Multiple grid and Osher’s scheme for the efficient solution of the steady Euler equations. (English) Zbl 0612.76077
An iterative method is developed for the solution of the steady Euler equations for inviscid flow. The system of hyperbolic conservation laws is discretized by a finite-volume Osher-discretization. The iterative method is a multiple grid (FAS) iteration with symmetric Gauss-Seidel (SGS) as a relaxation method. Initial estimates are obtained by fully multigrid (FMG). In the pointwise relaxation the equations are kept in block-coupled form and local linearization of the equations and the boundary conditions is considered. The efficient formulation of Osher’s discretization of the 2-D non-isentropic steady Euler equations and its linearization is presented. The efficiency of FAS-SGS iteration is shown for a transonic model problem. It appears that, for the problem considered, the rate of convergence is almost independent of the gridsize and that for all meshizes the discrete system is solved up to truncation error accuracy in only a few (2 or 3) iteration cycles.
MSC:
| 76H05 | Transonic flows |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 76M99 | Basic methods in fluid mechanics |
| 76L05 | Shock waves and blast waves in fluid mechanics |
Keywords:
iterative method; steady Euler equations; inviscid flow; hyperbolic conservation laws; finite-volume Osher-discretization; pointwise relaxation; local linearization; boundary conditions; Osher’s discretization; non-isentropic steady Euler equations; transonic model problem; rate of convergenceSoftware:
HLLEReferences:
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