On the finite difference-based lattice Boltzmann method in curvilinear coordinates
Journal of Computational Physics
A characteristic Galerkin method for discrete Boltzmann equation
Journal of Computational Physics
Numerical Recipes in FORTRAN: The Art of Scientific Computing
Numerical Recipes in FORTRAN: The Art of Scientific Computing
Journal of Computational Physics
Flux modelling in the finite-volume lattice Boltzmann approach
International Journal of Computational Fluid Dynamics
Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh
Journal of Computational Physics
A spectral-element discontinuous Galerkin lattice Boltzmann method for nearly incompressible flows
Journal of Computational Physics
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Two-dimensional finite difference lattice Boltzmann models for single-component fluids are discussed and the corresponding macroscopic equations for mass and momentum conservation are derived by performing a Chapman-Enskog expansion. In order to recover the correct mass equation, characteristic-based finite difference schemes should be associated with the forward Euler scheme for the time derivative, while the space centered and second-order upwind schemes should be associated to second-order schemes for the time derivative. In the incompressible limit, the characteristic based schemes lead to spurious numerical contributions to the apparent value of the kinematic viscosity in addition to the physical value that enters the Navier-Stokes equation. Formulae for these spurious numerical viscosities are in agreement with results of simulations for the decay of shear waves.