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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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spelling 2021-02-26T14:45:13.6844263 v2 56254 2021-02-15 An implicit HDG method for linear convection-diffusion with dual time stepping b542c87f1b891262844e95a682f045b6 0000-0002-0061-6214 Rubén Sevilla Rubén Sevilla true false 2021-02-15 CIVL 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. Journal Article Journal of Computational Physics 434 110201 Elsevier BV 0021-9991 Discontinuous Galerkin; Hybrid method; Dual time; Convection; Diffusion 1 6 2021 2021-06-01 10.1016/j.jcp.2021.110201 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University UKRI, EP/T009071/1 2021-02-26T14:45:13.6844263 2021-02-15T09:06:40.4353365 College of Engineering Engineering Rubén Sevilla 0000-0002-0061-6214 1 56254__19377__64ae7dcc909146abbcd2a7eb5f91061c.pdf 56254 (2).pdf 2021-02-26T10:06:35.2374449 Output 2310988 application/pdf Version of Record true © 2021 The Author(s). This is an open access article under the CC BY license true eng http://creativecommons.org/licenses/by/4.0/
title An implicit HDG method for linear convection-diffusion with dual time stepping
spellingShingle An implicit HDG method for linear convection-diffusion with dual time stepping
Rubén Sevilla
title_short An implicit HDG method for linear convection-diffusion with dual time stepping
title_full An implicit HDG method for linear convection-diffusion with dual time stepping
title_fullStr An implicit HDG method for linear convection-diffusion with dual time stepping
title_full_unstemmed An implicit HDG method for linear convection-diffusion with dual time stepping
title_sort An implicit HDG method for linear convection-diffusion with dual time stepping
author_id_str_mv b542c87f1b891262844e95a682f045b6
author_id_fullname_str_mv b542c87f1b891262844e95a682f045b6_***_Rubén Sevilla
author Rubén Sevilla
author2 Rubén Sevilla
format Journal article
container_title Journal of Computational Physics
container_volume 434
container_start_page 110201
publishDate 2021
institution Swansea University
issn 0021-9991
doi_str_mv 10.1016/j.jcp.2021.110201
publisher Elsevier BV
college_str College of Engineering
hierarchytype
hierarchy_top_id collegeofengineering
hierarchy_top_title College of Engineering
hierarchy_parent_id collegeofengineering
hierarchy_parent_title College of Engineering
department_str Engineering{{{_:::_}}}College of Engineering{{{_:::_}}}Engineering
document_store_str 1
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description 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.
published_date 2021-06-01T04:11:44Z
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score 10.900759