present a family of relativistic lattice kinetic schemes for the efficient simulation of relativistic flows in both strongly (fluid) and weakly (rarefied gas) interacting regimes. The method can deal with both massless and massive particles, thereby encompassing ultra- and mildly relativistic regimes alike. The computational performance of the method for the simulation of relativistic flows across the aforementioned regimes is discussed in detail, along with prospects of future applications.
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Affiliation(s)
- V E Ambruş
- Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität, Frankfurt, Germany
- Department of Physics, West University of Timişoara, Timisoara, Romania
| | - L Bazzanini
- Università di Ferrara and INFN-Ferrara, Ferrara, Italy
| | - A Gabbana
- Eindhoven University of Technology, Eindhoven, Netherlands
| | - D Simeoni
- Università di Ferrara and INFN-Ferrara, Ferrara, Italy.
- Bergische Universität Wuppertal, Wuppertal, Germany.
- University of Cyprus, Physics department, Nicosia, Cyprus.
| | - S Succi
- Center for Life, Nano & Neuro Science @ La Sapienza, Italian Institute of Technology, Roma, Italy
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - R Tripiccione
- Università di Ferrara and INFN-Ferrara, Ferrara, Italy
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2
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Kallikounis NG, Dorschner B, Karlin IV. Multiscale semi-Lagrangian lattice Boltzmann method. Phys Rev E 2021; 103:063305. [PMID: 34271620 DOI: 10.1103/physreve.103.063305] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2021] [Accepted: 05/20/2021] [Indexed: 11/07/2022]
Abstract
We present a multi-scale lattice Boltzmann scheme, which adaptively refines particles' velocity space. Different velocity sets of lower and higher order are consistently and efficiently coupled, allowing us to use the higher-order model only when and where needed. This includes regions of high Mach or high Knudsen numbers. The coupling procedure of discrete velocity sets consists of either a projection of the higher-order populations onto the lower-order lattice or lifting of the lower-order populations to the higher-order velocity space. Both lifting and projection are local operations, which enable a flexible adaptive velocity set. The proposed scheme is formulated for both a static and an optimal, co-moving reference frame, in the spirit of the recently introduced Particles on Demand method. The multi-scale scheme is validated with an advection of an athermal vortex and in a jet flow setup. The performance of the proposed scheme is further investigated in the shock structure problem and a high-Knudsen-number Couette flow, typical examples of highly non-equilibrium flows in which the order of the velocity set plays a decisive role. The results demonstrate that the proposed multi-scale scheme can operate accurately, with flexibility in terms of the underlying models and with reduced computational requirements.
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Affiliation(s)
- N G Kallikounis
- Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland
| | - B Dorschner
- Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland
| | - I V Karlin
- Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland
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3
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A discrete reactive collision scheme for the lattice Boltzmann method. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.115871] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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4
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Zhang JJ, Wu HZ, Pu S, Qin GY, Wang Q. Towards a full solution of the relativistic Boltzmann equation for quark-gluon matter on GPUs. Int J Clin Exp Med 2020. [DOI: 10.1103/physrevd.102.074011] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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5
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Saadat MH, Bösch F, Karlin IV. Semi-Lagrangian lattice Boltzmann model for compressible flows on unstructured meshes. Phys Rev E 2020; 101:023311. [PMID: 32168653 DOI: 10.1103/physreve.101.023311] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2019] [Accepted: 02/04/2020] [Indexed: 11/07/2022]
Abstract
Compressible lattice Boltzmann model on standard lattices [M. H. Saadat, F. Bösch, and I. V. Karlin, Phys. Rev. E 99, 013306 (2019).2470-004510.1103/PhysRevE.99.013306] is extended to deal with complex flows on unstructured grid. Semi-Lagrangian propagation [A. Krämer et al., Phys. Rev. E 95, 023305 (2017).2470-004510.1103/PhysRevE.95.023305] is performed on an unstructured second-order accurate finite-element mesh and a consistent wall boundary condition is implemented which makes it possible to simulate compressible flows over complex geometries. The model is validated through simulation of Sod shock tube, subsonic and supersonic flow over NACA0012 airfoil and shock-vortex interaction in Schardin's problem. Numerical results demonstrate that the present model on standard lattices is able to simulate compressible flows involving shock waves on unstructured meshes with good accuracy and without using any artificial dissipation or limiter.
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Affiliation(s)
- M H Saadat
- Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland
| | - F Bösch
- Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland
| | - I V Karlin
- Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland
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6
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Gabbana A, Simeoni D, Succi S, Tripiccione R. Relativistic dissipation obeys Chapman-Enskog asymptotics: Analytical and numerical evidence as a basis for accurate kinetic simulations. Phys Rev E 2019; 99:052126. [PMID: 31212459 DOI: 10.1103/physreve.99.052126] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2019] [Indexed: 11/07/2022]
Abstract
We present an analytical derivation of the transport coefficients of a relativistic gas in (2+1) dimensions for both Chapman-Enskog (CE) asymptotics and Grad's expansion methods. We further develop a systematic calibration method, connecting the relaxation time of relativistic kinetic theory to the transport parameters of the associated dissipative hydrodynamic equations. Comparison of our analytical results and numerical simulations shows that the CE method correctly captures dissipative effects, while Grad's method does not, in agreement with previous analyses performed in the (3+1)-dimensional case. These results provide a solid basis for accurately calibrated computational studies of relativistic dissipative flows.
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Affiliation(s)
- A Gabbana
- Department of Physics and Earth Sciences, Università di Ferrara and INFN-Ferrara, I-44122 Ferrara, Italy.,Chair of Applied Mathematics and Numerical Analysis, Bergische Universität Wuppertal, D-42119 Wuppertal, Germany
| | - D Simeoni
- Department of Physics and Earth Sciences, Università di Ferrara and INFN-Ferrara, I-44122 Ferrara, Italy.,Chair of Applied Mathematics and Numerical Analysis, Bergische Universität Wuppertal, D-42119 Wuppertal, Germany.,Department of Physics, University of Cyprus, CY-1678 Nicosia, Cyprus
| | - S Succi
- Center for Life Nano Science @ La Sapienza, Italian Institute of Technology, Viale Regina Elena 295, I-00161 Roma, Italy.,Istituto Applicazioni del Calcolo, National Research Council of Italy, Via dei Taurini 19, I-00185 Roma, Italy
| | - R Tripiccione
- Department of Physics and Earth Sciences, Università di Ferrara and INFN-Ferrara, I-44122 Ferrara, Italy
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7
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Gabbana A, Polini M, Succi S, Tripiccione R, Pellegrino FMD. Prospects for the Detection of Electronic Preturbulence in Graphene. PHYSICAL REVIEW LETTERS 2018; 121:236602. [PMID: 30576199 DOI: 10.1103/physrevlett.121.236602] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2018] [Indexed: 06/09/2023]
Abstract
Based on extensive numerical simulations, accounting for electrostatic interactions and dissipative electron-phonon scattering, we propose experimentally realizable geometries capable of sustaining electronic preturbulence in graphene samples. In particular, preturbulence is predicted to occur at experimentally attainable values of the Reynolds number between 10 and 50, over a broad spectrum of frequencies between 10 and 100 GHz.
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Affiliation(s)
- A Gabbana
- Università di Ferrara and INFN-Ferrara, I-44122 Ferrara, Italy
- Bergische Universität Wuppertal, D-42119 Wuppertal, Germany
| | - M Polini
- Istituto Italiano di Tecnologia, Graphene Labs, Via Morego 30, I-16163 Genova, Italy
| | - S Succi
- Center for Life Nano Science at La Sapienza, Italian Institute of Technology, Viale Regina Elena 295, I-00161 Roma, Italy
- Istituto Applicazioni del Calcolo, National Research Council of Italy, Via dei Taurini 19, I-00185 Roma, Italy
| | - R Tripiccione
- Università di Ferrara and INFN-Ferrara, I-44122 Ferrara, Italy
| | - F M D Pellegrino
- Dipartimento di Fisica e Astronomia, Università di Catania, Via S. Sofia 64, I-95123 Catania, Italy
- INFN, Sezione Catania, I-95123 Catania, Italy
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8
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Solórzano S, Mendoza M, Succi S, Herrmann HJ. Lattice Wigner equation. Phys Rev E 2018; 97:013308. [PMID: 29448404 DOI: 10.1103/physreve.97.013308] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2017] [Indexed: 11/07/2022]
Abstract
We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.
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Affiliation(s)
- S Solórzano
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich, Switzerland
| | - M Mendoza
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich, Switzerland
| | - S Succi
- Istituto per le Applicazioni del Calcolo C.N.R., Via dei Taurini, 19 00185 Rome, Italy and Institute for Advanced Computational Science, Harvard University, 29 Oxford Street, Cambridge, Massachusetts 02138, USA
| | - H J Herrmann
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich, Switzerland
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9
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Atif M, Kolluru PK, Thantanapally C, Ansumali S. Essentially Entropic Lattice Boltzmann Model. PHYSICAL REVIEW LETTERS 2017; 119:240602. [PMID: 29286719 DOI: 10.1103/physrevlett.119.240602] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2017] [Indexed: 06/07/2023]
Abstract
The entropic lattice Boltzmann model (ELBM), a discrete space-time kinetic theory for hydrodynamics, ensures nonlinear stability via the discrete time version of the second law of thermodynamics (the H theorem). Compliance with the H theorem is numerically enforced in this methodology and involves a search for the maximal discrete path length corresponding to the zero dissipation state by iteratively solving a nonlinear equation. We demonstrate that an exact solution for the path length can be obtained by assuming a natural criterion of negative entropy change, thereby reducing the problem to solving an inequality. This inequality is solved by creating a new framework for construction of Padé approximants via quadrature on appropriate convex function. This exact solution also resolves the issue of indeterminacy in case of nonexistence of the entropic involution step. Since our formulation is devoid of complex mathematical library functions, the computational cost is drastically reduced. To illustrate this, we have simulated a model setup of flow over the NACA-0012 airfoil at a Reynolds number of 2.88×10^{6}.
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Affiliation(s)
- Mohammad Atif
- Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
| | - Praveen Kumar Kolluru
- Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
| | | | - Santosh Ansumali
- Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
- SankhyaSutra Labs Private Limited, Bangalore 560064, India
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10
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Dorschner B, Chikatamarla SS, Karlin IV. Entropic multirelaxation-time lattice Boltzmann method for moving and deforming geometries in three dimensions. Phys Rev E 2017; 95:063306. [PMID: 28709335 DOI: 10.1103/physreve.95.063306] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2017] [Indexed: 06/07/2023]
Abstract
Entropic lattice Boltzmann methods have been developed to alleviate intrinsic stability issues of lattice Boltzmann models for under-resolved simulations. Its reliability in combination with moving objects was established for various laminar benchmark flows in two dimensions in our previous work [B. Dorschner, S. Chikatamarla, F. Bösch, and I. Karlin, J. Comput. Phys. 295, 340 (2015)JCTPAH0021-999110.1016/j.jcp.2015.04.017] as well as for three-dimensional one-way coupled simulations of engine-type geometries in B. Dorschner, F. Bösch, S. Chikatamarla, K. Boulouchos, and I. Karlin [J. Fluid Mech. 801, 623 (2016)JFLSA70022-112010.1017/jfm.2016.448] for flat moving walls. The present contribution aims to fully exploit the advantages of entropic lattice Boltzmann models in terms of stability and accuracy and extends the methodology to three-dimensional cases, including two-way coupling between fluid and structure and then turbulence and deforming geometries. To cover this wide range of applications, the classical benchmark of a sedimenting sphere is chosen first to validate the general two-way coupling algorithm. Increasing the complexity, we subsequently consider the simulation of a plunging SD7003 airfoil in the transitional regime at a Reynolds number of Re=40000 and, finally, to access the model's performance for deforming geometries, we conduct a two-way coupled simulation of a self-propelled anguilliform swimmer. These simulations confirm the viability of the new fluid-structure interaction lattice Boltzmann algorithm to simulate flows of engineering relevance.
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Affiliation(s)
- B Dorschner
- Aerothermochemistry and Combustion Systems Lab, Department of Mechanical and Process Engineering, ETH Zurich, CH-8092 Zurich, Switzerland
| | - S S Chikatamarla
- Aerothermochemistry and Combustion Systems Lab, Department of Mechanical and Process Engineering, ETH Zurich, CH-8092 Zurich, Switzerland
| | - I V Karlin
- Aerothermochemistry and Combustion Systems Lab, Department of Mechanical and Process Engineering, ETH Zurich, CH-8092 Zurich, Switzerland
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11
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Gabbana A, Mendoza M, Succi S, Tripiccione R. Towards a unified lattice kinetic scheme for relativistic hydrodynamics. Phys Rev E 2017; 95:053304. [PMID: 28618566 DOI: 10.1103/physreve.95.053304] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2016] [Indexed: 11/07/2022]
Abstract
We present a systematic derivation of relativistic lattice kinetic equations for finite-mass particles, reaching close to the zero-mass ultrarelativistic regime treated in the previous literature. Starting from an expansion of the Maxwell-Jüttner distribution on orthogonal polynomials, we perform a Gauss-type quadrature procedure and discretize the relativistic Boltzmann equation on space-filling Cartesian lattices. The model is validated through numerical comparison with standard tests and solvers in relativistic fluid dynamics such as Boltzmann approach multiparton scattering and previous relativistic lattice Boltzmann models. This work provides a significant step towards the formulation of a unified relativistic lattice kinetic scheme, covering both massive and near-massless particles regimes.
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Affiliation(s)
- A Gabbana
- Università di Ferrara and INFN-Ferrara, Via Saragat 1, I-44122 Ferrara, Italy
| | - M Mendoza
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Schafmattstraße 6, HIF, CH-8093 Zürich, Switzerland
| | - S Succi
- Istituto per le Applicazioni del Calcolo C.N.R., Via dei Taurini, 19 00185 Rome, Italy
| | - R Tripiccione
- Università di Ferrara and INFN-Ferrara, Via Saragat 1, I-44122 Ferrara, Italy
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12
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Frapolli N, Chikatamarla SS, Karlin IV. Lattice Kinetic Theory in a Comoving Galilean Reference Frame. PHYSICAL REVIEW LETTERS 2016; 117:010604. [PMID: 27419555 DOI: 10.1103/physrevlett.117.010604] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2016] [Indexed: 05/22/2023]
Abstract
We prove that the fully discrete lattice Boltzmann method is invariant with respect to Galilean transformation. Based on this finding, a novel class of shifted lattices is proposed which dramatically increases the operating range of lattice Boltzmann simulations, in particular, for gas dynamics applications. A simulation of vortex-shock interaction is used to demonstrate the accuracy and efficiency of the proposed lattices. With one single algorithm it is now possible to simulate a broad range of applications, from low Mach number flows to transonic and supersonic flow regimes.
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Affiliation(s)
- N Frapolli
- Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland
| | - S S Chikatamarla
- Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland
| | - I V Karlin
- Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland
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13
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Abstract
Current approaches to Direct Numerical Simulation (DNS) are computationally quite expensive for most realistic scientific and engineering applications of Fluid Dynamics such as automobiles or atmospheric flows. The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, it is often preferred due to its flexibility and better parallel scaling. However, direct simulation of realistic applications, without the use of turbulence models, remains a distant dream even with highly efficient methods such as LBM. In LBM, a fictitious lattice with suitable isotropy in the velocity space is considered to recover Navier-Stokes hydrodynamics in macroscopic limit. The same lattice is mapped onto a cartesian grid for spatial discretization of the kinetic equation. In this paper, we present an inverted argument of the LBM, by making spatial discretization as the central theme. We argue that the optimal spatial discretization for LBM is a Body Centered Cubic (BCC) arrangement of grid points. We illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of DNS for realistic flows.
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14
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Ilseven E, Mendoza M. Lattice Boltzmann model for numerical relativity. Phys Rev E 2016; 93:023303. [PMID: 26986435 DOI: 10.1103/physreve.93.023303] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2015] [Indexed: 06/05/2023]
Abstract
In the Z4 formulation, Einstein equations are written as a set of flux conservative first-order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for numerical relativity and validate it with well-established tests, also known as "apples with apples." Furthermore, we find that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improve. Finally, in order to show the potential of our approach, a linear scaling law for parallelization with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.
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Affiliation(s)
- E Ilseven
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich, Switzerland
| | - M Mendoza
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich, Switzerland
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15
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Bösch F, Chikatamarla SS, Karlin IV. Entropic multirelaxation lattice Boltzmann models for turbulent flows. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:043309. [PMID: 26565366 DOI: 10.1103/physreve.92.043309] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2015] [Indexed: 06/05/2023]
Abstract
We present three-dimensional realizations of a class of lattice Boltzmann models introduced recently by the authors [I. V. Karlin, F. Bösch, and S. S. Chikatamarla, Phys. Rev. E 90, 031302(R) (2014)] and review the role of the entropic stabilizer. Both coarse- and fine-grid simulations are addressed for the Kida vortex flow benchmark. We show that the outstanding numerical stability and performance is independent of a particular choice of the moment representation for high-Reynolds-number flows. We report accurate results for low-order moments for homogeneous isotropic decaying turbulence and second-order grid convergence for most assessed statistical quantities. It is demonstrated that all the three-dimensional lattice Boltzmann realizations considered herein converge to the familiar lattice Bhatnagar-Gross-Krook model when the resolution is increased. Moreover, thanks to the dynamic nature of the entropic stabilizer, the present model features less compressibility effects and maintains correct energy and enstrophy dissipation. The explicit and efficient nature of the present lattice Boltzmann method renders it a promising candidate for both engineering and scientific purposes for highly turbulent flows.
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Affiliation(s)
- Fabian Bösch
- Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland
| | - Shyam S Chikatamarla
- Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland
| | - Ilya V Karlin
- Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland
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16
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Mezzacapo A, Sanz M, Lamata L, Egusquiza IL, Succi S, Solano E. Quantum Simulator for Transport Phenomena in Fluid Flows. Sci Rep 2015; 5:13153. [PMID: 26278968 PMCID: PMC4538376 DOI: 10.1038/srep13153] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2015] [Accepted: 07/21/2015] [Indexed: 12/01/2022] Open
Abstract
Transport phenomena still stand as one of the most challenging problems in computational physics. By exploiting the analogies between Dirac and lattice Boltzmann equations, we develop a quantum simulator based on pseudospin-boson quantum systems, which is suitable for encoding fluid dynamics transport phenomena within a lattice kinetic formalism. It is shown that both the streaming and collision processes of lattice Boltzmann dynamics can be implemented with controlled quantum operations, using a heralded quantum protocol to encode non-unitary scattering processes. The proposed simulator is amenable to realization in controlled quantum platforms, such as ion-trap quantum computers or circuit quantum electrodynamics processors.
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Affiliation(s)
- A Mezzacapo
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain
| | - M Sanz
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain
| | - L Lamata
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain
| | - I L Egusquiza
- Department of Theoretical Physics and History of Science, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain
| | - S Succi
- Istituto per le Applicazioni del Calcolo "M. Picone" CNR, I-00185 Rome, Italy.,Institute for Applied Computational Science, Harvard University, Oxford Street, 33, 02138 Cambridge, USA
| | - E Solano
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain.,IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain
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17
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Mohseni F, Mendoza M, Succi S, Herrmann HJ. Lattice Boltzmann model for resistive relativistic magnetohydrodynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:023309. [PMID: 26382548 DOI: 10.1103/physreve.92.023309] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2015] [Indexed: 06/05/2023]
Abstract
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to σ-1/2, σ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere.
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Affiliation(s)
- F Mohseni
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich, Switzerland
| | - M Mendoza
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich, Switzerland
| | - S Succi
- Istituto per le Applicazioni del Calcolo C.N.R., Via dei Taurini, 19 00185 Rome, Italy and Freiburg Institute for Advanced Studies, Albertstrasse 19, D-79104 Freiburg, Germany
| | - H J Herrmann
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich, Switzerland
- Departamento de Física, Universidade Federal do Ceará, Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil
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18
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Debus JD, Mendoza M, Herrmann HJ. Dean instability in double-curved channels. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:053308. [PMID: 25493905 DOI: 10.1103/physreve.90.053308] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2014] [Indexed: 06/04/2023]
Abstract
We study the Dean instability in curved channels using the lattice Boltzmann model for generalized metrics. For this purpose, we first improve and validate the method by measuring the critical Dean number at the transition from laminar to vortex flow for a streamwise curved rectangular channel, obtaining very good agreement with the literature values. Taking advantage of the easy implementation of arbitrary metrics within our model, we study the fluid flow through a double-curved channel, using ellipsoidal coordinates, and study the transition to vortex flow in dependence of the two perpendicular curvature radii of the channel. We observe transitions not only to two-cell vortex flow but also to four-cell and even six-cell vortex flow, and we find that the critical Dean number at the transition to two-cell vortex flow exhibits a minimum when the two curvature radii are approximately equal.
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Affiliation(s)
- J-D Debus
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Str. 27, HIT, CH-8093 Zürich, Switzerland
| | - M Mendoza
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Str. 27, HIT, CH-8093 Zürich, Switzerland
| | - H J Herrmann
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Str. 27, HIT, CH-8093 Zürich, Switzerland
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Karlin IV, Bösch F, Chikatamarla SS. Gibbs' principle for the lattice-kinetic theory of fluid dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:031302. [PMID: 25314388 DOI: 10.1103/physreve.90.031302] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2014] [Indexed: 06/04/2023]
Abstract
Gibbs' seminal prescription for constructing optimal states by maximizing the entropy under pertinent constraints is used to derive a lattice kinetic theory for the computation of high Reynolds number flows. The notion of modifying the viscosity to stabilize subgrid simulations is challenged in this kinetic framework. A lattice Boltzmann model for direct simulation of turbulent flows is presented without any need for tunable parameters and turbulent viscosity. Simulations at very high Reynolds numbers demonstrate a major extension of the operation range for fluid dynamics.
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Affiliation(s)
- I V Karlin
- Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland
| | - F Bösch
- Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland
| | - S S Chikatamarla
- Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland
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20
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Yang JY, Yan CY, Huang JC, Li Z. Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation. Proc Math Phys Eng Sci 2014; 470:20140061. [PMID: 25104904 DOI: 10.1098/rspa.2014.0061] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2014] [Accepted: 05/22/2014] [Indexed: 11/12/2022] Open
Abstract
Computations of rarefied gas dynamical flows governed by the semiclassical Boltzmann ellipsoidal-statistical (ES) kinetic model equation using an accurate numerical method are presented. The semiclassical ES model was derived through the maximum entropy principle and conserves not only the mass, momentum and energy, but also contains additional higher order moments that differ from the standard quantum distributions. A different decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. The numerical method in phase space combines the discrete-ordinate method in momentum space and the high-resolution shock capturing method in physical space. Numerical solutions of two-dimensional Riemann problems for two configurations covering various degrees of rarefaction are presented and various contours of the quantities unique to this new model are illustrated. When the relaxation time becomes very small, the main flow features a display similar to that of ideal quantum gas dynamics, and the present solutions are found to be consistent with existing calculations for classical gas. The effect of a parameter that permits an adjustable Prandtl number in the flow is also studied.
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Affiliation(s)
- Jaw-Yen Yang
- Institute of Applied Mechanics , National Taiwan University , Taipei 10764, Taiwan, Republic of China ; Center for Advanced Study in Theoretical Science , National Taiwan University , Taipei 10764, Taiwan, Republic of China
| | - Chin-Yuan Yan
- Institute of Applied Mechanics , National Taiwan University , Taipei 10764, Taiwan, Republic of China
| | - Juan-Chen Huang
- Department of Merchant Marine , National Taiwan Ocean University , Keelung 20224, Taiwan, Republic of China
| | - Zhihui Li
- China Aerodynamics Research and Development Center, Mianyang 621000, People's Republic of China
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21
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Mendoza M, Succi S, Herrmann HJ. Flow through randomly curved manifolds. Sci Rep 2013; 3:3106. [PMID: 24173367 PMCID: PMC3813940 DOI: 10.1038/srep03106] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2013] [Accepted: 10/15/2013] [Indexed: 11/09/2022] Open
Abstract
We present a computational study of the transport properties of campylotic (intrinsically curved) media. It is found that the relation between the flow through a campylotic media, consisting of randomly located curvature perturbations, and the average Ricci scalar of the system, exhibits two distinct functional expressions, depending on whether the typical spatial extent of the curvature perturbation lies above or below the critical value maximizing the overall scalar of curvature. Furthermore, the flow through such systems as a function of the number of curvature perturbations is found to present a sublinear behavior for large concentrations, due to the interference between curvature perturbations leading to an overall less curved space. We have also characterized the flux through such media as a function of the local Reynolds number and the scale of interaction between impurities. For the purpose of this study, we have also developed and validated a new lattice Boltzmann model.
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Affiliation(s)
- M Mendoza
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, CH-8093 Zürich (Switzerland)
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Bösch F, Karlin IV. Exact lattice Boltzmann equation. PHYSICAL REVIEW LETTERS 2013; 111:090601. [PMID: 24033015 DOI: 10.1103/physrevlett.111.090601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2013] [Indexed: 06/02/2023]
Abstract
The lattice Boltzmann equation is derived from the Bhatnagar-Gross-Krook kinetic equation using the Euler-Maclaurin integration formula. Unlike previous attempts to connect the lattice Boltzmann method with the kinetic theory, the result is free of any relaxation-type approximation. It shows that the conventional lattice Bhatnagar-Gross-Krook simulations of hydrodynamics belong to a parameter domain which is disconnected from the kinetic theory domain.
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Affiliation(s)
- F Bösch
- Aerothermochemistry and Combustion Systems Lab, ETH Zurich, 8092 Zurich, Switzerland
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23
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Oettinger D, Mendoza M, Herrmann HJ. Gaussian quadrature and lattice discretization of the Fermi-Dirac distribution for graphene. Phys Rev E 2013; 88:013302. [PMID: 23944578 DOI: 10.1103/physreve.88.013302] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2013] [Indexed: 11/07/2022]
Abstract
We construct a lattice kinetic scheme to study electronic flow in graphene. For this purpose, we first derive a basis of orthogonal polynomials, using as the weight function the ultrarelativistic Fermi-Dirac distribution at rest. Later, we use these polynomials to expand the respective distribution in a moving frame, for both cases, undoped and doped graphene. In order to discretize the Boltzmann equation and make feasible the numerical implementation, we reduce the number of discrete points in momentum space to 18 by applying a Gaussian quadrature, finding that the family of representative wave (2+1)-vectors, which satisfies the quadrature, reconstructs a honeycomb lattice. The procedure and discrete model are validated by solving the Riemann problem, finding excellent agreement with other numerical models. In addition, we have extended the Riemann problem to the case of different dopings, finding that by increasing the chemical potential the electronic fluid behaves as if it increases its effective viscosity.
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Affiliation(s)
- D Oettinger
- ETH Zürich, Department of Physics, CH-8093 Zürich, Switzerland
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Abstract
Based on the recently developed picture of an electronic ideal relativistic fluid at the Dirac point, we present an analytical model for the conductivity in graphene that is able to describe the linear dependence on the carrier density and the existence of a minimum conductivity. The model treats impurities as submerged rigid obstacles, forming a disordered medium through which graphene electrons flow, in close analogy with classical fluid dynamics. To describe the minimum conductivity, we take into account the additional carrier density induced by the impurities in the sample. The model, which predicts the conductivity as a function of the impurity fraction of the sample, is supported by extensive simulations for different values of ε, the dimensionless strength of the electric field, and provides excellent agreement with experimental data.
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Burgener T, Kadau D, Herrmann HJ. Clustering of inelastic soft spheres in homogeneous turbulence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:036321. [PMID: 23031027 DOI: 10.1103/physreve.86.036321] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2012] [Indexed: 06/01/2023]
Abstract
In this paper we numerically investigate the influence of dissipation during particle collisions in an homogeneous turbulent velocity field by coupling a discrete element method to a lattice-Boltzmann simulation with spectral forcing. We show that even at moderate particle volume fractions the influence of dissipative collisions is important. We also investigate the transition from a regime where the turbulent velocity field significantly influences the spatial distribution of particles to a regime where the distribution is mainly influenced by particle collisions.
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Affiliation(s)
- Thomas Burgener
- Institute for Building Materials, ETH Zurich, 8093 Zürich, Switzerland.
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Tsai IN, Huang JC, Tsai SS, Yang JY. Unsteady relativistic shock-wave diffraction by cylinders and spheres. Phys Rev E 2012; 85:026317. [PMID: 22463327 DOI: 10.1103/physreve.85.026317] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2011] [Revised: 10/01/2011] [Indexed: 11/07/2022]
Abstract
The unsteady relativistic shock-wave diffraction patterns generated by a relativistic blast wave impinging on a circular cylinder and a sphere are numerically simulated using some high-resolution relativistic kinetic beam schemes in a general coordinate system for solving the relativistic Euler equations of gas dynamics. The diffraction patterns are followed through about 6 radii of travel of the incident shock past the body. The complete diffraction patterns, including regular reflection, transition from regular to Mach reflection, slip lines, and the complex shock-on-shock interaction at the wake region resulting from the Mach shocks collision behind the body are reported in detail. Computational results of several incident shock Mach numbers covering the near ultrarelativistic limit are studied. Various contours of flow properties including the Lorentz factor and velocity streamline plots are also presented to add a better understanding of the complex diffraction phenomena. The three-dimensional relieving effects of the sphere cases are evident and can be quantitatively evaluated as compared with the corresponding cylinder cases.
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Affiliation(s)
- I-Nan Tsai
- Department of Applied Mathematics, Tatung University, Taipei 104, Taiwan
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27
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Hupp D, Mendoza M, Bouras I, Succi S, Herrmann HJ. Relativistic lattice Boltzmann method for quark-gluon plasma simulations. Int J Clin Exp Med 2011. [DOI: 10.1103/physrevd.84.125015] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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28
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Zhou JG. Axisymmetric lattice Boltzmann method revised. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:036704. [PMID: 22060526 DOI: 10.1103/physreve.84.036704] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2011] [Revised: 07/19/2011] [Indexed: 05/31/2023]
Abstract
A reformulated lattice Boltzmann model is described for incompressible axisymmetric flows with or without swirling. It is a further development and improvement on the author's axisymmetric lattice Boltzmann method. The main features of the revised scheme are (a) all the macroscopic variables such as velocities are determined in the same formulas as those in the conventional lattice Boltzmann approach to the Navier-Stokes equations and (b) the added sink or source and force terms are simple with no calculation for a derivative. Such features distinguish the present method from the other existing simplified schemes, leading to a simple and efficient model. The scheme is naturally suitable for generic incompressible axisymmetric rotational flows involving more physical phenomena. The numerical solutions to Womersley and cylindrical cavity flows are presented to demonstrate its accuracy and capability.
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Affiliation(s)
- Jian Guo Zhou
- School of Engineering, University of Liverpool, Liverpool L69 3GQ, United Kingdom
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29
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Mendoza M, Herrmann HJ, Succi S. Preturbulent regimes in graphene flow. PHYSICAL REVIEW LETTERS 2011; 106:156601. [PMID: 21568589 DOI: 10.1103/physrevlett.106.156601] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2010] [Indexed: 05/07/2023]
Abstract
We provide numerical evidence that electronic preturbulent phenomena in graphene could be observed, under current experimental conditions, through current fluctuations, echoing the detachment of vortices past localized micron-sized impurities. Vortex generation, due to micron-sized constriction, is also explored with special focus on the effects of relativistic corrections to the normal Navier-Stokes equations. These corrections are found to cause a delay in the stability breakout of the fluid as well as a small shift in the vortex shedding frequency.
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Affiliation(s)
- M Mendoza
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Schafmattstrasse 6, HIF, CH-8093 Zürich, Switzerland.
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Yano R, Suzuki K. Inelastic collisional effect on a dilute granular shock layer with a heated wall. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2011; 34:31. [PMID: 21437794 DOI: 10.1140/epje/i2011-11031-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2010] [Accepted: 02/18/2011] [Indexed: 05/30/2023]
Abstract
The inelastic collisional effect on a shock layer of a dilute granular gas with a heated wall is numerically studied. To investigate the inelastic collisional effect via the gain term in the inelastic Boltzmann equation on the shock layer, an inelastic Bhatnagar-Gross-Krook (BGK) type equation, whose loss term is equivalent to that in the inelastic Boltzmann equation, is formulated on the basis of the kinetic theory of the granular gas. The inelastic BGK-type equation formulated for a hard-sphere particle is generalized to that for an inverse power law (IPL) molecule. Numerical results in a weakly inelastic regime confirm the nonequilirium contribution to the cooling rate, when the collision frequency depends on the particle velocity. The profile of the negative high-velocity tail of the distribution function in the generation regime of the shock wave obtained by the Direct Simulation Monte Carlo method is higher than that obtained by the proposed BGK-type equation when the collision frequency depends on the particle velocity because of the inelastic collisional effect via the gain term in the inelastic Boltzmann equation, which is not included in the proposed BGK-type equation.
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Affiliation(s)
- R Yano
- Department of Advanced Energy, University of Tokyo, Kashiwanoha, Kashiwa, Chiba, Japan.
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31
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Mendoza M, Muñoz JD. Three-dimensional lattice Boltzmann model for electrodynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:056708. [PMID: 21230620 DOI: 10.1103/physreve.82.056708] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2010] [Revised: 09/16/2010] [Indexed: 05/30/2023]
Abstract
In this paper we introduce a three-dimensional Lattice-Boltzmann model that recovers in the continuous limit the Maxwell equations in materials. In order to build conservation equations with antisymmetric tensors, like the Faraday law, the model assigns four auxiliary vectors to each velocity vector. These auxiliary vectors, when combined with the distribution functions, give the electromagnetic fields. The evolution is driven by the usual Bhatnager-Gross-Krook (BGK) collision rule, but with a different form for the equilibrium distribution functions. This lattice Bhatnager-Gross-Krook (LBGK) model allows us to consider for both dielectrics and conductors with realistic parameters, and therefore it is adequate to simulate the most diverse electromagnetic problems, like the propagation of electromagnetic waves (both in dielectric media and in waveguides), the skin effect, the radiation pattern of a small dipole antenna and the natural frequencies of a resonant cavity, all with 2% accuracy. Actually, it shows to be one order of magnitude faster than the original Finite-difference time-domain (FDTD) formulation by Yee to reach the same accuracy. It is, therefore, a valuable alternative to simulate electromagnetic fields and opens lattice Boltzmann for a broad spectrum of new applications in electrodynamics.
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Affiliation(s)
- M Mendoza
- Simulation of Physical Systems Group, Ceiba-Complejidad, Departamento de Fisica, Universidad Nacional de Colombia, Crr 30 # 45-03, Ed. 404, Of. 348, Bogotá D.C., Colombia.
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