An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
An approximate Riemann solver for ideal magnetohydrodynamics
Journal of Computational Physics
Extension of the piecewise parabolic method to multidimensional ideal magnetohydrodynamics
Journal of Computational Physics
Accurate monotonicity-preserving schemes with Runge-Kutta time stepping
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
An unsplit Godunov method for ideal MHD via constrained transport
Journal of Computational Physics
A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics
Journal of Computational Physics
An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamics
Journal of Computational Physics
Development of low dissipative high order filter schemes for multiscale Navier-Stokes/MHD systems
Journal of Computational Physics
Accurate monotonicity- and extrema-preserving methods through adaptive nonlinear hybridizations
Journal of Computational Physics
Short Note: A limiter for PPM that preserves accuracy at smooth extrema
Journal of Computational Physics
An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics
Journal of Computational Physics
Hi-index | 31.45 |
Stable, accurate, divergence-free simulation of magnetized supersonic turbulence is a severe test of numerical MHD schemes and has been surprisingly difficult to achieve due to the range of flow conditions present. Here we present a new, higher order-accurate, low dissipation numerical method which requires no additional dissipation or local ''fixes'' for stable execution. We describe PPML, a local stencil variant of the popular PPM algorithm for solving the equations of compressible ideal magnetohydrodynamics. The principal difference between PPML and PPM is that cell interface states are evolved rather that reconstructed at every timestep, resulting in a compact stencil. Interface states are evolved using Riemann invariants containing all transverse derivative information. The conservation laws are updated in an unsplit fashion, making the scheme fully multidimensional. Divergence-free evolution of the magnetic field is maintained using the higher order-accurate constrained transport technique of Gardiner and Stone. The accuracy and stability of the scheme is documented against a bank of standard test problems drawn from the literature. The method is applied to numerical simulation of supersonic MHD turbulence, which is important for many problems in astrophysics, including star formation in dark molecular clouds. PPML accurately reproduces in three-dimensions a transition to turbulence in highly compressible isothermal gas in a molecular cloud model. The low dissipation and wide spectral bandwidth of this method make it an ideal candidate for direct turbulence simulations.