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Mon, 12 Nov 2001 00:00:00 +0100Mon, 12 Nov 2001 00:00:00 +0100Maximum Entropy Moment Systems and Galilean Invariance
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1276
In this article, we investigate the maximum entropy moment closure in gas dynamics. We show that the usual choice of polynomial weight functions may lead to hyperbolic systems with an unpleasant state space: equilibrium states are boundary points with possibly singular fluxes. In order to avoid singularities, the necessary arises to find weight functions which growing sub-quadratically at infinity. Unfortunately, this requirement leads to a conflict with Galilean invariance of the moment systems because we can show that rotational and translational invariant, finite dimensional function spaces necessarily consist of polynomials.Michael Junk; Andreas Unterreiterpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1276Tue, 11 Dec 2001 00:00:00 +0100Hyperbolic Conservation Laws and Industrial Applications
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1270
Michael Junkpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1270Mon, 10 Dec 2001 00:00:00 +0100A limiter based on kinetic theory
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1271
Mapundi K. Banda; Michael Junk; Axel Klarpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1271Mon, 10 Dec 2001 00:00:00 +0100Do Finite Volume Methods Need a Mesh?
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1272
In this article, finite volume discretizations of hyperbolic conservation laws are considered, where the usual triangulation is replaced of unity on the computational domain.Michael Junkpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1272Mon, 10 Dec 2001 00:00:00 +0100Rigorous Navier-Stokes Limit of the Lattice Boltzmann Equation
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1273
Here we riqorously investigate the diffusive limit of a velocity-discrete Boltzmann equation which is used in the lattice Boltzmann method to construct approximate solutions of the incompressible Navier-Stokes equation.Michael Junk; Wen-An Yongpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1273Mon, 10 Dec 2001 00:00:00 +0100A Hybrid Simulation Method for Radivative Transfer Equations
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1274
We consider heat transfer processes where radiation in a large number of frequency bands plays a dominant role.Michael Junk; A. Unterreiter; F. Zingsheimpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1274Mon, 10 Dec 2001 00:00:00 +0100On the approximation of kinetic equations by moment systems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1115
The aim of this article is to show that moment approximations of kinetic equations based on a Maximum Entropy approach can suffer from severe drawbacks if the kinetic velocity space is unbounded. As example, we study the Fokker Planck equation where explicit expressions for the moments of solutions to Riemann problems can be derived. The quality of the closure relation obtained from the Maximum Entropy approach as well as the Hermite/Grad approach is studied in the case of five moments. It turns out that the Maximum Entropy closure is even singular in equilibrium states while the Hermite/Grad closure behaves reasonably. In particular, the admissible moments may lead to arbitrary large speeds of propagation, even for initial data arbitrary close to global eqilibrium.Wolfgang Dreyer; Michael Junk; Matthias Kunikpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1115Thu, 17 Aug 2000 00:00:00 +0200Exponentially exact hyperbolic systems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1111
Starting with general hyperbolic systems of conservation laws, a special sub - class is extracted in which classical solutions can be expressed in terms of a linear transport equation. A characterizing property of this sub - class which contains, for example, all linear systems and non - linear scalar equations, is the existence of so called exponentially exact entropies.Michael Junkpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1111Mon, 14 Aug 2000 00:00:00 +0200Consistency analysis of mesh-free methods for conservation laws
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1112
Based on general partitions of unity and standard numerical flux functions, a class of mesh-free methods for conservation laws is derived. A Lax-Wendroff type consistency analysis is carried out for the general case of moving partition functions. The analysis leads to a set of conditions which are checked for the finite volume particle method FVPM. As a by-product, classical finite volume schemes are recovered in the approach for special choices of the partition of unity.Michael Junk; Jens Struckmeierpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1112Mon, 14 Aug 2000 00:00:00 +0200Discretizations for the Incompressible Navier-Stokes Equations based on the Lattice Boltzmann Method
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/652
A discrete velocity model with spatial and velocity discretization based on a lattice Boltzmann method is considered in the low Mach number limit. A uniform numerical scheme for this model is investigated. In the limit, the scheme reduces to a finite difference scheme for the incompressible Navier-Stokes equation which is a projection method with a second order spatial discretization on a regular grid. The discretization is analyzed and the method is compared to Chorin's original spatial discretization. Numerical results supporting the analytical statements are presented.Michael Junk; Axel Klarpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/652Sun, 25 Jun 2000 08:20:00 +0200Particle Methods for Evolution Equations
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/602
Michael Junk; Axel Klar; Jens Struckmeier; Sudarshan Tiwaripreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/602Mon, 03 Apr 2000 00:00:00 +0200A Finite Difference Interpretation of the Lattice Boltzmann Method
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/651
Compared to conventional techniques in computational fluid dynamics, the lattice Boltzmann method (LBM) seems to be a completely different approach to solve the incompressible Navier-Stokes equations. The aim of this article is to correct this impression by showing the close relation of LBM to two standard methods: relaxation schemes and explicit finite difference discretizations. As a side effect, new starting points for a discretization of the incompressible Navier-Stokes equations are obtained.Michael Junkpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/651Mon, 03 Apr 2000 00:00:00 +0200A new perspective on kinetic schemes
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/795
Compared to standard numerical methods for hyperbolic systems of conservation laws, Kinetic Schemes model propagation of information by particles instead of waves. In this article, the wave and the particle concept are shown to be closely related. Moreover, a general approach to the construction of Kinetic Schemes for hyperbolic conservation laws is given which summarizes several approaches discussed by other authors. The approach also demonstrates why Kinetic Schemes are particularly well suited for scalar conservation laws and why extensions to general systems are less natural.Michael Junkpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/795Wed, 03 Nov 1999 00:00:00 +0100On the Construction of Discrete Equilibrium Distributions for Kinetic Schemes
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/848
A general approach to the construction of discrete equilibrium dis- tributions is presented. Such distribution functions can be used to set up Kinetic Schemes as well as Lattice Boltzmann methods. The general principles are also applied to the construction of Chapman Enskog dis- tributions which are used in Kinetic Schemes for compressible Navier Stokes equations.Michael Junkpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/848Mon, 20 Sep 1999 00:00:00 +0200A new discrete velocity method for Navier-Stokes equations
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/849
The relation between the Lattice Boltzmann Method, which has re- cently become popular, and the Kinetic Schemes, which are routinely used in Computational Fluid Dynamics, is explored. A new discrete velocity model for the numerical solution of Navier-Stokes equations for incom- pressible uid ow is presented by combining both the approaches. The new scheme can be interpreted as a pseudo-compressibility method and, for a particular choice of parameters, this interpretation carries over to the Lattice Boltzmann Method.Michael Junk; S. V. Raghurama Raopreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/849Mon, 20 Sep 1999 00:00:00 +0200