We present second-order accurate central finite volume methods adapted here to three-dimensional problems in ideal magnetohydrodynamics. These methods alternate between two staggered grids, thus leading to Riemann solver-free algorithms with relatively favorable computing times.
The original grid considered in this paper is Cartesian, while the dual grid features either Cartesian or diamond-shaped oblique dual cells.
The div.B = 0 constraint on the magnetic field is enforced with a suitable adaptation of the constrained transport method to our central schemes.
Numerical experiments show the feasibility of these methods and our results are in good agreement with existing results in the literature.
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Arminjon, P., Viallon, M.C.: Généralisation du schéma de Nessayahu-Tadmor pour une équation hyperbolique à deux dimensions d’espace. In: C.R. Acad. Sci. Paris, 320 (I), 85–88 (1995)
Arminjon, P., Stanescu, D., Viallon, M.C.: A two-dimensional finite volume extension of the Lax-Friedrichs and Nessyahu-Tadmor schemes for compressible flows. In: Hafez, M., Oshima, K. (Eds.) Proc. 6th. Int. Symp. on Comp. Fluid Dynamics, Vol. 4, 7–14 (1995)
Arminjon, P., Touma, R.: Central Finite volume methods with constrained transport divergence treatment for ideal MHD. J. Comp. Phys., 204, 737–759 (2005)
Dai, W., Woodward, P.R.: A simple finite difference scheme for multidimensional magnetohydro-dynamical equations. J. Comp. Phys., 142, 331–369 (1998)
Evans, C.R., Hawley, J.F.: Simulation of magnetohydrodynamic flows: A constrained transport method. Astrophys. J., 332, 659–677 (1988)
Jeffrey, A., Taniuti, T.: Non-Linear Wave Propagation. Academic Press, New York (1964)
Nessyahu, H., Tadmor, E.: Non-oscillatory central differencing for hyperbolic conservation laws. J. Comp. Phys., 87, 408–463 (1990)
Nodes, C., Gritschneder, G.T., Lesch, H.: Radio emission and particle acceleration in plerionic supernova remnants. Astronomy and Astrophysics 423, 13–19 (2004).
Panofsky, W.K.H, Phillips, M.: Classical Electricity and Magnetism. Addisson-Wesley, Reading (Mass.), (1955)
Touma, R.: Méthodes de volumes finis pour les systèmes d’équations hyperboliques: applications en aérodynamique et en magnétohydrodynamique. PhD Thesis, Université de Montréal, Montréal (2005)
Touma, R., Arminjon, P.: Central finite volume schemes with constrained transport divergence treatment for three-dimensional ideal MHD. J. Comp. Phys., 212, 617–636 (2006)
Tóth, G.: The ∇⋅B = 0 Constraint in Shock-Capturing Magnetohydrodynamics Codes. J. Comp. Phys., 161, 605–652 (2000)
Ziegler, U.: A central-constrained transport scheme for ideal magnetohydrodynamics. J. Comp. Phys., 192, 393–416 (2004)
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Arminjon, P., Touma, R. (2008). Finite Volume Central Schemes for Three-Dimensional Ideal MHD. In: Benzoni-Gavage, S., Serre, D. (eds) Hyperbolic Problems: Theory, Numerics, Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75712-2_27
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DOI: https://doi.org/10.1007/978-3-540-75712-2_27
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