High-order central ENO finite-volume scheme for ideal MHD

JOURNAL OF COMPUTATIONAL PHYSICS

卷:250

Article

Susanto, A.¹  Ivan, L.¹  De Sterck, H.¹  Groth, C. P. T.² 

[1] Univ Waterloo, Dept Appl Math, Waterloo, ON N2L 3G1, Canada

[2] Univ Toronto, Inst Aerosp Studies, Toronto, ON M3H 5T6, Canada

关键词: Magnetohydrodynamics (MHD);    High-order schemes;    Essentially non-oscillatory (ENO);    Central ENO (CENO);    Adaptive mesh refinement (AMR);    Body-fitted grids;    Divergence cleaning for MHD;    Generalized Lagrange multiplier (GLM);   

DOI  :  10.1016/j.jcp.2013.04.040

来源: Elsevier

【 摘 要 】

A high-order accurate finite-volume scheme for the compressible ideal magnetohydrodynamics (MHD) equations is proposed. The high-order MHD scheme is based on a central essentially non-oscillatory (CENO) method combined with the generalized Lagrange multiplier divergence cleaning method for MHD. The CENO method uses k-exact multidimensional reconstruction together with a monotonicity procedure that switches from a high-order reconstruction to a limited low-order reconstruction in regions of discontinuous or under-resolved solution content. Both reconstructions are performed on central stencils, and the switching procedure is based on a smoothness indicator. The proposed high-order accurate MHD scheme can be used on general polygonal grids. A highly sophisticated parallel implementation of the scheme is described that is fourth-order accurate on two-dimensional dynamically-adaptive body-fitted structured grids. The hierarchical multi-block body-fitted grid permits grid lines to conform to curved boundaries. High-order accuracy is maintained at curved domain boundaries by employing high-order spline representations and constraints at the Gauss quadrature points for flux integration. Detailed numerical results demonstrate high-order convergence for smooth flows and robustness against oscillations for problems with shocks. A new MHD extension of the well-known Shu-Osher test problem is proposed to test the ability of the high-order MHD scheme to resolve small-scale flow features in the presence of shocks. The dynamic mesh adaptation capabilities of the approach are demonstrated using adaptive time-dependent simulations of the Orszag-Tang vortex problem with high-order accuracy and unprecedented effective resolution. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free