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A new multidimensional Euler scheme
(1992)SAM Research ReportA new idea is presented to solve the multidimensional Euler equations numerically. The aim of this idea is to obtain a robust shock capturing method without the use of dimensional splitting. The starting point is the idea of the one-dimensional flux vector splitting and the homogeneity of the Euler equations. Using this concept it is shown that a different interpretation of the one-dimensional waves and the use of some physical properties ...Report -
Stagnation point analysis
(1992)SAM Research ReportThe numerical solution of a symmetric hypersonic blunt body flow in two space dimensions is considered, and the problem of the arising chemical boundary layer is discussed. Analytical and numerical investigations are used to analyze the solution on the stagnation point streamline. We point out the necessary assumptions to obtain an equivalent system of ordinary differential equations along this line and to get a unique solution. We also ...Report -
Numerical solution of a nozzle flow
(1992)SAM Research ReportThe problem of a high enthalpy nozzle flow is considered. Rotational symmetry is assumed. The governing inhomogeneous Euler equations are given, and the special treatment of the high temperature gas, the vibrational and chemical equilibrium is described. Some numerical boundary conditions are given and the problem of rotational symmetry is mentioned. At the end some numerical results are shown.Report -
A Simple Multidimensional Euler-Scheme
(1992)SAM Research ReportThe idea of the decomposition of the vector of conserved quantities of the multidimensional Euler equations into three multidimensional waves is briefly described. It is implemented in the so-called transport method. Starting from this idea, the necessary properties of these waves to prove the consistency of a numerical scheme are collected. These properties are then used to construct a new and very simple method which preserves all the ...Report -
Influence of numerical diffusion in high temperature flow
(1991)SAM Research ReportIn high temperature flow it is necessary to introduce new physical phenomena to the governing equations. Chemical reactions and vibrational excitation of the molecules lead to inhomogeneous Euler equations with a source term and an additional equation of conservation of mass for each species. From the mathematical point of view we only get additional contact discontinuities for the different species. From the numerical perspective the ...Report -
An Accuracy Barrier for Stable Three-Time-Level DifferenceSchemes for Hyperbolic Equations
(1997)SAM Research ReportWe consider three-time-level difference schemes for the linear constant coefficient advection equation $u_t$ = $cu_x$. In 1985 it was conjectured that the varrier to the local order $p$ of schemes which are stable is giben by $p \le $2 min {$R$,$S$}. Here $R$ and $S$ denote the number of downwind and upwind points, respectively, in the difference stencil with respect to the characteristic of the differential equation through the update ...Report -
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