Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
A higher-order Godunov method for multidimensional ideal magnetohydrodynamics
SIAM Journal on Scientific Computing
Extension of the piecewise parabolic method to multidimensional ideal magnetohydrodynamics
Journal of Computational Physics
Notes on the eigensystem of magnetohydrodynamics
SIAM Journal on Applied Mathematics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A High-Order Godunov-Type Scheme for Shock Interactions in Ideal Magnetohydrodynamics
SIAM Journal on Scientific Computing
Accurate monotonicity-preserving schemes with Runge-Kutta time stepping
Journal of Computational Physics
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
A simple finite difference scheme for multidimensional magnetohydrodynamical equations
Journal of Computational Physics
Journal of Computational Physics
A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
A solution-adaptive upwind scheme for ideal magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
Hyperbolic divergence cleaning for the MHD equations
Journal of Computational Physics
Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws
Journal of Computational Physics
Finite-volume WENO schemes for three-dimensional conservation laws
Journal of Computational Physics
Locally Divergence-preserving Upwind Finite Volume Schemes for Magnetohydrodynamic Equations
SIAM Journal on Scientific Computing
High order WENO schemes: investigations on non-uniform converges for MHD Riemann problems
Journal of Computational Physics
An unsplit, cell-centered Godunov method for ideal MHD
Journal of Computational Physics
An unsplit Godunov method for ideal MHD via constrained transport
Journal of Computational Physics
An Unstaggered, High-Resolution Constrained Transport Method for Magnetohydrodynamic Flows
SIAM Journal on Scientific Computing
A simple and accurate Riemann solver for isothermal MHD
Journal of Computational Physics
Accurate monotonicity- and extrema-preserving methods through adaptive nonlinear hybridizations
Journal of Computational Physics
An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws
Journal of Computational Physics
Increasing the accuracy in locally divergence-preserving finite volume schemes for MHD
Journal of Computational Physics
An unsplit Godunov method for ideal MHD via constrained transport in three dimensions
Journal of Computational Physics
Short Note: A limiter for PPM that preserves accuracy at smooth extrema
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Third-order Energy Stable WENO scheme
Journal of Computational Physics
Compact third-order limiter functions for finite volume methods
Journal of Computational Physics
Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics
Journal of Computational Physics
E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO Scheme
Journal of Computational Physics
High-order central ENO finite-volume scheme for ideal MHD
Journal of Computational Physics
Hi-index | 31.46 |
We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities. We suggest a numerical formulation based on a cell-centered approach where all of the primary flow variables are discretized at the zone center. The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. [J. Comput. Phys. 175 (2002) 645-673]. The resulting family of schemes is robust, cost-effective and straightforward to implement. Compared to previous existing approaches, it completely avoids the CPU intensive workload associated with an elliptic divergence cleaning step and the additional complexities required by staggered mesh algorithms. Extensive numerical testing demonstrate the robustness and reliability of the proposed framework for computations involving both smooth and discontinuous features.