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Prof. Dr. Miloslav Feistauer

Theory and adaptivity in numerical schemes for compressible high-speed flow

Abstract: The subject-matter of this talk is the analysis of numerical schemes for the simulation of inviscid as well viscous compressible transonic flow in domains of complex geometry. The goal is to develop a sufficiently robust and efficient solvers for the compressible Euler and Navier-Stokes equations. The complete system describing viscous compressible flow equipped with boundary and initial conditions is discretized with the aid of the inviscid -- viscous operator splitting. One time step is divided into two fractional steps: inviscid finite volume (FV) step (resolving the Euler equations) and viscous finite element (FE) step (for purely viscous part). In this way we obtain a combined FV -- FE method which can also be treated without the operator splitting and can be used for the numerical solution of general convection -- diffusion problems.
In order to get a sufficiently precise solution with a precise and correct resolution of important details including shock waves, boundary layers and wakes some ingredients should be used. Special attention is paid to mesh refinement techniques. We have applied several approaches leading to isotropic as well as anisotropic refinement.
In order to support the application of the developed schemes from the qualitative point of view, precise theoretical analysis of the convergence and error estimates was carried out in the case of a scalar nonlinear convection -- diffusion equation.
Some technically relevant computational results will be presented.

Zeit: Freitag, 03. Dezember 1999, 14.15 Uhr
Ort:FU Berlin, Arnimallee 2-6, Raum 032 im EG

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