An implicit HDG method for linear convection-diffusion with dual time stepping
An implicit HDG method for linear convection-diffusion with dual time stepping
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DOI：
10.1016/j.jcp.2021.110201
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发表时间：
2021-06
期刊：
影响因子：
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通讯作者：
R. Sevilla
中科院分区：
文献类型：
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作者：
R. Sevilla
本文首次提出了一种双重时间步长(DTS)方法来求解对流扩散问题的混合禁用不连续Galerkin(HDG)形式的整体方程组。证明了具有DTS的HDG整体问题的定态解的存在唯一性。利用von Neumann分析导出了DTS方法的稳定极限，得到了临界对偶时间步长的封闭形式表达式。文中还给出了产生所有频率最大阻尼值的双时间步长的最优选择。通过对定常和非定常对流扩散问题的数值模拟，验证了DTS方法的有效性，并着重研究了对流占优的问题。文中还考虑了两种加速DTS方法收敛的简单方法，并对三种不同的双时间推进方法进行了比较。
This work presents, for the first time, a dual time stepping (DTS) approach to solve the global system of equations that appears in the hybridisable discontinuous Galerkin (HDG) formulation of convection-diffusion problems. A proof of the existence and uniqueness of the steady state solution of the HDG global problem with DTS is presented. The stability limit of the DTS approach is derived using a von Neumann analysis, leading to a closed form expression for the critical dual time step. An optimal choice for the dual time step, producing the maximum damping for all the frequencies, is also derived. Steady and transient convection-diffusion problems are considered to demonstrate the performance of the proposed DTS approach, with particular emphasis on convection dominated problems. Two simple approaches to accelerate the convergence of the DTS approach are also considered and three different time marching approaches for the dual time are compared.