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 |