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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 -
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 -
Time discretization of parabolic boundary integral equations
(1991)SAM Research ReportIn time-dependent boundary integral equations, a boundary element me\-thod in space can be coupled with a different type of discretization in time. For the latter a procedure based on linear multistep methods is proposed, which is applicable whenever the Laplace transform of the fundamental solution is known. The stability properties of the method are obtained from those of the underlying multistep method. In the absence of a space ...Report -
On the definition of nonlinear stability for numerical methods
(1991)SAM Research ReportIn this paper a new definition of nonlinear stability for the general nonlinear problem F(u)=0 and the corresponding family of discretized problems Fh(uh)=0 is given. The notion of nonlinear stability introduced by Keller and later by Lopéz-Marcos and Sanz-Serna have the disadvantage that the Lipschitz constant of the derivative of Fh(uh) has to be known which, in many applications, is not practicable. The modification here proposed allows ...Report -
Behelf für die Durchführung von Sicherheitsüberprüfungen (Safety Audits)
(1991)ESCIS Schriftenreihe SicherheitReport -
An algebra of properties
(1991)ETH, Eidgenössische Technische Hochschule Zürich, Departement Informatik, Institut für Wissenschaftliches RechnenThe purpose of this paper is to build a framework and give algorithms to solve queries of the form obj ∈ Prop where the object obj is expressible in terms of other given objects. We develop an algebra of properties, PROP, in which we carry out computations. We present a set of rules (Axioms Ax1 - Ax7) for the behaviour of the basic functions on properties. In addition, we represent the algorithmic components such as if and while by algebra ...Report -
Risikoanalyse im Zusammenhang mit der Störfallverordnung (StFV)
(1991)ESCIS Schriftenreihe SicherheitReport -
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