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- Particle Methods (2)
- Boltzmann Equation (1)
- Domain Decomposition (1)
- Evolution Equations (1)
- Hybrid Codes (1)
- Numerical Simulation (1)
- Smoothed Particle Hydrodynamics (1)

Particle methods to simulate rarefied gas flows have found an increasing interest in Computational Fluid Dynamics during the last decade, see for example [1], [2], [3] and [4]. The general goal is to develop numerical schemes which are reliable enough to substitute real windtunnel experiments, needed for example in space research, by computer experiments. In order to achieve this goal one needs numerical methods solving the Boltzmann equation including all important physical effects. In general this means 3D computations for a chemically reacting rarefied gas. With codes of this kind at hand, Boltzmann simulation becomes a powerful tool in studying rarefied gas phenomena.

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.

This paper contains the basic ideas and practical aspects for numerical methods for solving the Boltzmann Equation. The main field of application considered is the reentry of a Space Shuttle in the transition from free molecular flow to continuum flow. The method used will be called Finite Pointset Method (FPM) approximating the solution by finite sets of particles in a rigorously defined way. Convergence results are cited while practical aspects of the algorithm are emphasized. Ideas for the transition to the Navier Stokes domain are shortly discussed.

This report contains the following three papers about computations of rarefied gas flows:; ; a) Rarefied gas flow around a disc with different angles of attack, published in the proceedings of the 17th RGD Symposium, Aachen, 1990.; ; b) Hypersonic flow calculations around a 3D-deltawing at low Knudsen numbers, published in the proceedings of the 17th RGD Symposium,; Aachen, 1990.; ; c) Rarefied gas flow around a 3D-deltawing, published in the proceedings of the Workshop on Hypersonic Flows for Reentry Problems,; Part 1, Antibes, France, January 22-25, 1990.; ; All computations are part of the HERMES Research and Development Program.

As an alternative to the commonly used Monte Carlo Simulation methods for solving the Boltzmann equation we have developed a new code with certain important improvements. We present results of calculations on the reentry phase of a space shuttle. One aim was to test physical models of internal energies and of gas-surface interactions.