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A second-order unsplit Godunov scheme for cell-centered MHD: the CTU-GLM scheme. (English) Zbl 1303.76142
Summary: We assess the validity of a single step Godunov scheme for the solution of the magnetohydrodynamics equations in more than one dimension. The scheme is second-order accurate and the temporal discretization is based on the dimensionally unsplit Corner Transport Upwind (CTU) method of Colella. The proposed scheme employs a cell-centered representation of the primary fluid variables (including magnetic field) and conserves mass, momentum, magnetic induction and energy. A variant of the scheme, which breaks momentum and energy conservation, is also considered. Divergence errors are transported out of the domain and damped using the mixed hyperbolic/parabolic divergence cleaning technique by A. Dedner et al. [in: Hyperbolic problems: Theory, numerics, applications. Proceedings of the ninth international conference on hyperbolic problems, 2002. Berlin: Springer, 509–518 (2003; Zbl 1061.76036)]. The strength and accuracy of the scheme are verified by a direct comparison with the eight-wave formulation (also employing a cell-centered representation) and with the popular constrained transport method, where magnetic field components retain a staggered collocation inside the computational cell. Results obtained from two- and three-dimensional test problems indicate that the newly proposed scheme is robust, accurate and competitive with recent implementations of the constrained transport method while being considerably easier to implement in existing hydro codes.

MSC:
76W05 Magnetohydrodynamics and electrohydrodynamics
76M12 Finite volume methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
Software:
Pluto
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