An implicit HDG method for linear convection-diffusion with dual time stepping

JOURNAL OF COMPUTATIONAL PHYSICS

卷:434

Article

Sevilla, Ruben¹ 

[1] Swansea Univ, Fac Sci & Engn, Zienkiewicz Ctr Computat Engn, Swansea SA1 8EN, W Glam, Wales

关键词: Discontinuous Galerkin;    Hybrid method;    Dual time;    Convection;    Diffusion;   

DOI  :  10.1016/j.jcp.2021.110201

来源: Elsevier

【 摘 要 】

The hybridisable discontinuous Galerkin (HDG) method, proposed by Cockburn and co-workers [1?5], has gained popularity in the last decade due to its ability to reduce the global number of coupled degrees of freedom required by other DG approaches. Applications of HDG methods can be found in many areas, including fluid mechanics [2,6?13], solid mechanics [14?18] and wave propagation [19?23]. As with other implicit methods, the computational cost and memory requirements of the HDG method can become 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. ? 2021 The Author(s). Published by Elsevier Inc. This is an open access article under the

【 授权许可】

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