Implicit-Explicit Local Discontinuous Galerkin Methods with Generalized Alternating Numerical Fluxes for Convection-Diffusion Problems
Implicit-Explicit Local Discontinuous Galerkin Methods with Generalized Alternating Numerical Fluxes for Convection-Diffusion Problems
复制标题
对流扩散问题的广义交替数值通量隐式-显式局部不连续伽辽金方法
DOI：
10.1007/s10915-019-01072-4
复制
发表时间：
2019
影响因子：
2.5
通讯作者：
Shu Chi Wang
中科院分区：
文献类型：
--
作者：
Wang Haijin;Zhang Qiang;Shu Chi Wang
本文研究了求解对流扩散问题的广义交替数值通量局部间断Galerkin方法与隐-显时间推进的耦合，其中显式部分采用强稳定的Runge-Kutta格式，隐式部分采用L-稳定的对角隐式Runge-Kutta方法。基于广义交替数值通量，我们建立了梯度与数值解界面跳跃之间的重要关系，并给出了梯度的独立数值解，这对获得所提格式的无条件稳定性起着关键作用.借助于广义Gauss-Radau投影，可以给出最优误差估计。数值实验验证了不同数值通量下格式的稳定性和精度。
Local discontinuous Galerkin methods with generalized alternating numerical fluxes coupled with implicit–explicit time marching for solving convection–diffusion problems is analyzed in this paper, where the explicit part is treated by a strong-stability-preserving Runge–Kutta scheme, and the implicit part is treated by an L-stable diagonally implicit Runge–Kutta method. Based on the generalized alternating numerical flux, we establish the important relationship between the gradient and interface jump of the numerical solution with the independent numerical solution of the gradient, which plays a key role in obtaining the unconditional stability of the proposed schemes. Also by the aid of the generalized Gauss–Radau projection, optimal error estimates can be shown. Numerical experiments are given to verify the stability and accuracy of the proposed schemes with different numerical fluxes.