A notion of non-negativity preserving relaxation for a mono-dimensional three velocities scheme with relative velocity

Dubois, F and Graille, B and Rao, SVR (2020) A notion of non-negativity preserving relaxation for a mono-dimensional three velocities scheme with relative velocity. In: Journal of Computational Science, 47 .

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Abstract

In this contribution, we study a stability notion for a fundamental linear one-dimensional lattice Boltzmann scheme, this notion being related to the maximum principle. We seek to characterize the parameters of the scheme that guarantee the preservation of the non-negativity of the particle distribution functions. In the context of the relative velocity schemes, we derive necessary and sufficient conditions for the non-negativity preserving property. These conditions are then expressed in a simple way when the relative velocity is reduced to zero. For the general case, we propose some simple necessary conditions on the relaxation parameters and we put in evidence numerically the non-negativity preserving regions. Numerical experiments show finally that no oscillations occur for the propagation of a non-smooth profile if the non-negativity preserving property is satisfied. © 2020 Elsevier B.V.

Item Type:	Journal Article
Publication:	Journal of Computational Science
Publisher:	Elsevier B.V.
Additional Information:	Copyright for this article belongs to Elsevier B.V.
Keywords:	Distribution functions, A-stability; Non-negativity; Numerical experiments; One-dimensional lattice; Particle distribution functions; Relative velocity; Relaxation parameter, Velocity
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	11 Nov 2020 11:24
Last Modified:	11 Nov 2020 11:24
URI:	http://eprints.iisc.ac.in/id/eprint/66965

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