J. Struckmeier - Academia.edu (original) (raw)

Papers by J. Struckmeier

Identification of Deterministic Nonlinear Dynamical Systems

Proceedings of the Second European Symposium on Mathematics in Industry, 1988

We propose an identification procedure for state-space-systems with nonlinearities in the state. ... more We propose an identification procedure for state-space-systems with nonlinearities in the state. The theoretical background and the algorithm are described. To show the efficiency of the algorithm we apply it to two real world examples.

Homogeneous Relaxation and Shock Wave Structure for a Polyatomic Gas

Introduction In the last few years several scattering models of polyatomic gases have been propos... more Introduction In the last few years several scattering models of polyatomic gases have been proposed by researchers working on direct simulation Monte Carlo methods (DSMC) to solve the Boltzmann equation. In the present paper the homogeneous relaxation and the structure of a shock wave for a polyatomic gas is studied, making use of a new model for the differential cross section appearing in the Boltzmann equation for gases of classical rigid molecules [1]. This kind of model applies to a polyatomic gas in the temperature range where only the rotational degrees of freedom are excited and has been extensively studied in the last few years. The model has already been applied to the calculation of transport coefficients for linear molecules [1], [2]. 2 Equations and References We follow the same approach and notations used by Kuscer [3]. We use the distribution function f(c; E ; r; t), where<F1

Modelling and simulation of fires in vehicle tunnels

International Journal for Numerical Methods in Fluids, 2004

Applying a low-Mach asymptotic for the compressible Navier-Stokes equations, we derive a new flui... more Applying a low-Mach asymptotic for the compressible Navier-Stokes equations, we derive a new fluid dynamics model,which should be capable to model large temperature differences in combination with the low-Mach number limit. The model is used to simulate fires in vehicle tunnels, where the standard Boussinesq-approximation for the incompressible Navier-Stokes seems to be inappropriate due to the high temperatures developing in the tunnel. The model is implemented using a modified finite-difference approach for the incompressible Navier-Stokes equations and tested in some realistic fire events.

this paper to give even a rough overview of the existing literature. Instead we refer the interes... more this paper to give even a rough overview of the existing literature. Instead we refer the interested reader to [9] for an excellent review. In the sequel we shall make extensive use of the fact that our model problem (1.1), (1.2) has a unique solution. This existence- and uniqueness result is well-known and a special case of much more general results [2, 3, 4]. We are interested in the case where the diffusion equations degenerate to a singularly perturbed problem due to slow diffusion in one of the two phases [7], e.g. k 1 = " ø k 2 = 1. 2 J. Struckmeier and A. Unterreiter

Notes on Numerical Fluid Mechanics (NNFM), 1998

Journal für Mathematik-Didaktik, 2010

In this paper, we describe mathematical modelling activities, which deal with authentic problems.... more In this paper, we describe mathematical modelling activities, which deal with authentic problems. These kinds of problems have been tackled in various modelling activities, amongst others in a modelling week. After a description of the theoretical approach used, one of these authentic modelling problems is described in detail showing students' solutions. Based on the evaluation of a modelling week with several hundred students, it is argued that these kinds of authentic problems are feasible with students from upper secondary level. Furthermore, it became apparent that most students would appreciate these kinds of examples included in school mathematics in order to promote their skills to use mathematics in their real life. Keywords Teaching and learning of mathematical modelling • Authentical modelling examples • Students' reactions on mathematical modelling

Rarefied Gas Flow Around a 3D-Deltawing

Hypersonic Flows for Reentry Problems, 1991

This paper presents numerical results for hypersonic flows around a 3D-deltawing at a low Knudsen... more This paper presents numerical results for hypersonic flows around a 3D-deltawing at a low Knudsen number. The underlying body geometry as well as the physical parameters correspond to testcase 7.2.1. of the workshop. The numerical method used for the calculations is the Finite-Pointset-Method (FPM) developed at the University of Kaiserslautern since 1987. The paper gives a short introduction to the method and then follows the required output formats of the workshop. Further calculations can be found in [3],[4].

Numerische Methoden zur Berechnung von Strömungen um Raumfähren in größeren Höhen

Supercomputer ’90, 1990

Monte-Carlo-Methoden oder auch Simulationsverfahren sind viel benutzte Hilfsmittel insbesondere v... more Monte-Carlo-Methoden oder auch Simulationsverfahren sind viel benutzte Hilfsmittel insbesondere von Reaktortechnikern, aber auch von Raumfahrtingenieuren und Halbleiterspezialisten; trotzdem haben diese Worte bei Mathematikern keinen besonders guten Klang, als numerische Verfahren werden die oben genannten Prozeduren selten anerkannt. Die Erfinder solcher Methoden, z.B. G. Bird, der zur Berechnung des Verhaltens verdunnter Gase die sogenannte „Direct Simulation Monte Carlo“ Methode (DSMC) entwickelte, sprechen haufig davon, das ihr Verfahren keine Gleichung lose, sondern „die Natur nachspiele“ („What is real — nature or the Boltzmann equation“, Vortrag von Bird beim 16. International Symposium on Rarefied Gas Dynamics, Pasadena 88) — ein Argument, das vielleicht das Vertrauen der Physiker, sicher nicht das der Mathematiker zu diesen Methoden erweckt. Dies gilt umsomehr, als der Anspruch, die Natur nachzuspielen, selten gerechtfertigt ist — auch ein verdunntes Gas hat noch 1019 Teilchen pro m3 und selbst dann, wenn man nur das Verhalten einer Stichprobe aus 105 Molekulen genau der Natur entsprechend nachspielte, sprengt man die Leistungsfahigkeit jedes Supercomputers. In der Tat verandern alle diese Verfahren die Mikrokinetik, d.h. die Interaktion der beteiligten Teilchen, im Vergleich zur Natur, allerdings so, das dadurch das makroskopische Verfahren nicht geandert wird. Dadurch entsteht aber das Problem, wie man beurteilen will, das dieses makroskopische Verhalten richtig wiedergegeben wird. Eine Moglichkeit ist naturlich der Vergleich mit dem Experiment und wenn man fur eine grosere Zahl von Experimenten gute Ubereinstimmung gefunden hat, wird die Neigung, die Simulation selbst wie ein Experiment zu werten, sehr gros (man vergleiche etwa den Ubersichtsartikel von Muntz,

Applied and Industrial Mathematics, 1990

In the present paper a review on particle methods and their applicationsto evolution equations is... more In the present paper a review on particle methods and their applicationsto evolution equations is given. In particular, particle methods forEuler- and Boltzmann equations are considered.0 IntroductionParticle methods offer a long history, originated by the famous article ofMetropolis and Ulam "The Monte Carlo Method" [MU] published in 1949.Afterwards, several scientists used Monte Carlo methods in various fields: atthe beginning of

Ein Projekt zur Unterstützung angehender Mathematiklehrkräfte in der ersten Phase ihres Studiums

PAMM, 2003

Modeling and Simulation of Fires in Vehicle Tunnels Starting with compressible Navier-Stokes equa... more Modeling and Simulation of Fires in Vehicle Tunnels Starting with compressible Navier-Stokes equations we derive a new fluid model by applying a low-Mach number asymptotic. The model is used to simulate fire events in vehicular tunnels.

Pamm, 2003

Transport Theory and Statistical Physics, 1996

Transition from Kinetic theory to macroscopic fluid equations: A problem for domain decomposition and a source for new algorithms

Transport Theory and Statistical Physics, 2000

ABSTRACT In the paper we discuss the transition from kinetic theory to macroscopic fluid equation... more ABSTRACT In the paper we discuss the transition from kinetic theory to macroscopic fluid equations, where the macroscopic equations are defined as asymptotic limits of a kinetic equation. This relation can be used to derive computationally efficient domain decomposition schemes for the simulation 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. 1 Introduction In the kinetic theory of gases one works with a time--dependent density function f(t; x; v) on the phase spaceOmega Theta IR 3 to describe non--equilibrium effects, where x 2 Omega denotes the space variable and v 2 IR 3 the individual velocity of a gas particle. This density function evolves according to a kinetic transport equation, the Boltzmann equation, given by ...

Physics of Fluids, 1995

Simulation methods like DSMC are an efficient tool to compute rarefied gas flows. Using supercomp... more 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.

Parallel Computing, 1993

The paper presents a parallelization technique for the finite pointset method, a numerical method... more The paper presents a parallelization technique for the finite pointset method, a numerical method for rarefied gas flows. First we give a short introduction to the Boltzmann equation, which describes the behaviour of rarefied gas flows. The basic ideas of the finite pointset method are presented and a strategy to parallelize the algorithm will be explained. It is shown that a static processor partition leads to an insufficient load-balance of the processors. Therefore an optimized parallelization technique based on an adaptive processor partition will be introduced, which improves the efficiency of the simulation code over the whole region of interesting flow situation. Finally we present a comparison of the CPU-times between a parallel computer and a vector computer.

Optics Letters, 2002

We introduce a new concept for a wavelength-tunable frequency-doubled laser diode with a single c... more We introduce a new concept for a wavelength-tunable frequency-doubled laser diode with a single control parameter. The concept is based on intracavity frequency doubling in an external resonator geometry with spatial separation of the spectral components. The use of a fan-structured periodically poled LiTaO 3 crystal permits tuning of both the fundamental and the second harmonic simultaneously with one aperture. We demonstrate tunability over more than 10 nm in the blue (480.4 to 490.6 nm) with output powers of the order of 50 nW.

New models for the differential cross section of a polyatomic gas in the frame of the scattering kernel theory

Mechanics Research Communications, 1998

ABSTRACT This paper is concerned with the scattering kernel theory for polyatomic gases. First, t... more ABSTRACT This paper is concerned with the scattering kernel theory for polyatomic gases. First, the authors derive the Boltzmann equation for distribution function f(v,ℰ,r,t), where ℰ is the rotational energy, and then review earlier models of elastic and maximally inelastic interactions, as well as discuss the one-parameter Borgnakke-Larsen (B-L) model, which is a linear interpolation of the two above-mentioned models. Then the authors introduce two new two-parameter scattering kernels, one of which reduces to the B-L model in a parameter limit. The kernels are used to calculate the transport coefficients like viscosity or thermal conductivity. A comparison with experiments shows that the new models are more accurate than the B-L model, and some theoretical reasoning for this is provided.