On Triangular Lattice Boltzmann Schemes for Scalar Problems

On rotational invariance of lattice Boltzmann schemes

We propose the derivation of acoustic-type isotropic partial differential equations that are equivalent to linear lattice Boltzmann schemes with a density scalar field and a momentum vector field as conserved moments. The corresponding linear equivalent partial differential equations are generated with a new “Berliner version” of the Taylor expansion method. The details of the implementation ar...

ADER Schemes on Adaptive Triangular Meshes for Scalar Conservation Laws

ADER schemes are recent finite volume methods for hyperbolic conservation laws, which can be viewed as generalizations of the classical first order Godunov method to arbitrary high orders. In the ADER approach, high order polynomial reconstruction from cell averages is combined with high order flux evaluation, where the latter is done by solving generalized Riemann problems across cell interfac...

Implicit Schemes for the Lattice Boltzmann Equation

Diffusion on unstructured triangular grids using Lattice Boltzmann

In this paper, we present a Lattice Boltzmann scheme for diffusion on unstructured triangular grids. In this formulation there is no need for interpolation, as is required in other LB schemes on irregular grids. At the end of the propagation step, the lattice gas particles arrive exactly at neighbouring lattice sites, as is the case in LB schemes on Bravais lattices. The scheme is constructed u...

Towards higher order lattice Boltzmann schemes

In this contribution we extend the Taylor expansion method proposed previously by one of us and establish equivalent partial differential equations of the lattice Boltzmann scheme proposed by d’Humières [11] at an arbitrary order of accuracy. We derive formally the associated dynamical equations for classical thermal and linear fluid models in one to three space dimensions. We use this approach...