Fully-Lagrangian and lattice-Boltzmann methods for solving systems of conservation equations
Journal of Computational Physics
Simulation of cavity flow by the lattice Boltzmann method
Journal of Computational Physics
SIAM Journal on Scientific Computing
Grid refinement for lattice-BGK models
Journal of Computational Physics
Scientific Computing
SIAM Journal on Scientific Computing
A steady-state lattice Boltzmann model for incompressible flows
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Numerical Method Based on the Lattice Boltzmann Model for the Kuramoto-Sivashinsky Equation
Journal of Scientific Computing
Optimal relaxation collisions for lattice Boltzmann methods
Computers & Mathematics with Applications
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A truncation error analysis is performed for models based on the lattice Boltzmann (LB) equation. This analysis involves two steps: the recursive application of the LB equation and a Taylor series expansion. Unlike previous analytical studies of LB methods, the present work does not assume an asymptotic relationship between the temporal and spatial discretization parameters or between the probability distribution function, f, and its equilibrium, distribution, feq. Effective finite difference stencils are derived for both the distribution function and the primitive variables, i.e., density and velocity. The governing partial differential equations are also recovered. The associated truncation errors are derived and the results are validated by numerical simulation of analytic flows. Analysis of the truncation errors elucidates the roles of the kinetic theory relaxation parameter, τ and the discretization parameters, Δx and Δt. The effects of initial and boundary conditions are also addressed and are shown to significantly affect the overall accuracy of the method.