A simple method for preserving divergence-free is obtained by projecting the velocity onto the divergence-free space after generating the new mesh at the last iterative step.
These methods are conservative in that they locally preserve "divergence" or charge.
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.
Of those, only one preserves divergence and, thus, is guaranteed to be stable in the presence of moving charged particles.
New schemes are developed on triangular grids for solving ideal magnetohydrodynamic equations while preserving globally divergence-free magnetic field.
This algorithm combines the corner transport upwind (CTU) method of Colella for multidimensional integration, and the constrained transport (CT) algorithm for preserving the divergence-free constraint on the magnetic field.
We describe a single step, second-order accurate Godunov scheme for ideal MHD based on combining the piecewise parabolic method (PPM) for performing spatial reconstruction, the corner transport upwind (CTU) method of Colella for multidimensional integration, and the constrained transport (CT) algorithm for preserving the divergence-free constraint on the magnetic field.
We also show that these numerical methods preserve the divergence.
To preserve the divergence constraints on the electric and magnetic fields two different approaches are used.
We present new second-order prolongation and restriction formulas which preserve the divergence and, in some cases, the curl of a discretized vector field.
It is shown that the averaged energy increases linearly with respect to the evolution of time and the flow of stochastic Maxwell equations with additive noise preserves the divergence in the sense of expectation.
