A Second-Order Unsplit Godunov Scheme for Cell-Centered MHD: the CTU-GLM scheme - Astrophysics > Instrumentation and Methods for AstrophysicsReport as inadecuate




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Abstract: We assess the validity of a single step Godunov scheme for the solution ofthe magneto-hydrodynamics equations in more than one dimension. The scheme issecond-order accurate and the temporal discretization is based on thedimensionally unsplit Corner Transport Upwind CTU method of Colella. Theproposed scheme employs a cell-centered representation of the primary fluidvariables including magnetic field and conserves mass, momentum, magneticinduction and energy. A variant of the scheme, which breaks momentum and energyconservation, is also considered. Divergence errors are transported out of thedomain and damped using the mixed hyperbolic-parabolic divergence cleaningtechnique by Dedner et al. J. Comput. Phys., 175, 2002. The strength andaccuracy of the scheme are verified by a direct comparison with the eight-waveformulation also employing a cell-centered representation and with thepopular constrained transport method, where magnetic field components retain astaggered collocation inside the computational cell. Results obtained from two-and three-dimensional test problems indicate that the newly proposed scheme isrobust, accurate and competitive with recent implementations of the constrainedtransport method while being considerably easier to implement in existing hydrocodes.



Author: A. Mignone, P. Tzeferacos

Source: https://arxiv.org/







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