Commun. Comput. Phys., 7 (2010), pp. 473-509.


Finite Volume Methods for Wave Propagation in Stratified Magneto-Atmospheres

Franz Georg Fuchs 1, Andrew D. McMurry 1, Siddhartha Mishra 1*, Nils Henrik Risebro 1, Knut Waagan 2

1 Centre of Mathematics for Applications (CMA), University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway.
2 High Altitude Observatory (HAO), National Center of Atmospheric Research, P.O. Box 3000, Boulder, 80307-3000 Colorado, USA.

Received 26 September 2008; Accepted (in revised version) 7 May 2009
Available online 1 September 2009
doi:10.4208/cicp.2009.08.154

Abstract

We present a model for simulating wave propagation in stratified magneto-atmospheres. The model is based on equations of ideal MHD together with gravitational source terms. In addition, we present suitable boundary data and steady states to model wave propagation. A finite volume framework is developed to simulate the waves. The framework is based on HLL and Roe type approximate Riemann solvers for numerical fluxes, a positivity preserving fractional steps method for discretizing the source and modified characteristic and Neumann type numerical boundary conditions. Second-order spatial and temporal accuracy is obtained by using an ENO piecewise linear reconstruction and a stability preserving Runge-Kutta method respectively. The boundary closures are suitably modified to ensure mass balance. The numerical framework is tested on a variety of test problems both for hydrodynamic as well as magnetohydrodynamic configurations. It is observed that only suitable choices of HLL solvers for the numerical fluxes and balanced Neumann type boundary closures yield stable results for numerical wave propagation in the presence of complex magnetic fields.

AMS subject classifications: 65M06, 35L45, 8508
Key words: Solar atmospheres, MHD equations, finite volume methods, non-reflecting boundary conditions.

*Corresponding author.
Email: franzf@math.uio.no (F. G. Fuchs), a.d.mcmurry@ifi.uio.no (A. D. McMurry), siddharm@cma.uio.no (S. Mishra), nilshr@math.uio.no (N. H. Risebro), knutwa@ucar.edu (K. Waagan)
 

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