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Tue, 17 Oct 2000 00:00:00 +0200Tue, 17 Oct 2000 00:00:00 +0200Boltzmann Simulations with Axisymmetric Geometry
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/721
The paper presents theoretical and numerical investigations on simulation methods for the Boltzmann equation with axisymmetric geometry. The main task is to reduce the computational effort by taking advantage of the symmetry in the solution of the Boltzmann equation.; The reduction automatically leads to the concept of weighting functions for the radial space coordinate and therefore to a modified Boltzmann equation. Consequently the classical simulation methods have to be modified according to the new equation.; The numerical results shown in this paper - rarefied gas flows around a body with axisymmetric geometry - were done in the framework of the European space project HERMES.Jens Struckmeier; Konrad Steinerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/721Tue, 17 Oct 2000 00:00:00 +0200A Comparison of Simulation Methods for Rarefied Gas Flows
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/730
Simulation methods like DSMC are an efficient tool to compute rarefied gas flows. Using supercomputers it is possible to include various real gas effects like vibrational energies or chemical reactions in a gas mixture. Nevertheless it is still necessary to improve the accuracy of the current simulation methods in order to reduce the computational effort. To support this task the paper presents a comparison of the classical DSMC method with the so called finite Pointset Method. This new approach was developed during several years in the framework of the European space project HERMES. The comparison given in the paper is based on two different testcases: a spatially homogeneous relaxation problem and a 2-dimensional axisymmetric flow problem at high Mach numbers.Jens Struckmeier; Konrad Steinerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/730Tue, 17 Oct 2000 00:00:00 +0200Second Order Scheme for the Spatially Homogeneous Boltzmann Equation with Maxwellian Molecules
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/557
In the standard approach, particle methods for the Boltzmann equation are obtained using an explicit time discretization of the spatially homogeneous Boltzmann equation. This kind of discretization leads to a restriction of the discretization parameter as well as on the differential cross section in the case of the general Boltzmann equation. Recently, it was shown, how to construct an implicit particle scheme for the Boltzmann equation with Maxwellian molecules. The present paper combines both approaches using a linear combination of explicit and implicit discretizations. It is shown that the new method leads to a second order particle method, when using an equiweighting of explicit and implicit discretization.Jens Struckmeier; Konrad Steinerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/557Mon, 03 Apr 2000 00:00:00 +0200Weighted Particle Methods Solving Kinetic Equations for Dilute Ionized Gases
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/588
Konrad Steinerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/588Mon, 03 Apr 2000 00:00:00 +0200An Analysis of Baganoff" s Shuffle Algorithm
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/725
The paper presents the shuffle algorithm proposed by Baganoff, which can be implemented in simulation methods for the Boltzmann equation to simplify the binary collision process. It is shown that the shuffle algborithm is a discrete approximation of an isotropic collision law. The transition probability as well as the scattering cross section of the shuffle algorithm are opposed to the corresponding quantities of a hard-sphere model. The discrepancy between measures on a sphere is introduced in order to quantify the approximation error by using the shuffle algorithm.Konrad Steinerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/725Mon, 03 Apr 2000 00:00:00 +0200A Finite - Volume Particle Method for CompressibleFlows
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/739
We derive a new class of particle methods for conservation laws, which are based on numerical flux functions to model the interactions between moving particles. The derivation is similar to that of classical Finite-Volume methods; except that the fixed grid structure in the Finite-Volume method is substituted by so-called mass packets of particles. We give some numerical results on a shock wave solution for Burgers equation as well as the well-known one-dimensional shock tube problem.Dietmar Hietel; Konrad Steiner; Jens Struckmeierpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/739Mon, 03 Apr 2000 00:00:00 +0200