Efficient finite-volume schemes for magnetohydrodynamic simulations in solar physics

We present efficient finite-volume schemes for solving the equations of (compressible) magnetohydrodynamics (MHD) in one, two, and three spatial dimensions. We introduce a new approximate Riemann solver for the ideal gas MHD equations (MHD-HLLEM) that outperforms all other solvers considered. We present and compare several Riemann solvers that are suitable for the real gas case of an arbitrary equation of state (EOS) (e.g., RGDW and RGMHD-HLLEM). If the evaluation of the EOS is expensive, we suggest using an adaptively-refined table for the EOS. Our error indicator facilitates a significant enhancement of the codes' efficiencies by using locally-adapted grids. We introduce a new limiter (DEOmod) for linear reconstructions on unstructured triangular grids in 2d that represents a clear improvement of the approaches commonly used. Simulations in physically-unbounded domains are enabled by the proposed transparent boundary conditions. We show that the new hyperbolic divergence cleaning technique is a highly effective and efficient approach for reducing errors in the divergence of the numerical approximation to the magnetic field. Our 3d code is parallelized for distributed-memory machines and comprises dynamic load balancing and local grid adaption on unstructured hexahedral or tetrahedral grids.<br><br>All our comparisons of solvers are based on considering their efficiencies, i.e., the computational time required for reaching the same errors. We construct one- and two-dimensional Riemann problems whose exact solution is known at least in parts of the computational domain. The suitability and efficiency of our multidimensional codes for applications from solar physics is demonstrated by simulations of magnetic fluxtubes. However, neither our new approaches nor their implementations are restricted to solar physics. Furthermore, our new limiter and the error indicator can be used for arbitrary time-dependent hyperbolic systems of conservation laws.

Author dc:creator

• Wesenberg, Matthias

Contributors dc:contributor

• Kröner, Dietmar

• Allgemeine Zustandsgleichung
• Approximative Riemannlöser
• Lineare Rekonstruktion
• Lokale Adaption
• Effizienzvergleich
• solar physics
• conservation laws
• approximate Riemann solvers
• high-resolution techniques
• general equation of state

Repository record source_url

https://freidok.uni-freiburg.de/data/792

OAI identifier oai:identifier

oai:freidok.uni-freiburg.de:792