Adaptive mesh refinement based on Revised Integral Deferred Correction Method for Plasma physics

摘要

In this work, we study a new AMR-RIDC method for hyperbolic conservation laws and problems from Plasma physics. This method combines the adaptive mesh refinement (AMR) framework [1,2] with Revised Integral Deferred Correction (RIDC) Method [3,4] to get a high order (4th order in time) adaptive solver for the solutions with shock. We hope to accomplish an efficient method for solving problems such as viscous Burgers' Equation, by taking use of the parallel structure of RIDC method and mesh adaptivity of AMR. Our high order method is realized by coupling high order interpolation in time (Hermite) for the ghost points, high order integrator of RIDC on the coarse mesh and the total variation diminishing (TVD) Runge-Kutta (RK) method on the fine mesh. We will demonstrate the accuracy of the AMR-RIDC method by the problems from hyperbolic conservation laws and Plasma physics on Shishkin mesh first, and check it on the real AMR mesh next. We expect our method is accurate and computationally efficient.