A residual-based artificial viscosity finite difference method for scalar conservation laws

JOURNAL OF COMPUTATIONAL PHYSICS

卷:430

Article

Stiernstrom, Vidar¹  Lundgren, Lukas¹  Nazarov, Murtazo¹  Mattsson, Ken¹ 

[1] Uppsala Univ, Dept Informat Technol, POB 337, S-75105 Uppsala, Sweden

关键词: High-order finite difference methods;    Conservation laws;    Shock-capturing;    Artificial viscosity;    Residual-based error estimator;    SBP-SAT;   

DOI  :  10.1016/j.jcp.2020.110100

来源: Elsevier

【 摘 要 】

In this paper, we present an accurate, stable and robust shock-capturing finite difference method for solving scalar non-linear conservation laws. The spatial discretization uses high-order accurate upwind summation-by-parts finite difference operators combined with weakly imposed boundary conditions via simultaneous-approximation-terms. The method is an extension of the residual-based artificial viscosity methods developed in the finite- and spectral element communities to the finite difference setting. The three main ingredients of the proposed method are: (i) shock detection provided by a residual-based error estimator; (ii) first-order viscosity applied in regions with strong discontinuities; (iii) additional dampening of spurious oscillations provided by high-order dissipation from the upwind finite difference operators. The method is shown to be stable for skew-symmetric discretizations of the advective flux. Accuracy and robustness are shown by solving several benchmark problems in 2D for convex and non-convex fluxes. (C) 2020 The Author(s). Published by Elsevier Inc.

【 授权许可】

Free