Repository: Freie Universit├Ąt Berlin, Math Department

A dimensionally split Cartesian cut cell method for hyperbolic conservation laws

Gokhale, N. and Nikiforakis, N. and Klein, R. (2018) A dimensionally split Cartesian cut cell method for hyperbolic conservation laws. Journal of Computational Physics, 364 . pp. 186-208. ISSN 0021-9991

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Official URL: https://doi.org/10.1016/j.jcp.2018.03.005

Abstract

We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a full description of its three-dimensional implementation in the dimensionally split framework of Klein et al. [1]. The convergence and stability of the method are proved for the one-dimensional linear advection equation, while its multi-dimensional numerical performance is investigated through the computation of solutions to a number of test problems for the linear advection and Euler equations. When compared to the cut cell flux of Klein et al., it was found that the new flux alleviates the problem of oscillatory boundary solutions produced by the former at higher Courant numbers, and also enables the computation of more accurate solutions near stagnation points. Being dimensionally split, the method is simple to implement and extends readily to multiple dimensions.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:2013
Deposited By: Ulrike Eickers
Deposited On:30 Jan 2017 13:02
Last Modified:18 Mar 2019 10:39

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