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

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...

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational physics 2013-10, Vol.250, p.141-164
Main Authors: Susanto, A., Ivan, L., De Sterck, H., Groth, C.P.T.
Format: Article
Language:English
Subjects:
Accuracy
Adaptive mesh refinement (AMR)
Body-fitted grids
Boundaries
Central ENO (CENO)
Curved
Divergence cleaning for MHD
Essentially non-oscillatory (ENO)
Fluid flow
Generalized Lagrange multiplier (GLM)
High-order schemes
Magnetohydrodynamics
Magnetohydrodynamics (MHD)
Mathematical analysis
MHD
Reconstruction
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2013.04.040