TVD differencing on three-dimensional unstructured meshes with monotonicity-preserving correction of mesh skewness

JOURNAL OF COMPUTATIONAL PHYSICS

卷:298

Article

Denner, Fabian¹  van Wachem, Berend G. M.¹ 

[1] Univ London Imperial Coll Sci Technol & Med, Dept Mech Engn, Thermofluids Div, London SW7 2AZ, England

关键词: TVD schemes;    Hyperbolic partial differential equations;    Monotonicity;    Mesh skewness;    Unstructured meshes;   

DOI  :  10.1016/j.jcp.2015.06.008

来源: Elsevier

【 摘 要 】

Total variation diminishing (TVD) schemes are a widely applied group of monotonicity-preserving advection differencing schemes for partial differential equations in numerical heat transfer and computational fluid dynamics. These schemes are typically designed for one-dimensional problems or multidimensional problems on structured equidistant quadrilateral meshes. Practical applications, however, often involve complex geometries that cannot be represented by Cartesian meshes and, therefore, necessitate the application of unstructured meshes, which require a more sophisticated discretisation to account for their additional topological complexity. In principle, TVD schemes are applicable to unstructured meshes, however, not all the data required for TVD differencing is readily available on unstructured meshes, and the solution suffers from considerable numerical diffusion as a result of mesh skewness. In this article we analyse TVD differencing on unstructured three-dimensional meshes, focusing on the non-linearity of TVD differencing and the extrapolation of the virtual upwind node. Furthermore, we propose a novel monotonicity-preserving correction method for TVD schemes that significantly reduces numerical diffusion caused by mesh skewness. The presented numerical experiments demonstrate the importance of accounting for the non-linearity introduced by TVD differencing and of imposing carefully chosen limits on the extrapolated virtual upwind node, as well as the efficacy of the proposed method to correct mesh skewness. (C) 2015 The Authors. Published by Elsevier Inc.

【 授权许可】

Free