Minimally implicit Runge-Kutta methods for Resistive Relativistic MHD

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

Aloy, Miguel-Á.^1 ; Cordero-Carrión, Isabel^2

Departamento de Astronomía y Astrofísica, Universidad de Valencia, C/ Dr. Moliner 50, Burjassot

46100, Spain^1

Departamento de Matemática Aplicada, Universidad de Valencia, C/ Dr. Moliner 50, Burjassot

E-46100, Spain^2

关键词: Computational costs;    Explicit Runge-Kutta methods;    Explicit time integration method;    Finite conductivity;    Ideal magnetohydrodynamics;    Implicit Runge-Kutta method;    Numerical instability;    Resistive magnetohydrodynamics;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/719/1/012015/pdf
DOI  :  10.1088/1742-6596/719/1/012015

来源: IOP

【 摘 要 】

The Relativistic Resistive Magnetohydrodynamic (RRMHD) equations are a hyperbolic system of partial differential equations used to describe the dynamics of relativistic magnetized fluids with a finite conductivity. Close to the ideal magnetohydrodynamic regime, the source term proportional to the conductivity becomes potentially stiff and cannot be handled with standard explicit time integration methods. We propose a new class of methods to deal with the stiffness fo the system, which we name Minimally Implicit Runge-Kutta methods. These methods avoid the development of numerical instabilities without increasing the computational costs in comparison with explicit methods, need no iterative extra loop in order to recover the primitive (physical) variables, the analytical inversion of the implicit operator is trivial and the several stages can actually be viewed as stages of explicit Runge-Kutta methods with an effective time-step. We test these methods with two different one-dimensional test beds in varied conductivity regimes, and show that our second-order schemes satisfy the theoretical expectations.