A Third Order Accurate Cellwise Relaxation Implicit Discontinuous Galerkin Scheme for Unstructured Hybrid Meshes

A Third Order Accurate Cellwise Relaxation Implicit Discontinuous Galerkin Scheme for Unstructured Hybrid Meshes

A third order accurate cellwise relaxation implicit Discontinuous Galerkin (DG) scheme for RANS simulations using unstructured hybrid meshes is presented. A scalar parabolic equation is first examined to clarify what is really important in construction of implicit matrix to keep its diagonal dominan...

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Main Authors: Hiroyuki Asada, Yousuke Ogino, Kanako Yasue, Keisuke Sawada
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2014/176752
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spelling doaj-f714593795de429f88e11b765b2347442020-11-24T23:19:29ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472014-01-01201410.1155/2014/176752176752A Third Order Accurate Cellwise Relaxation Implicit Discontinuous Galerkin Scheme for Unstructured Hybrid MeshesHiroyuki Asada0Yousuke Ogino1Kanako Yasue2Keisuke Sawada3Department of Aerospace Engineering, Tohoku University, 6-6-01 Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8579, JapanDepartment of Aerospace Engineering, Tohoku University, 6-6-01 Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8579, JapanInstitute of Aeronautical Technology, Japan Aerospace Exploration Agency, 7-44-1 Jindaiji-Higashi, Chofu, Tokyo 182-8522, JapanDepartment of Aerospace Engineering, Tohoku University, 6-6-01 Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8579, JapanA third order accurate cellwise relaxation implicit Discontinuous Galerkin (DG) scheme for RANS simulations using unstructured hybrid meshes is presented. A scalar parabolic equation is first examined to clarify what is really important in construction of implicit matrix to keep its diagonal dominance for the third and fourth order cellwise relaxation implicit DG schemes. In addition, discussions are given to approximated construction of implicit matrix for reducing computational cost. Then, the third order accurate cellwise relaxation implicit DG scheme for RANS simulations is successfully developed utilizing the expertise learned in the study of solving the parabolic equation. Superior spatial accuracy of the third order accurate cellwise relaxation implicit DG scheme for RANS simulations, while retaining reasonable convergence properties, is demonstrated for typical aerospace applications.http://dx.doi.org/10.1155/2014/176752
collection DOAJ
language English
format Article
sources DOAJ
author Hiroyuki Asada
Yousuke Ogino
Kanako Yasue
Keisuke Sawada
spellingShingle Hiroyuki Asada
Yousuke Ogino
Kanako Yasue
Keisuke Sawada
A Third Order Accurate Cellwise Relaxation Implicit Discontinuous Galerkin Scheme for Unstructured Hybrid Meshes
Mathematical Problems in Engineering
author_facet Hiroyuki Asada
Yousuke Ogino
Kanako Yasue
Keisuke Sawada
author_sort Hiroyuki Asada
title A Third Order Accurate Cellwise Relaxation Implicit Discontinuous Galerkin Scheme for Unstructured Hybrid Meshes
title_short A Third Order Accurate Cellwise Relaxation Implicit Discontinuous Galerkin Scheme for Unstructured Hybrid Meshes
title_full A Third Order Accurate Cellwise Relaxation Implicit Discontinuous Galerkin Scheme for Unstructured Hybrid Meshes
title_fullStr A Third Order Accurate Cellwise Relaxation Implicit Discontinuous Galerkin Scheme for Unstructured Hybrid Meshes
title_full_unstemmed A Third Order Accurate Cellwise Relaxation Implicit Discontinuous Galerkin Scheme for Unstructured Hybrid Meshes
title_sort third order accurate cellwise relaxation implicit discontinuous galerkin scheme for unstructured hybrid meshes
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2014-01-01
description A third order accurate cellwise relaxation implicit Discontinuous Galerkin (DG) scheme for RANS simulations using unstructured hybrid meshes is presented. A scalar parabolic equation is first examined to clarify what is really important in construction of implicit matrix to keep its diagonal dominance for the third and fourth order cellwise relaxation implicit DG schemes. In addition, discussions are given to approximated construction of implicit matrix for reducing computational cost. Then, the third order accurate cellwise relaxation implicit DG scheme for RANS simulations is successfully developed utilizing the expertise learned in the study of solving the parabolic equation. Superior spatial accuracy of the third order accurate cellwise relaxation implicit DG scheme for RANS simulations, while retaining reasonable convergence properties, is demonstrated for typical aerospace applications.
url http://dx.doi.org/10.1155/2014/176752
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