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Accurancy barriers of three time level difference schemes for hyperbolic equations
(1991)SAM Research ReportA basic assumption for the interior scheme when solving hyperbolic mixed initial boundary value problems is that it satisfies the von Neumann stability condition. Here we show that this condition limits the order of accuracy a scheme with a given difference stencil can have. The proofs use order stars.Report -
The dynamic programming algorithm as a finite automation
(1991)ETH, Eidgenössische Technische Hochschule Zürich, Departement Informatik, Institut für ComputersystemeReport -
Towards a divide and conquer algorithm for the real nonsymmetric eigenvalue problem
(1991)ETH, Eidgenössische Technische Hochschule Zürich, Departement Informatik, Institut für Wissenschaftliches RechnenReport -
Grid alignment effects and rotated methods for computing complex flows in astrophysics
(1991)SAM Research ReportWe discuss some advantages and difficulties of Cartesian grid calculations on high Mach number flows. We show and explain strong grid alignment effects even in smooth flow regions and in steady state solutions. We present first order rotated schemes for the Euler equations which are able to overcome some of the difficulties, but still display strong dependence of shock positions and speeds on the underlying scheme.Report -
Classification of the Riemann problem for two-dimensional gas dynamics
(1991)SAM Research ReportThe Riemann problem for two-dimensional gas dynamics with isentropic and polytropic gas is considered. The initial data is constant in each quadrant and chosen so that only a rarefaction wave, shock wave, or slip line connects two neighboring constant initial states. With this restriction the existence of sixteen (resp. fifteen) genuinely different wave combinations for isentropic (resp. polytropic) gas is proved. For each configuration ...Report -