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An unsplit Godunov method for ideal MHD via constrained transport in three dimensions. (English) Zbl 1317.76057
Summary: We present a single step, second-order accurate Godunov scheme for ideal MHD which is an extension of the method described by the authors [J. Comput. Phys. 205, No. 2, 509–539 (2005; Zbl 1087.76536)] to three dimensions. This algorithm combines the corner transport upwind (CTU) method of Colella for multidimensional integration, and the constrained transport (CT) algorithm for preserving the divergence-free constraint on the magnetic field. We describe the calculation of the PPM interface states for 3D ideal MHD which must include multidimensional “MHD source terms” and naturally respect the balance implicit in these terms by the \(\nabla\cdot \mathbf B=0\) condition. We compare two different forms for the CTU integration algorithm which require either 6- or 12-solutions of the Riemann problem per cell per time-step, and present a detailed description of the 6-solve algorithm. Finally, we present solutions for test problems to demonstrate the accuracy and robustness of the algorithm.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
76N99 Compressible fluids and gas dynamics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
Software:
HLLE; ZEUS
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References:
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