An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Adaptive grid generation from harmonic maps on Reimannian manifolds
Journal of Computational Physics
An adaptive grid with directional control
Journal of Computational Physics
A higher-order Godunov method for multidimensional ideal magnetohydrodynamics
SIAM Journal on Scientific Computing
Flux-corrected transport in a moving grid
Journal of Computational Physics
Numerical simulation of the MHD equations by a kinetic-type method
Journal of Scientific Computing
An implicit scheme for nonideal magnetohydrodynamics
Journal of Computational Physics
Moving mesh methods with upwinding schemes for time-dependent PDEs
Journal of Computational Physics
A High-Order Godunov-Type Scheme for Shock Interactions in Ideal Magnetohydrodynamics
SIAM Journal on Scientific Computing
Numerical solution of the quasilinear Poisson equation in a nonuniform triangle mesh
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Journal of Computational Physics
A simple finite difference scheme for multidimensional magnetohydrodynamical equations
Journal of Computational Physics
An Adaptive Grid Method and Its Application to Steady Euler Flow Calculations
SIAM Journal on Scientific Computing
An r-adaptive finite element method based upon moving mesh PDEs
Journal of Computational Physics
Journal of Computational Physics
An adaptive finite element method for magnetohydrodynamics
Journal of Computational Physics
On Godunov-type schemes for magnetohydrodynamics
Journal of Computational Physics
A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Gas-kinetic theory-based flux splitting method for ideal magnetohydrodynamics
Journal of Computational Physics
MHD: a fluctuation splitting wave model for planar magnetohydrodynamics
Journal of Computational Physics
A solution-adaptive upwind scheme for ideal magnetohydrodynamics
Journal of Computational Physics
An iterative grid redistribution method for singular problems in multiple dimensions
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
A high-order gas-kinetic method for multidimensional ideal magnetohydrodynamics
Journal of Computational Physics
Divergence-free adaptive mesh refinement for Magnetohydrodynamics
Journal of Computational Physics
An efficient dynamically adaptive mesh for potentially singular solutions
Journal of Computational Physics
Moving mesh methods in multiple dimensions based on harmonic maps
Journal of Computational Physics
A Moving Mesh Method for One-dimensional Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
Variational Barrier Method of Adaptive Grid Generation in Hyperbolic Problems of Gas Dynamics
SIAM Journal on Numerical Analysis
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
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)
Journal of Computational Physics
A novel approach of divergence-free reconstruction for adaptive mesh refinement
Journal of Computational Physics
A three-dimensional adaptive method based on the iterative grid redistribution
Journal of Computational Physics
Moving mesh methods with locally varying time steps
Journal of Computational Physics
Moving Mesh Finite Element Methods for the Incompressible Navier--Stokes Equations
SIAM Journal on Scientific Computing
An HLLC Riemann solver for magneto-hydrodynamics
Journal of Computational Physics
Second-order Godunov-type scheme for reactive flow calculations on moving meshes
Journal of Computational Physics
Piecewise parabolic method on a local stencil for magnetized supersonic turbulence simulation
Journal of Computational Physics
An adaptive GRP scheme for compressible fluid flows
Journal of Computational Physics
A finite volume spectral element method for solving magnetohydrodynamic (MHD) equations
Applied Numerical Mathematics
The adaptive GRP scheme for compressible fluid flows over unstructured meshes
Journal of Computational Physics
Journal of Scientific Computing
Hi-index | 31.46 |
This paper presents an adaptive moving mesh algorithm for two-dimensional (2D) ideal magnetohydrodynamics (MHD) that utilizes a staggered constrained transport technique to keep the magnetic field divergence-free. The algorithm consists of two independent parts: MHD evolution and mesh-redistribution. The first part is a high-resolution, divergence-free, shock-capturing scheme on a fixed quadrangular mesh, while the second part is an iterative procedure. In each iteration, mesh points are first redistributed, and then a conservative-interpolation formula is used to calculate the remapped cell-averages of the mass, momentum, and total energy on the resulting new mesh; the magnetic potential is remapped to the new mesh in a non-conservative way and is reconstructed to give a divergence-free magnetic field on the new mesh. Several numerical examples are given to demonstrate that the proposed method can achieve high numerical accuracy, track and resolve strong shock waves in ideal MHD problems, and preserve divergence-free property of the magnetic field. Numerical examples include the smooth Alfven wave problem, 2D and 2.5D shock tube problems, two rotor problems, the stringent blast problem, and the cloud-shock interaction problem.