Numerical Relativistic Magnetohydrodynamics with ADER Discontinuous Galerkin methods on adaptively refined meshes.

10th International Conference on Numerical Modeling of Space Plasma Flows: ASTRONUM-2015

Zanotti, O.^1 ; Dumbser, M.^1 ; Fambri, F.^1

Laboratory of Applied Mathematics, Via Mesiano 77, Trento

38123, Italy^1

关键词: Adaptive mesh refinement;    Arbitrary accuracy;    Discontinuous galerkin;    Discontinuous Galerkin methods;    Finite volume schemes;    Local time stepping;    Relativistic magnetohydrodynamics;    Special relativity;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/719/1/012024/pdf
DOI  :  10.1088/1742-6596/719/1/012024

来源: IOP

【 摘 要 】

We describe a new method for the solution of the ideal MHD equations in special relativity which adopts the following strategy: (i) the main scheme is based on Discontinuous Galerkin (DG) methods, allowing for an arbitrary accuracy of order N+1, where N is the degree of the basis polynomials; (ii) in order to cope with oscillations at discontinuities, an "a-posteriori" sub-cell limiter is activated, which scatters the DG polynomials of the previous time-step onto a set of 2N+1 sub-cells, over which the solution is recomputed by means of a robust finite volume scheme; (iii) a local spacetime Discontinuous-Galerkin predictor is applied both on the main grid of the DG scheme and on the sub-grid of the finite volume scheme; (iv) adaptive mesh refinement (AMR) with local time-stepping is used. We validate the new scheme and comment on its potential applications in high energy astrophysics.