Explicit Time Marching Methods for the Time-Dependent Euler Computations

✍ Scribed by C.H. Tai; D.C. Chiang; Y.P. Su

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 524 KB
• Volume: 130
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.5577

✦ Synopsis

these methods are very good candidates for the computations of the time-dependent compressible flows. Although Four explicit type time marching methods, including one proposed by the authors, are examined. The TVD conditions of these methods succeed in different cases, detailed comparithis method are analyzed with the linear conservation law as the son is still lacking and the choice among these methods is model equation. Performance of these methods when applied to rather a matter of taste. In this paper, four kinds of the the Euler equations are numerically tested. Seven examples are explicit time marching methods are compared with the tested, the main concern is the performance of the methods when same spatial discretization implemented. The four methods discontinuities with different strengths are encountered. When the discontinuity is getting stronger, spurious oscillation shows up for tested are the Euler forward method, the predictorthree existing methods, while the method proposed by the authors corrector method, the Runge-Kutta method, and one proalways gives the results with satisfaction. The effect of the limiter posed by the authors.

is also investigated. To put these methods in the same basis for

As is well known nowadays, with high order of accuracy, the comparison the same spatial discretization is used. Roe's solver linear schemes will generate spurious oscillation wherever is used to evaluate the fluxes at the cell interface; spatially secondorder accuracy is achieved by the MUSCL reconstruction. ᮊ 1997 the solution is not smooth. Recently, the concept of TVD Academic Press

[7] has been widely adopted to prevent the spurious oscillation. The methods studied in this paper are thus derived in their TVD form. The linear scalar conservation law is