Towards higher order lattice Boltzmann schemes

Details Towards higher order lattice Boltzmann schemes Towards higher order lattice Boltzmann schemes

2008-11-04

arxiv.org/abs/0811.0599v3

Journal of Statistical Mechanics 2009, P06 (2009) P06006

Mathematics

Numerical Analysis

Scientific paper

In this contribution we extend the Taylor expansion method proposed previously by one of us and establish equivalent partial differential equations of DDH lattice Boltzmann scheme 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 to adjust relaxation parameters in order to enforce fourth order accuracy for thermal model and diffusive relaxation modes of the Stokes problem. We apply the resulting scheme for numerical computation of associated eigenmodes and compare our results with analytical references.

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