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Hyperbolic divergence cleaning for the MHD equations

- A. Dedner, F. Kemm, D. Kröner, C. Munz, T. Schnitzer, M. Wesenberg
- Mathematics
- 20 January 2002

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… Expand

Numerical Schemes for Conservation Laws

- D. Kröner
- Mathematics
- 6 March 1997

Initial Value Problems for Scalar Conservation Laws in 1-D. Initial Value Problems for Scalar Conservation Laws in 2-D. Initial Value Problems for Systems in 1-D. Initial Value Problems for Systems… Expand

A posteriori error estimates for upwind finite volume schemes for nonlinear conservation laws in multi dimensions

- D. Kröner, M. Ohlberger
- Computer Science, Mathematics
- Math. Comput.
- 2000

TLDR

Convergence of locally divergence-free discontinuous-Galerkin methods for the induction equations of the 2D-MHD system

We present the convergence analysis of locally divergence-free discontinuous Galerkin methods for the induction equations which appear in the ideal magnetohydrodynamic system. When we use a second… Expand

Measure-valued Solutions of the Euler Equations for Ideal Compressible Polytropic Fluids

- D. Kröner, W. Zajaczkowski
- Mathematics
- 1 February 1996

The existence of global measure-valued solutions to the Euler equations describing the motion of an ideal compressible and heat conducting fluid is proved. The motion is considered in a bounded… Expand

Convergence of upwind finite volume schemes for scalar conservation laws in two dimensions

This paper proves the convergence of a general class of monotone finite volume methods for numerical schemes of scalar conservation laws in two dimensions on unstructured meshes. There are… Expand

Numerical Solutions to Compressible Flows in a Nozzle with Variable Cross-section

TLDR

The Sharp-Interface Limit for the Navier–Stokes–Korteweg Equations

We investigate the sharp-interface limit for the Navier–Stokes–Korteweg model, which is an extension of the compressible Navier–Stokes equations. By means of compactness arguments, we show that… Expand

Convergence of higher order
upwind finite volume schemes on
unstructured grids for scalar conservation laws
in several space dimensions

Summary.
We prove convergence of a class of higher order upwind
finite
volume schemes on unstructured grids for scalar conservation laws in
several space dimensions. The result is applied to the… Expand

A robust numerical method for approximating solutions of a model of two-phase flows and its properties

- M. Thanh, D. Kröner, C. Chalons
- Mathematics, Computer Science
- Appl. Math. Comput.
- 1 September 2012

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