Berichte der Arbeitsgruppe Technomathematik (AGTM Report)
Year of publication
- 1999 (4) (remove)
- On a Recursive Approximation of Singularity Perturbed Parabolic Equations (extended version) (1999)
- The asymptotic analysis of IBVPs for the singularly perturbed parabolic PDE ... in the limit epsilon to zero motivate investigations of certain recursively defined approximative series ("ping-pong expansions"). The recursion formulae rely on operators assigning to a boundary condition at the left or the right boundary a solution of the parabolic PDE. Sufficient conditions for uniform convergence of ping-pong expansions are derived and a detailed analysis for the model problem ... is given.
- A Singular-Perturbed Two-Phase Stefan Problem Due to Slow Diffusion (1999)
- The asymptotic behaviour of a singular-perturbed two-phase Stefan problem due to slow diffusion in one of the two phases is investigated. In the limit the model equations reduce to a one-phase Stefan problem. A boundary layer at the moving interface makes it necessary to use a corrected interface condition obtained from matched asymptotic expansions. The approach is validated by numerical experiments using a front-tracking method.
- Applications of a New Model for the Differential Cross-Section of a Classical Polyatomic Gas (1999)
- We give a comparison of various differential cross-section models for a classical polyatomic gas for a homogeneous relaxation problem and the shock wave profiles at Mach numbers 1.71 and 12.9. Besides the standard Borgnakke-Larsen model and its generalizations to an energy dependent coefficient to control the amnount of rotationally elastic and completely inelastic collisions, we discuss some new models recently proposed by the same authors. Moreover, we present numerical algorithms to implement the models in a particle or Monte-Carlo code and compare the numerical shock wave profiles with existing experimental data.
- Transition from Kinetic Theory to Macroscopic Fluid Equations: A Problem fo Domain Decomposition and a Source for New Algorithms (1999)
- In the paper we discuss the transition from kinetic theory to macroscopic fluid equations, where the macroscopic equations are defined as aymptotic limits of a kinetic equation. This relation can be used to derive computationally efficient domain decomposition schemes for the simulaion of rarefied gas flows close to the continuum limit. Moreover, we present some basic ideas for the derivation of kinetic induced numerical schemes for macroscopic equations, namely kinetic schemes for general conservation laws as well as Lattice-Boltzmann methods for the incompressible Navier-Stokes equations.