Cyclic matrices applied to unsteady flow computations

J. Edenhofer, G. Schmitz

Research output: Contribution to journalArticlepeer-review

Abstract

The application of the new implicit method of characteristics (IMOC) to the hyperbolic differential equations describing unsteady flow is presented. Using the IMOC approach, the C.F.L.-criterion is of no consequence to stability and convergence. Depending on details of discretization, the resulting systems are linear resp. nonlinear: z = Tz + b(*) or y = T̃(y) .y + b̃(y) (**). Identifying T and T̃ as cyclic matrices, a fully developed theory to solve (*) resp. (**) iteratively is available. But the solution z of (*) can be obtained explicitly. As z differs from the solution y of the nonlinear scheme (**) only by terms 0(Δ2), it represents a good approximative solution of the basic equations. For computations of even higher precision, z represents an ideal starting vector for the iteration to solve (**). It is shown how the negative influence of boundary conditions (f.e. stage-discharge relationship) on convergence can be suppressed.

Original languageEnglish
Pages (from-to)295-299
Number of pages5
JournalApplied Mathematical Modelling
Volume5
Issue number4
DOIs
StatePublished - Aug 1981

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