Extension of the piecewise parabolic method to multidimensional ideal magnetohydrodynamics
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
Divergence-free adaptive mesh refinement for Magnetohydrodynamics
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Hyperbolic divergence cleaning for the MHD equations
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)
Locally divergence-free discontinuous Galerkin methods for the Maxwell equations
Journal of Computational Physics
Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
Journal of Computational Physics
Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
SIAM Journal on Scientific Computing
Locally Divergence-Free Discontinuous Galerkin Methods for MHD Equations
Journal of Scientific Computing
An unsplit Godunov method for ideal MHD via constrained transport
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics
Journal of Computational Physics
A fourth-order divergence-free method for MHD flows
Journal of Computational Physics
Journal of Computational Physics
Positivity-preserving DG and central DG methods for ideal MHD equations
Journal of Computational Physics
High order well-balanced CDG-FE methods for shallow water waves by a Green-Naghdi model
Journal of Computational Physics
Hi-index | 31.46 |
Ideal magnetohydrodynamic (MHD) equations consist of a set of nonlinear hyperbolic conservation laws, with a divergence-free constraint on the magnetic field. Neglecting this constraint in the design of computational methods may lead to numerical instability or nonphysical features in solutions. In our recent work [F. Li, L. Xu, S. Yakovlev, Central discontinuous Galerkin methods for ideal MHD equations with the exactly divergence-free magnetic field, Journal of Computational Physics 230 (2011) 4828-4847], second and third order exactly divergence-free central discontinuous Galerkin methods were proposed for ideal MHD equations. In this paper, we further develop such methods with higher order accuracy. The novelty here is that the well-established H(div)-conforming finite element spaces are used in the constrained transport type framework, and the magnetic induction equations are extensively explored in order to extract sufficient information to uniquely reconstruct an exactly divergence-free magnetic field. The overall algorithm is local, and it can be of arbitrary order of accuracy. Numerical examples are presented to demonstrate the performance of the proposed methods especially when they are fourth order accurate.