A lattice Boltzmann (LB) method based on the linearized Boltzmann Bhatnagar-Gross-Krook equation for numerical simulation of oscillatory (unsteady) Stokes flow is proposed. Unlike the conventional (nonlinear) LB method that utilizes the time domain exclusively, the proposed method is formulated in the frequency domain to allow for direct access to the complex-valued stress, force, and velocity ...

In this article, we perform a numerical stability and convergence analysis of the constrained runs initialization scheme for a lattice Boltzmann model. Gear and Kevrekidis developed this scheme in the context of coarse-grained equation-free computing. Given the macroscopic initial fields, we study the mapping of these variables to the higher-dimensional space of lattice Boltzmann variables. The...

Recently, several methods were proposed to accelerate a time integrator that uses a time step that is much smaller than the dominant slow time scales of the dynamics of the system. In this paper, we apply these methods to accelerate the lattice Boltzmann BGK model for the one-dimensional FitzHugh-Nagumo reaction-diffusion system. We compare the projective method proposed by Gear and Kevrekidis ...

Liquid distributions in unsaturated porous media under different gravitational accelerations and corresponding macroscopic gaseous diffusion coefficients were investigated to enhance understanding of plant growth conditions in microgravity. We used a single-component, multiphase lattice Boltzmann code to simulate liquid configurations in two-dimensional porous media at varying water contents fo...

Based on the lattice Boltzmann method (LBM), the lattice Boltzmann flux solver (LBFS), which combines the advantages of conventional Navier–Stokes solvers and lattice Boltzmann solvers, was proposed recently. Specifically, LBFS applies the finite volume method to solve the macroscopic governing equations which provide solutions for macroscopic flow variables at cell centers. In the meantime, nu...

To confine a spatial domain to a smaller computational domain, one needs artificial boundaries. This work considers the lattice Boltzmann method and deals with boundary conditions for these open boundaries. Ideally, such a condition does not interact with the fluid at all. We present a novel two-dimensional discrete artificial boundary conditions to pursue that goal and we discuss four differen...

In this paper, the lattice Boltzmann method is reviewed for specific applications to numerical simulation of multiphase flow problems. A thorough literature review regarding the multi-phase lattice Boltzmann method was conducted with special focus on flows with large density and viscosity ratios between the two phases. A multiphase model with the capability of handling large-density-ratios is c...

– In this letter, we derive entropy functions whose local equilibria are suitable to recover the Navier-Stokes equations in the framework of the Lattice Boltzmann method. For the two-dimensional nine-velocity lattice we demonstrate that such an entropy function is unique, and that the expansion of the corresponding local equilibrium is the well-known local equilibrium of Y. H. Qian et al. (Euro...