Friedemann Kemm

Universität Kassel · Institute of Mathematics

Like many other voting systems, Majority Judgement suffers from the weaknesses of the underlying mathematical model: Elections as problem of choice or ranking. We show how the model can be enhanced to take into account the complete process starting from the whole set of persons having passive electoral rights and even the aspect of reelection. By a...

While traditional approaches to prevent the carbuncle phenomenon in gas dynamics simulations increase the viscosity on entropy and shear waves near shocks, it was quite recently suggested to instead decrease the viscosity on the acoustic waves for low Mach numbers. The goal is to achieve what, in this paper, we call Mach number consistency: for all...

In this paper we propose a new diffuse interface model for the numerical simulation of inviscid compressible flows around fixed and moving solid bodies of arbitrary shape. The solids are assumed to be moving rigid bodies, without any elastic properties. The mathematical model is a simplified case of the seven-equation Baer-Nunziato model of compres...

In this paper we propose a new diffuse interface model for the numerical simulation of inviscid compressible flows around fixed and moving solid bodies of arbitrary shape. The solids are assumed to be moving rigid bodies, without any elastic properties. The model is a simplified case of the seven-equation Baer-Nunziato model of compressible multi-p...

In current textbooks the use of Chebyshev nodes with Newton interpolation is advocated as the most efficient numerical interpolation method in terms of approximation accuracy and computational effort. However, we show numerically that the approximation quality obtained by Newton interpolation with Fast Leja (FL) points is competitive to the use of...

In this study, we investigate the so called carbuncle phenomenon by means of numerical experiments and heuristic considerations. We identify two main sources for the carbuncle: instability of the 1d shock position and low numerical viscosity on shear waves. We also describe how higher order stabilizes the 1d shock position and, thus, reduces the ca...

We discuss Roe-type linearizations for non-conservative shallow water magnetohydrodynamics without and with hyperbolic divergence cleaning.

The carbuncle phenomenon, an instability of discrete shock profiles, has been known in gas dynamics simulations for a long time. Only recently, it was also observed in shallow water simulations. It was shown that the mechanisms and cures in shallow water are closely related to the mechanisms and cures in gas dynamics. In this paper, we give further...

A classic problem in gas dynamics simulation is the occurrence of the carbuncle phenomenon, a breakdown of discrete shock profiles. We show that for high Froude number, this also occurs in shallow water simulations. Numerical evidence is given that commonly accepted cures developed for the numerics of gas dynamics should also work for shallow water...

This paper discusses the initial and boundary conditions as well as the size of the computational domain for the double Mach reflection problem when set up as a test for the resolution of an Euler scheme for gas dynamics.

The AUFS scheme by Sun and Takayama is a flux splitting scheme without breakdown of discrete shock profiles, usually called carbuncle, but still with a good resolution of entropy waves. Unfortunately, numerical tests with this scheme yield that the viscosity on entropy waves is too small while the viscosity on shear waves is too large. In this pape...

This paper investigates the origin of divergence errors in MHD simulations. For that purpose, we introduce the concept of discrete involutions for discretized conservation laws. This is done in analogue to the concept of involutions for hyperbolic conservation laws, introduced by Dafermos. By exploring the connection between discrete involutions an...

This paper gives a comparative study of TVD-limiters for standard explicit Finite Volume schemes. In contrast to older studies, it includes also unsymmetrical limiter functions that depend on the local CFL-number. We classify the limiters and show how to extend these families of limiters. We introduce a new member of the Superbee family, which is a...

In this paper we introduce the concept of discrete involutions for discretized conservation laws. This is done analogously to the concept of involutions for hyperbolic conservation laws, introduced by Dafermos. Many systems are equipped with such an involution, the most famous of which is the \(\nabla \cdot \mathbf B = 0\) condition for magnetohydr...

Based on the idea of the HLLEM scheme, we propose a novel ansatz to cure the well known carbuncle instability. Instead of testing all neighboring cells for strong shocks we test the Riemann problem for contact and shear waves. As an indicator we suggest the residual of the Rankine–Hugoniot condition for the linear waves. By using known approaches,...

Es kann in der Praxis sinnvoll sein, für physikalische Vorgänge mathematische Modelle zu betrachten, die mehr enthalten als die Realität. Dies gilt insbesondere dann, wenn das Modell für Computersimulationen verwendet wird. Als Beispiel werden elektromagnetische Wellen gezeigt, deren Simulation tatsächlich besser gelingt, wenn man magnetische Ladun...

Es werden Lösungsansätze für zwei wesentliche Problembereiche bei der Simulation kompressibler idealer magnetohydrodynamischer Strömungen entwickelt: - Schwach kompressible Strömungen, - Auftreten magnetischer Monopole in der numerischen Lösung. Für den erstgenannten Problembereich wird ein Ansatz aus der schwach kompressiblen Gasdynamik für die MH...

The charge conservation laws in general are not strictly obeyed in computational electromagnetics and Magnetohydrodynamics (MHD), due to the presence of various types of numerical errors. In this paper, a field theoretical method for the treatment of the often violated charge conservation laws in computational electrodynamics and MHD has been inves...

The new field theoretical method for computations magnetohydrodynamic and (or) Maxwell equations is presented. This method is strictly obeying the charge conservation laws and is consistent with the symmetries of Maxwell equations. The Lorentz-, gauge- and duality-symmetries are shortly reviewed. Violation of the charge conservation laws the electr...

In simulations of magnetohydrodynamic (MHD) processes the violation of the divergence constraint causes severe stability problems. In this paper we develop and test a new approach to the stabilization of numerical schemes. Our technique can be easily implemented in any existing code since there is no need to modify the solver for the MHD equations....

Summary: One of the important properties for the solutions of Maxwell equations is the conservation of the electric and magnetic charges. But, these charge conservation laws, mathematically described by elliptic divergence equations, are not strictly obeyed by numerical solutions of Maxwell and MHD equations, due to the presence of various types of...

Besides evolution equations the mathematical models for problems with electro-magnetic waves also contain divergence constraints for the electric or magnetic fields. Due to the approximation errors in these constraints these errors may increase during numerical simulation in time and produce unphysical solutions. This can be avoided by coupling the...