Fully decoupled, linear and unconditionally energy stable time discretization scheme for solving the magneto-hydrodynamic equations
Fully decoupled, linear and unconditionally energy stable time discretization scheme for solving the magneto-hydrodynamic equations
复制标题
用于求解磁流体动力学方程的完全解耦、线性和无条件能量稳定时间离散方案
DOI：
10.1016/j.cam.2019.112636
复制
发表时间：
2020-05-01
影响因子：
2.4
通讯作者：
Yang，Xiaofeng
中科院分区：
文献类型：
--
作者：
Zhang，Guo-Dong;He，Xiaoming;Yang，Xiaofeng
在本文中，我们考虑数值近似求解磁流体动力学方程，它耦合的Navier-Stokes方程和麦克斯韦方程在一起。数值求解该模型的一个挑战性问题是时间离散化，即，如何为非线性项开发合适的时间离散化，以保持离散水平上的能量稳定性。我们解决了这个问题，本文开发了一个线性的，完全解耦的一阶时间推进格式，结合投影方法的Navier-Stokes方程和一些微妙的隐式显式处理的非线性耦合项。我们进一步证明了该格式是无条件能量稳定的，并严格地给出了半离散化的最优误差估计。各种数值模拟来证明的稳定性和准确性。
In this paper, we consider numerical approximations for solving the magneto-hydrodynamic equations, which couples the Navier–Stokes equations and Maxwell equations together. A challenging issue to solve this model numerically is the time discretization, i.e., how to develop suitable temporal discretizations for the nonlinear terms in order to preserve the energy stability at the discrete level. We solve this issue in this paper by developing a linear, fully decoupled first order time marching scheme, by combining the projection method for Navier–Stokes equations and some subtle implicit–explicit treatments for nonlinear coupling terms. We further prove that the scheme is unconditional energy stable and derive the optimal error estimates of the semi-discretization rigorously. Various numerical simulations are implemented to demonstrate the stability and the accuracy.