Computational Methods for Self-similar Solutions of the Compressible Euler Equations

✍ Scribed by Ravi Samtaney

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 894 KB
• Volume: 132
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.5639

✦ Synopsis

as an initial value problem with appropriate boundary conditions. In this paper, we seek the self-similar solutions Computations of self-similar solutions of the compressible Euler equations as a boundary value problem in similarity coordinates of the compressible Euler equations as a boundary value ( ϭ x/t, ϭy/t) are presented. Two new implicit methods namely problem after a suitable self-similar transformation is the implicit Godunov method and the implicit Equilibrium Flux made. The self-similar transformation reduces the number Method are presented. The Jacobians for the implicit methods are

of independent variables by one. The solution we seek is analytically evaluated. In general the self-similar solutions exhibit a steady solution in the ( ϵ x/t, ϵ y/t ) space. We believe sharper discontinuities than corresponding solutions of the initial value problem. ᮊ 1997 Academic Press that, intuitively, it is easier to deal with a steady state solution than one which is time-dependent. In addition, many of the test problems in the literature on numerical