A novel averaging technique for discrete entropy-stable dissipation operators for ideal MHD

@article{Derigs2016ANA,
  title={A novel averaging technique for discrete entropy-stable dissipation operators for ideal MHD},
  author={Dominik Derigs and Andrew R. Winters and Gregor J. Gassner and Stefanie Walch},
  journal={J. Comput. Phys.},
  year={2016},
  volume={330},
  pages={624-632}
}
View PDF on arXiv
34 Citations
Highly Influential Citations
2
Background Citations
20
Methods Citations
6
Results Citations
3

Figures and Tables from this paper

34 Citations

Comparison of Some Entropy Conservative Numerical Fluxes for the Euler Equations

The flux differencing theory is extended, guaranteeing high-order for general symmetric and consistent numerical fluxes and investigating entropy stability in a generalised framework of summation-by-parts operators applicable to multiple dimensions and simplex elements.

Comparison of Some Entropy Conservative Numerical Fluxes for the Euler Equations

Entropy conservation and stability of numerical methods in gas dynamics have received much interest. Entropy conservative numerical fluxes can be used as ingredients in two kinds of schemes: firstly,…

Formulation of Entropy-Stable schemes for the multicomponent compressible Euler equations

High-order accurate entropy stable nodal discontinuous Galerkin schemes for the ideal special relativistic magnetohydrodynamics

Ideal GLM-MHD: About the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations

Preventing Pressure Oscillations Does Not Fix Local Linear Stability Issues of Entropy-Based Split-Form High-Order Schemes

This paper investigates if pressure equilibrium preservation is a remedy to these recently found local linear stability issues of entropy-conservative/dissipative high-order split-form discontinuous Galerkin methods for the compressible Euler equations, and characterize numerical fluxes for the Euler equation that are entropy- conservative, kinetic-energy-preserving, pressure-equilibrium-Preserving, and have a density flux that does not depend on the pressure.

Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics

This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for…

Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics

This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for…

An Entropy-stable Ideal EC-GLM-MHD Model for the Simulation of the Three-dimensional Ambient Solar Wind

The main aim of the current work is to apply the Roe+Lax–Friedrichs (LF) hybrid entropy-stable scheme to the simulation of the three-dimensional ambient solar wind. The governing equations for the…

An Entropy Stable Nodal Discontinuous Galerkin Method for the resistive MHD Equations. Part II: Subcell Finite Volume Shock Capturing

References

SHOWING 1-10 OF 13 REFERENCES

Affordable, entropy conserving and entropy stable flux functions for the ideal MHD equations

Kinetic energy preserving and entropy stable finite volume schemes for compressible Euler and Navier-Stokes equations

A novel entropy conservative flux that also preserves kinetic energy for the semi-discrete finite volume scheme has been proposed and scalar artificial dissipation terms which are kinetic energy stable and satisfy approximate/exact entropy condition are constructed.

Affordable, entropy-consistent Euler flux functions II: Entropy production at shocks

A novel high-order, entropy stable, 3D AMR MHD solver with guaranteed positive pressure

The numerical viscosity of entropy stable schemes for systems of conservation laws. I

It is shown that conservative schemes are entropy stable, if and (for three-point schemes) only they contain more viscosity than that present in the above-mentioned entropy-conservative ones.

Arbitrarily High-order Accurate Entropy Stable Essentially Nonoscillatory Schemes for Systems of Conservation Laws

Numerical experiments in one and two space dimensions are presented to illustrate the robust numerical performance of the TeCNO schemes.

An upwind differencing scheme for the equations of ideal magnetohydrodynamics

Numerical Methods for Gasdynamic Systems on Unstructured Meshes

  • T. Barth
  • Computer Science
    Theory and Numerics for Conservation Laws
  • 1997
This article considers stabilized finite element and finite volume discretization techniques for systems of conservation laws. Using newly developed techniques in entropy symmetrization theory,…

Roe Matrices for Ideal MHD and Systematic Construction of Roe Matrices for Systems of Conservation Laws

In this paper, the construction of a Roe's scheme for the conservative system of ideal magnetohydrodynamics (MHD) is presented. As this method relies on the computation of a Roe matrix, the problem…

Hyperbolic problems : theory, numerics, applications : proceedings of the Eleventh International Conference on Hyperbolic Problems held in Ecole Normale Supérieure, Lyon, July 17-21, 2006

Plenary Lectures.- General Relativistic Hydrodynamics and Magnetohydrodynamics: Hyperbolic Systems in Relativistic Astrophysics.- On Approximations for Overdetermined Hyperbolic Equations.- Stable…