A Staggered Mesh Algorithm Using High Order Godunov Fluxes to Ensure Solenoidal Magnetic Fields in Magnetohydrodynamic Simulations

@article{Balsara1999ASM,
  title={A Staggered Mesh Algorithm Using High Order Godunov Fluxes to Ensure Solenoidal Magnetic Fields in Magnetohydrodynamic Simulations},
  author={Dinshaw S. Balsara and Daniel Spicer},
  journal={Journal of Computational Physics},
  year={1999},
  volume={149},
  pages={270-292}
}
The equations of magnetohydrodynamics (MHD) have been formulated as a hyperbolic system of conservation laws. In that form it becomes possible to use higher order Godunov schemes for their solution. This results in a robust and accurate solution strategy. However, the magnetic field also satisfies a constraint that requires its divergence to be zero at all times. This is a property that cannot be guaranteed in the zone centered discretizations that are favored in Godunov schemes without… 
High-Order Upwind Schemes for Multidimensional Magnetohydrodynamics
A general method for constructing high-order upwind schemes for multidimensional magnetohydrodynamics (MHD), having as a main built-in condition the divergence-free constraint ∇ = 0 for the magnetic
A high order Godunov scheme with constrained transport and adaptive mesh refinement for astrophysical and geophysical MHD
TLDR
The proposed MUSCL-Hancock scheme for Euler equations is extended to the induction equation modeling the magnetic field evolution in kinematic dynamo problems and shows its versatility by applying it to the ABC dynamo problem and to the collapse of a magnetized cloud core.
A high-order WENO-based staggered Godunov-type scheme with constrained transport for force-free electrodynamics
The force-free (or low inertia) limit of magnetohydrodynamics (MHD) can be applied to many astrophysical objects, including black holes, neutron stars and accretion discs, where the electromagnetic
High-Order Discontinuous Galerkin Finite Element Methods with Globally Divergence-Free Constrained Transport for Ideal MHD
TLDR
This work shows how to extend the basic CT framework to the discontinuous Galerkin finite element method on both 2D and 3D Cartesian grids and introduces a novel CT scheme that is based on an element-centered magnetic vector potential that is updated via a discontinuousGalerkin scheme on the induction equation.
Efficient, high accuracy ADER-WENO schemes for hydrodynamics and divergence-free magnetohydrodynamics
AN UNSPLIT STAGGERED MESH SCHEME FOR MULTIDIMENSIONAL
We introduce an unsplit staggered mesh scheme (USM) that solves multidimensional magnetohydrodynamics (MHD) by a constrained transport method with high-order Godunov fluxes, incorporating three new
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 20 REFERENCES
On the Divergence-free Condition and Conservation Laws in Numerical Simulations for Supersonic Magnetohydrodynamical Flows
An approach to maintain exactly the eight conservation laws and the divergence-free condition of magnetic fields is proposed for numerical simulations of multidimensional magnetohdyrodynamic (MHD)
A multidimensional flux function with applications to the Euler and Navier-Stokes equations
Abstract A grid-independent approximate Riemann solver has been developed for use in both two- and three-dimensional flows governed by the Euler or Navier-Stokes equations. Fluxes on grid faces are
Extension of the Piecewise Parabolic Method to Multidimensional Ideal Magnetohydrodynamics
An extension of the piecewise parabolic method to treat multidimensional ideal magnetohydrodynamical equations is presented in this paper. The multidimensional scheme is constructed from a
A Higher-Order Godunov Method for Multidimensional Ideal Magnetohydrodynamics
TLDR
A higher-order Godunov method for the solution of the two- and three-dimensional equations of ideal magnetohydrodynamics (MHD) has no problems handling any of the three MHD waves, yet resolves shocks to three or four computational zones.
A Finite-Volume High-Order ENO Scheme for Two-Dimensional Hyperbolic Systems
TLDR
It is found that this two-dimensional scheme is readily applied to inviscid flow problems involving solid walls and non-trivial geometries, and high-order Runge-Kutta methods are employed for time integration, thus making such schemes best-suited for unsteady problems.
A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow. Final Report
TLDR
It is found that high-order ENO schemes remain stable under such situations and quantities related to large-scale features, such as the total circulation around the roll-up region, are adequately resolved.
...
1
2
...