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Mon, 03 Apr 2000 00:00:00 +0200Mon, 03 Apr 2000 00:00:00 +0200Boltzmann Simulation by Particle Methods
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/541
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.Helmut Neunzert; Jens Struckmeierpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/541Mon, 03 Apr 2000 00:00:00 +0200Particle Methods: Theory and Applications
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/586
In the present paper a review on particle methods and their applications to evolution equations is given. In particular, particle methods for Euler- and Boltzmann equations are considered.Helmut Neunzert; Axel Klar; Jens Struckmeierpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/586Mon, 03 Apr 2000 00:00:00 +0200Transition from Kinetic Theory to Macroscopic Fluid Equations: A Problem fo Domain Decomposition and a Source for New Algorithms
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/636
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.Axel Klar; Helmut Neunzert; Jens Struckmeierpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/636Mon, 03 Apr 2000 00:00:00 +0200Domain Decomposition: Linking Kinetic and Aerodynamic Descriptions
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/729
We discuss how kinetic and aerodynamic descriptions of a gas can be matched at some prescribed boundary. The boundary (matching) conditions arise from requirement that the relevant moments (p,u,...) of the particle density function be continuous at the boundary, and from the requirement that the closure relation, by which the aerodynamic equations (holding on one side of the boundary) arise from the kinetic equation (holding on the other side), be satisfied at the boundary. We do a case study involving the Knudsen gas equation on one side and a system involving the Burgers equation on the other side in section 2, and a discussion for the coupling of the full Boltzmann equation with the compressible Navier-Stokes equations in section 3.Reinhard Illner; Helmut Neunzertpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/729Mon, 03 Apr 2000 00:00:00 +0200Mathematics as a Key to Key Technologies
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/850
Helmut Neunzertpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/850Mon, 20 Sep 1999 00:00:00 +0200Industrial Mathematics - Ideas and Examples
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/622
Helmut Neunzert; Abul Hasan Siddiqipreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/622Wed, 01 Oct 1997 00:00:00 +0200Industrial Mathematics - Ideas and Examples
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/612
Helmut Neunzert; Abul Hasan Siddiqipreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/612Wed, 01 Jan 1997 00:00:00 +0100Particle Methods
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/544
Helmut Neunzertpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/544Sat, 01 Jan 1994 00:00:00 +0100Modelling and Numerical Simulation of Collisions
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/735
In these lectures we will mainly treat a billard game. Our particles will be hard spheres. Not always: We will also touch cases, where particles have interior energies due to rotation or vibration, which they exchange in a collision, and we will talk about chemical reactions happening during a collision. But many essential aspects occur already in the billard case which will be therefore paradigmatic. I do not know enough about semiconductors to handle collisions there - the Boltzmann case is certainly different but may give some idea even for the other cases.Helmut Neunzertpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/735Fri, 01 Jan 1993 00:00:00 +0100A 2-D Kaniel Kinetical Scheme for the Isentropic Compressible Flow
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/696
We have presented here a two-dimensional kinetical scheme for equations governing the motion of a compressible flow of an ideal gas (air) based on the Kaniel method. The basic flux functions are computed analytically and have been used in the organization of the flux computation. The algorithm is implemented and tested for the 1D shock and 2D shock-obstacle interaction problems.M. Bäcker; Helmut Neunzert; S. Sundar; S. Younispreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/696Tue, 01 Jan 1991 00:00:00 +0100Computational Methods for the Boltzmann Equation
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/677
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.F. Gropengießer; Helmut Neunzert; Jens Struckmeierpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/677Mon, 01 Jan 1990 00:00:00 +0100Several Computer Studies on Boltzmann Flows in Connection with Space Flight Problems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/681
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.F. Gropengießer; Helmut Neunzert; Jens Struckmeier; B. Wiesenpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/681Mon, 01 Jan 1990 00:00:00 +0100Industrial Mathematics: General Remarks and Some Case Studies
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/667
Industrial mathematics has many faces; but its essential feature is the cooperation of partners - from industry and from universities - with quite different interest (business versus academic carreer), normally working on different time scales. They measure success in a different way (selling rate against citing index), they have different hierarchies of values and are very often distrusting each other. Industry doubts that mathematicians are willing and/or able to produce something real practical and useful (and the mathematicians should not be too much surprised about this attitude, they very often doubt themselves) - mathematicians are afraid to loose their competence (their ideal of scientific truth, to say it more idealistically), to sell their souls.Helmut Neunzertpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/667Sun, 01 Jan 1989 00:00:00 +0100Low Discrepancy Methods for the Boltzmann Equation
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/665
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.H. Babovsky; F. Gropengießer; Helmut Neunzert; Jens Struckmeier; B. Wiesenpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/665Fri, 01 Jan 1988 00:00:00 +0100Pattern Recognition Using Measure Space Metrics
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/660
Patterns are considered as normalized measures and distances between them are defined as distances of the corresponding measures using metrics in measure spaces. This idea can be applied for pattern recognition if smeared patterns have to be compared with given ideal patterns. Different metrics are sensitive to different characteristics of the patterns - this is demonstrated in discussing examples. Particular attention is paid to a problem of Quality Control for an artificial fabric, where the distance to uniformity is defined and evaluated; the results are now used in industry.Helmut Neunzert; B. Wettonpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/660Thu, 01 Jan 1987 00:00:00 +0100Fundamentals of Identification of Time Series
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/560
W. Krüger; Helmut Neunzert; M. Schulz-Reesepreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/560Tue, 01 Jan 1985 00:00:00 +0100Mathematics in the University and Mathematics in Industry - Complement or Contrast?
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/673
Helmut Neunzert; M. Schulz-Reese; K.E. Hoffmannpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/673Sun, 01 Jan 1984 00:00:00 +0100An introduction to the nonlinear Boltzmann-Vlasov equation
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/814
Helmut Neunzertpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/814Sun, 01 Nov 1981 00:00:00 +0100An existence theorem for the unmodified Vlasov equation
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/803
Reinhard Illner; Helmut Neunzertpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/803Fri, 01 Dec 1978 00:00:00 +0100