Towards the ultimate understanding of MUSCL: Pitfalls in achieving third-order accuracy

被引:21
作者
van Leer, Bram [1 ]
Nishikawa, Hiroaki [2 ]
机构
[1] Univ Michigan, Dept Aerosp Engn, Ann Arbor, MI 48109 USA
[2] Natl Inst Aerosp, Hampton, VA 23666 USA
关键词
MUSCL; QUICK; Finite-volume; Finite-difference; Third-order; Deconvolution; DISCONTINUOUS GALERKIN METHOD; SCHEMES; DIFFERENCE; IMPLEMENTATION; SIMULATION; CONVECTION; LIMITER; FLOWS;
D O I
10.1016/j.jcp.2021.110640
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
We present a proof by analysis and numerical results that Van Leer's MUSCL conservative scheme with the discretization parameter kappa is third-order accurate for kappa = 1/3. We include both the original finite-volume MUSCL family, updating cell-averaged values of the solution, and the related finite-difference version, updating point values. The presentation is needed because in the CFD literature claims have been made that not kappa = 1/3 but kappa = 1/2 yields third-order accuracy, or even that no value of kappa can yield third-order accuracy. These false claims are the consequence of mixing up finite-difference concepts with finite-volume concepts. In a series of Pitfalls, we show how incorrect conclusions can be drawn when pointwise values of the discrete solution are interchanged with cell-averaged values. All flawed schemes presented in the Pitfalls, and some correct ones for comparison, are tested numerically and shown to behave as predicted by the analysis. We conclude with firm recommendations on how to achieve third-order accuracy at all output times, or just in a steady state. (C) 2021 Elsevier Inc. All rights reserved.
引用
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页数:26
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