Advection-diffusion lattice Boltzmann scheme for hierarchical grids

Authors:
Maik Stiebler;Jonas Tölke;Manfred Krafczyk
Affiliations:
Institute for Computer Applications in Civil Engineering, TU Braunschweig, Pockelsstr. 3, 38106 Braunschweig, Germany;Institute for Computer Applications in Civil Engineering, TU Braunschweig, Pockelsstr. 3, 38106 Braunschweig, Germany;Institute for Computer Applications in Civil Engineering, TU Braunschweig, Pockelsstr. 3, 38106 Braunschweig, Germany
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

In this paper we describe an extension of a recently developed lattice Boltzmann method for solving the advection-diffusion equation. Our proposed approach allows to couple grids of different grid resolutions and includes a staggered timestepping scheme, interpolations in space and time and finally a scaling step ensuring the continuity of the desired macroscopic quantities across the grid interface. After validating the basic lattice Boltzmann method on a uniform grid by a convergence study of analytic problems we demonstrate the consistency of our approach by solving benchmark problems and comparing results on uniform grids and multiply locally refined grids.