A dimensionally split Cartesian cut cell method for hyperbolic conservation laws

JOURNAL OF COMPUTATIONAL PHYSICS

卷:364

Article

Gokhale, Nandan¹  Nikiforakis, Nikos¹  Klein, Rupert² 

[1] Univ Cambridge, Lab Sci Comp, Cavendish Lab, Cambridge CB3 0HE, England

[2] Free Univ Berlin, Inst Math, FB Math & Informat, Arnimallee 6, D-14195 Berlin, Germany

关键词: Cartesian grid;    Cut cell;    Dimensional splitting;    Complex geometry;    Adaptive mesh refinement;    Immersed boundary method;   

DOI  :  10.1016/j.jcp.2018.03.005

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free