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Attractive invariant manifolds for maps: Existence, smoothness and continuous dependence on the map
(1992)SAM Research ReportA global invariant manifold result for maps is derived with conditions that are easy to verify for applications. The result supplies existence and smoothness of the attractive manifold as well as additional useful properties. It is also shown that a Ck,1-perturbation of the map yields a Ck-perturbation of the manifold. Moreover, it is proved that if there is an attractive invariant manifold for the time-T map of an ODE then this manifold ...Report -
The influence of a source term, an example: chemically reacting hypersonic flow
(1992)SAM Research ReportWe show, by way of an example, that the solution of a system of hyperbolic conservation laws exhibits an unexpected behavior if a source term is present. The example is the system of Euler equations for N species in two space dimensions. If the source term is not present and in the initial and inflow conditions a fixed mixture of species is prescribed then the solution basically behaves like the flow of an ideal gas, except that there are ...Report -
Special aspects of reacting inviscid blunt body flow
(1992)SAM Research ReportThe problem of a hypersonic blunt body flow in two space dimensions is considered. The governing inhomogeneous Euler equations are given and the special treatment of calorically non-perfect gas in chemical non-equilibrium is described. The chemical model is given. The problem of the arising chemical boundary layer is discussed. Analytical and numerical investigations are used to analyse this boundary layer and to get error estimates for ...Report -
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 -
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 -
GIPSY: a generator for incremental programming systems
(1992)TIK ReportGIPSY (Generator for Incremental Programming Systems) is an experimental system, which produces incremental programming environments from a given language definition. Besides its tasks in a conventional environment, the compiler of a GIPSY generated system serves as a program base by making syntax and semantic information about a program accessible to other tools. The compiler manages a program internally in a general data model and offers ...Report -
Integration of stiff mechanical systems by Runge-Kutta methods
(1992)SAM Research ReportThe numerical integration of stiff mechanical systems is studied in which a strong potential forces the motion to remain close to a manifold. The equations of motion are written as a singular singular perturbation problem with a small stiffness parameter $\epsilon$. Smooth solutions of such systems are characterized, in distinction to highly oscillatory general solutions. Implicit Runge-Kutta methods using step sizes larger than $\epsilon$ ...Report -
The Oberon system family
(1992)ETH, Eidgenössische Technische Hochschule Zürich, Departement Informatik, Institut für ComputersystemeReport -
Numerical Solution of the Riemann Problem for Two-Fimensional Gas Dynamics
(1992)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 sixteen (resp. fifteen) genuinely different wave combinations for isentropic (resp. polytropic) gas exist. For each configuration the numerical solution ...Report