Galilean-invariant preconditioned central-moment lattice Boltzmann method without cubic velocity errors for efficient steady flow simulations

Three-dimensional lattice Boltzmann model with self-tuning equation of state for multiphase flows

In this work, the recent lattice Boltzmann (LB) model with self-tuning equation of state (EOS) [Huang et al., Phys. Rev. E 99, 023303 (2019)2470-004510.1103/PhysRevE.99.023303] is extended to three dimensions for the simulation of multiphase flows, which is based on the standard three-dimensional 27-velocity lattice and multiple-relaxation-time collision operator. To achieve the self-tuning EOS, the equilibrium moment is devised by introducing a built-in variable, and the collision matrix is improved by introducing some velocity-dependent nondiagonal elements. Meanwhile, the additional cubic terms of velocity in recovering the Newtonian viscous stress are eliminated to enhance the numerical accuracy. For modeling multiphase flows, an attractive pairwise interaction force is introduced to mimic the long-range molecular interaction, and a consistent scheme is proposed to compensate for the ɛ^{3}-order discrete lattice effect. Thermodynamic consistency in a strict sense is established for the multiphase LB model with self-tuning EOS, and the wetting condition is also treated in a thermodynamically consistent manner. As a result, the contact angle, surface tension, and interface thickness can be independently adjusted in the present theoretical framework. Numerical tests are first performed to validate the multiphase LB model with self-tuning EOS and the theoretical analyses of bulk and surface thermodynamics. The collision of equal-sized droplets is then simulated to demonstrate the applicability and effectiveness of the present LB model for multiphase flows.

Unified directional parabolic-accurate lattice Boltzmann boundary schemes for grid-rotated narrow gaps and curved walls in creeping and inertial fluid flows

The goal of this work is to advance the characteristics of existing lattice Boltzmann Dirichlet velocity boundary schemes in terms of the accuracy, locality, stability, and mass conservation for arbitrarily grid-inclined straight walls, curved surfaces, and narrow fluid gaps, for both creeping and inertial flow regimes. We reach this objective with two infinite-member boundary classes: (1) the single-node "Linear Plus" (LI^{+}) and (2) the two-node "Extended Multireflection" (EMR). The LI^{+} unifies all directional rules relying on the linear combinations of up to three pre- or postcollision populations, including their "ghost-node" interpolations and adjustable nonequilibrium approximations. On this basis, we propose three groups of LI^{+} nonequilibrium local corrections: (1) the LI_{1}^{+} is parametrized, meaning that its steady-state solution is physically consistent: the momentum accuracy is viscosity-independent in Stokes flow, and it is fixed by the Reynolds number (Re) in inertial flow; (2) the LI_{3}^{+} is parametrized, exact for arbitrary grid-rotated Poiseuille force-driven Stokes flow and thus most accurate in porous flow; and (3) the LI_{4}^{+} is parametrized, exact for pressure and inertial term gradients, and hence advantageous in very narrow porous gaps and at higher Reynolds range. The directional, two-relaxation-time collision operator plays a crucial role for all these features, but also for efficiency and robustness of the boundary schemes due to a proposed nonequilibrium linear stability criterion which reliably delineates their suitable coefficients and relaxation space. Our methodology allows one to improve any directional rule for Stokes or Navier-Stokes accuracy, but their parametrization is not guaranteed. In this context, the parametrized two-node EMR class enlarges the single-node schemes to match exactness in a grid-rotated linear Couette flow modeled with an equilibrium distribution designed for the Navier-Stokes equation (NSE). However, exactness of a grid-rotated Poiseuille NSE flow requires us to perform (1) the modification of the standard NSE term for exact bulk solvability and (2) the EMR extension towards the third neighbor node. A unique relaxation and equilibrium exact configuration for grid-rotated Poiseuille NSE flow allows us to classify the Galilean invariance characteristics of the boundary schemes without any bulk interference; in turn, its truncated solution suggests how, when increasing the Reynolds number, to avoid a deterioration of the mass-leakage rate and momentum accuracy due to a specific Reynolds scaling of the kinetic relaxation collision rate. The optimal schemes and strategies for creeping and inertial regimes are then singled out through a series of numerical tests, such as grid-rotated channels and rotated Couette flow with wall-normal injection, cylindrical porous array, and Couette flow between concentric cylinders, also comparing them against circular-shape fitted FEM solutions.

Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows

Lattice Boltzmann (LB) methods are usually developed on cubic lattices that discretize the configuration space using uniform grids. For efficient computations of anisotropic and inhomogeneous flows, it would be beneficial to develop LB algorithms involving the collision-and-stream steps based on orthorhombic cuboid lattices. We present a new 3D central moment LB scheme based on a cuboid D3Q27 lattice. This scheme involves two free parameters representing the ratios of the characteristic particle speeds along the two directions with respect to those in the remaining direction, and these parameters are referred to as the grid aspect ratios. Unlike the existing LB schemes for cuboid lattices, which are based on orthogonalized raw moments, we construct the collision step based on the relaxation of central moments and avoid the orthogonalization of moment basis, which leads to a more robust formulation. Moreover, prior cuboid LB algorithms prescribe the mappings between the distribution functions and raw moments before and after collision by using a moment basis designed to separate the trace of the second order moments (related to bulk viscosity) from its other components (related to shear viscosity), which lead to cumbersome relations for the transformations. By contrast, in our approach, the bulk and shear viscosity effects associated with the viscous stress tensor are naturally segregated only within the collision step and not for such mappings, while the grid aspect ratios are introduced via simpler pre- and post-collision diagonal scaling matrices in the above mappings. These lead to a compact approach, which can be interpreted based on special matrices. It also results in a modular 3D LB scheme on the cuboid lattice, which allows the existing cubic lattice implementations to be readily extended to those based on the more general cuboid lattices. To maintain the isotropy of the viscous stress tensor of the 3D Navier–Stokes equations using the cuboid lattice, corrections for eliminating the truncation errors resulting from the grid anisotropy as well as those from the aliasing effects are derived using a Chapman–Enskog analysis. Such local corrections, which involve the diagonal components of the velocity gradient tensor and are parameterized by two grid aspect ratios, augment the second order moment equilibria in the collision step. We present a numerical study validating the accuracy of our approach for various benchmark problems at different grid aspect ratios. In addition, we show that our 3D cuboid central moment LB method is numerically more robust than its corresponding raw moment formulation. Finally, we demonstrate the effectiveness of the 3D cuboid central moment LB scheme for the simulations of anisotropic and inhomogeneous flows and show significant savings in memory storage and computational cost when used in lieu of that based on the cubic lattice.

Symmetrized operator split schemes for force and source modeling in cascaded lattice Boltzmann methods for flow and scalar transport

Operator split forcing schemes exploiting a symmetrization principle, i.e., Strang splitting, for cascaded lattice Boltzmann (LB) methods in two- and three-dimensions for fluid flows with impressed local forces are presented. Analogous scheme for the passive scalar transport represented by a convection-diffusion equation with a source term in a novel cascaded LB formulation is also derived. They are based on symmetric applications of the split solutions of the changes on the scalar field or fluid momentum due to the sources or forces over half time steps before and after the collision step. The latter step is effectively represented in terms of the post-collision change of moments at zeroth and first orders, respectively, to represent the effect of the sources on the scalar transport and forces on the fluid flow. Such symmetrized operator split cascaded LB schemes are consistent with the second-order Strang splitting and naturally avoid any discrete effects due to forces or sources by appropriately projecting their effects for higher-order moments. All the force or source implementation steps are performed only in the moment space and they do not require formulations as extra terms and their additional transformations to the velocity space. These result in particularly simpler and efficient schemes to incorporate forces or sources in the cascaded LB methods unlike those considered previously. Numerical study for various benchmark problems in 2D and 3D for fluid flow problems with body forces and scalar transport with sources demonstrate the validity and accuracy, as well as the second-order convergence rate of the symmetrized operator split forcing or source schemes for the cascaded LB methods.