Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second or...

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Bibliographic Details
Published in:Journal of computational physics 2009-08, Vol.228 (14), p.5262-5279
Main Authors: Patil, Dhiraj V., Lakshmisha, K.N.
Format: Article
Language:English
Subjects:
Channels
Computation
Computational techniques
Computer simulation
Exact sciences and technology
Finite element method
Finite volume
Lattice Boltzmann
Lattices
Limiters
Mathematical analysis
Mathematical methods in physics
Mathematical models
Navier-Stokes equations
Physics
TVD scheme
Unstructured mesh
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Summary:A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second order discretization using a Total Variation Diminishing (TVD) scheme for the terms representing advection of the distribution function in physical space, due to microscopic particle motion. The advantage of the LBE approach is exploited by implementing the scheme in a new computer code to run on a parallel computing system. Performance of the new formulation is systematically investigated by simulating four benchmark flows of increasing complexity, namely (1) flow in a plane channel, (2) unsteady Couette flow, (3) flow caused by a moving lid over a 2D square cavity and (4) flow over a circular cylinder. For each of these flows, the present scheme is validated with the results from Navier–Stokes computations as well as lattice Boltzmann simulations on regular mesh. It is shown that the scheme is robust and accurate for the different test problems studied.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2009.04.008