Robust numerical fluxes for unrealizable states

JOURNAL OF COMPUTATIONAL PHYSICS

卷:408

Article

关键词: Finite-volume;    Reconstruction;    Realizability;    Negative density;    Negative temperature;    Jacobian-free Newton-Krylov;   

DOI  :  10.1016/j.jcp.2020.109244

来源: Elsevier

【 摘 要 】

Simple modification techniques are proposed for making numerical fluxes amenable to unrealizable states (e.g., negative density) without degrading the design order of accuracy, so that a finite-volume solver never fails with unrealizable states arising in the solution reconstruction step and continues to run. The main idea is to evaluate quantities not affecting the order of accuracy but important for stabilization, e.g., a dissipation matrix, with low-order unreconstructed solutions. For the viscous flux, the viscosity is linearly extrapolated instead of being evaluated with linearly reconstructed temperatures to avoid a failure with a negative temperature. These ideas are quite general and may be applied to a wide range of numerical fluxes. In this paper, we illustrate them with the Roe flux and the alpha-damping viscous flux and demonstrate their effectiveness for cases, where a conventional technique encounters difficulties. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free