On Lattice Boltzmann Methods based on vector-kinetic models for hyperbolic partial differential equations

Anandan, M and Raghurama Rao, SV (2024) On Lattice Boltzmann Methods based on vector-kinetic models for hyperbolic partial differential equations. [Preprint]

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Abstract

In this paper, we are concerned about the lattice Boltzmann methods (LBMs) based on vector-kinetic models for hyperbolic partial differential equations. In addition to usual lattice Boltzmann equation (LBE) derived by explicit discretisation of vector-kinetic equation (VKE), we also consider LBE derived by semi-implicit discretisation of VKE and compare the relaxation factors of both. We study the properties such as H-inequality, total variation boundedness and positivity of both the LBEs, and infer that the LBE due to semi-implicit discretisation naturally satisfies all the properties while the LBE due to explicit discretisation requires more restrictive condition on relaxation factor compared to the usual condition obtained from Chapman-Enskog expansion. We also derive the macroscopic finite difference form of the LBEs, and utilise it to establish the consistency of LBEs with the hyperbolic system. Further, we extend this LBM framework to hyperbolic conservation laws with source terms, such that there is no spurious numerical convection due to imbalance between convection and source terms. We also present a D2Q9 model that allows upwinding even along diagonal directions in addition to the usual upwinding along coordinate directions. The different aspects of the results are validated numerically on standard benchmark problems. © 2024 Elsevier Ltd

Item Type:	Preprint
Publication:	Computers and Fluids
Publisher:	Elsevier Ltd
Additional Information:	The copyright for this article belongs to authors.
Keywords:	Boltzmann equation; Integral equations; Kinetic parameters; Kinetic theory; Numerical methods; Partial differential equations, Boundedness; Consistency; H-inequality; Kinetic models; Lattice Boltzmann method; Positivity; Source terms; Spurious numerical convection; Total variation boundedness; Total-variation; Vector-kinetic model, Vectors
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	17 Dec 2024 11:32
Last Modified:	17 Dec 2024 11:32
URI:	http://eprints.iisc.ac.in/id/eprint/85812

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