On numerical schemes for solving the Euler equations of gas dynamics
Abstract
The first-order upwind schemes of Godunov-Van Leer, Steger-Warming, Godunov, Roe, Osher and Glimm; Godunov type scheme I; the second-order upwind schemes of Van Leer, Fromm-Van Leer, Hancock-Van Leer, and Moretti; and the second-order centered schemes of Richtmyer, Mac Cormack, Lerat-Peyrat, and Jameson are described. Their performances for the shock-tube problem proposed by Sod are compared. The schemes of Godunov-Van Leer, Glimm, Fromm-Van Leer, and Hancock-Van Leer produced the best results. All the First-order upwind schemes, the Glimm scheme, the Jameson scheme, and the Hancock-Van Leer scheme can be extended to two dimensions in the finite element setting.
- Publication:
-
IN: Numerical methods for the Euler equations of fluid dynamics (A87-14085 03-34). Philadelphia
- Pub Date:
- 1985
- Bibcode:
- 1985nmee.proc..121D
- Keywords:
-
- Compressible Fluids;
- Computational Fluid Dynamics;
- Euler Equations Of Motion;
- Gas Dynamics;
- Inviscid Flow;
- Shock Tubes;
- Computational Grids;
- Conservation Equations;
- Riemann Manifold;
- Fluid Mechanics and Heat Transfer