High-order kinetic relaxation schemes as high-accuracy Poisson solvers

M. Mendoza (), S. Succi () and H. J. Herrmann
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M. Mendoza: ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Str. 27, HIT, CH-8093 Zürich, Switzerland
S. Succi: Istituto per le Applicazioni del Calcolo C.N.R., Via dei Taurini, 19 00185, Rome, Italy
H. J. Herrmann: ETH Zürich, Computational Physics for Engineering, Materials, Institute for Building Materials, Schafmattstrasse 6, HIF, CH-8093 Zürich, Switzerland

International Journal of Modern Physics C (IJMPC), 2015, vol. 26, issue 05, 1-16

Abstract: We present a new approach to find accurate solutions to the Poisson equation, as obtained from the steady-state limit of a diffusion equation with strong source terms. For this purpose, we start from Boltzmann's kinetic theory and investigate the influence of higher-order terms on the resulting macroscopic equations. By performing an appropriate expansion of the equilibrium distribution, we provide a method to remove the unnecessary terms up to a desired order and show that it is possible to find, with high level of accuracy, the steady-state solution of the diffusion equation for sizeable Knudsen numbers. In order to test our kinetic approach, we discretize the Boltzmann equation and solve the Poisson equation, spending up to six order of magnitude less computational time for a given precision than standard lattice Boltzmann methods (LBMs).

Keywords: High Knudsen number; higher-order moments; diffusion equation; Poisson equation; lattice Boltzmann (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0129183115500552

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