An adaptive multiresolution method for ideal magnetohydrodynamics using divergence cleaning with parabolic-hyperbolic correction
This work addresses the need for efficient and accurate numerical simulations of magnetohydrodynamics, a problem relevant to plasma physics and astrophysics, but the method is incremental as it combines existing techniques.
The paper presents an adaptive multiresolution method for 2D ideal magnetohydrodynamics simulations, using divergence cleaning with a hyperbolic-parabolic correction. The method achieves CPU time and memory savings while maintaining accuracy compared to fine mesh reference solutions.
We present an adaptive multiresolution method for the numerical simulation of ideal magnetohydrodynamics in two space dimensions. The discretization uses a finite volume scheme based on a Cartesian mesh and an explicit compact Rung-Kutta scheme for time integration. Harten's cell average multiresolution allows to introduce a locally refined spatial mesh while controlling the error. The incompressibility of the magnetic field is controlled by using a Generalized Lagrangian Multiplier (GLM) approach with a mixed hyperbolic-parabolic correction. Different applications to two-dimensional problems illustrate the properties of the method. For each application CPU time and memory savings are reported and numerical aspects of the method are discussed. The accuracy of the adaptive computations is assessed by comparison with reference solutions computed on a regular fine mesh.