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

Rubén Sevilla Orcid Logo

Journal of Computational Physics, Volume: 434, Start page: 110201

Swansea University Author: Rubén Sevilla Orcid Logo

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Abstract

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...

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Published in: Journal of Computational Physics
ISSN: 0021-9991
Published: Elsevier BV 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa56254
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Abstract: 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.
Keywords: Discontinuous Galerkin; Hybrid method; Dual time; Convection; Diffusion
College: College of Engineering
Funders: UKRI, EP/T009071/1
Start Page: 110201