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Morton, K. W.; Rudgyard, M. A.; Shaw, G. J.

Upwind iteration methods for the cell vertex scheme in one dimension. (English) Zbl 0811.65070

J. Comput. Phys. 114, No. 2, 209-226 (1994).
Model problems and their discretization by the cell vertex method are described. Methods for solving the arising algebraic equations are analyzed further. Some simple marching schemes based on the application of the symmetric Gauss-Seidel iteration to a system of discrete equations without diagonal dominance are introduced. It is shown that these methods have a convergence rate independent of the of unknowns for subcritical nozzle flow.
The Lax-Wendroff method upwind schemes as iteration schemes and their various generalizations are discussed. The aim in each case is to set to zero the residual for each cell, apart from exceptional cells such as those containing shocks. The ideal scheme for the transonic nozzle problem involves splitting a residual in the sonic cell and combining at the shock point.
Reviewer: K.Zlateva (Russe)

Cited in 3 Documents

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65H10 Numerical computation of solutions to systems of equations
35L67 Shocks and singularities for hyperbolic equations

Keywords:

upwind iteration methods; cell vertex method; marching schemes; symmetric Gauss-Seidel iteration; convergence; Lax-Wendroff method upwind schemes; shocks; transonic nozzle problem; splitting
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References:

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