An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
A discontinuous Galerkin method for the viscous MHD equations
Journal of Computational Physics
A solution-adaptive upwind scheme for ideal magnetohydrodynamics
Journal of Computational Physics
Divergence correction techniques for Maxwell solvers based on a hyperbolic model
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
Journal of Computational Physics
Divergence-free adaptive mesh refinement for Magnetohydrodynamics
Journal of Computational Physics
Hyperbolic divergence cleaning for the MHD equations
Journal of Computational Physics
A high-order-accurate unstructured mesh finite-volume scheme for the advection-diffusion equation
Journal of Computational Physics
Divergence- and curl-preserving prolongation and restriction formulas
Journal of Computational Physics
AN APPROXIMATE RIEMANN SOLVER FOR MAGNETOHYDRODYNAMICS (That Works in More than One Dimension)
AN APPROXIMATE RIEMANN SOLVER FOR MAGNETOHYDRODYNAMICS (That Works in More than One Dimension)
Non-oscillatory central schemes for one- and two-dimensional MHD equations: I
Journal of Computational Physics
Locally Divergence-Free Discontinuous Galerkin Methods for MHD Equations
Journal of Scientific Computing
SIAM Journal on Scientific Computing
An Unstaggered, High-Resolution Constrained Transport Method for Magnetohydrodynamic Flows
SIAM Journal on Scientific Computing
Journal of Computational Physics
Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics
Journal of Computational Physics
Accuracy preserving limiter for the high-order accurate solution of the Euler equations
Journal of Computational Physics
On the role of Riemann solvers in Discontinuous Galerkin methods for magnetohydrodynamics
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
A parallel solution - adaptive method for three-dimensional turbulent non-premixed combusting flows
Journal of Computational Physics
High-order conservative finite difference GLM-MHD schemes for cell-centered MHD
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
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.