Space-time discontinuous Galerkin method for the solution of fluid-structure interaction
The paper is concerned with the application of the space-time discontinuous Galerkin method (STDGM) to the numerical solution of the interaction of a compressible flow and an elastic structure. The flow is described by the system of compressible Navier-Stokes equations written in the conservative fo...
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| Veröffentlicht in: | Applications of Mathematics 2018-12, Vol.63 (6), p.739-764 |
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| creator | Balázsová, Monika Feistauer, Miloslav Horáček, Jaromír Hadrava, Martin Kosík, Adam |
| description | The paper is concerned with the application of the space-time discontinuous Galerkin method (STDGM) to the numerical solution of the interaction of a compressible flow and an elastic structure. The flow is described by the system of compressible Navier-Stokes equations written in the conservative form. They are coupled with the dynamic elasticity system of equations describing the deformation of the elastic body, induced by the aerodynamical force on the interface between the gas and the elastic structure. The domain occupied by the fluid depends on time. It is taken into account in the Navier-Stokes equations rewritten with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. The resulting coupled system is discretized by the STDGM using piecewise polynomial approximations of the sought solution both in space and time. The developed method can be applied to the solution of the compressible flow for a wide range of Mach numbers and Reynolds numbers. For the simulation of elastic deformations two models are used: the linear elasticity model and the nonlinear neo-Hookean model. The main goal is to show the robustness and applicability of the method to the simulation of the air flow in a simplified model of human vocal tract and the flow induced vocal folds vibrations. It will also be shown that in this case the linear elasticity model is not adequate and it is necessary to apply the nonlinear model. |
| doi_str_mv | 10.21136/AM.2018.0139-18 |
| format | Article |
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The flow is described by the system of compressible Navier-Stokes equations written in the conservative form. They are coupled with the dynamic elasticity system of equations describing the deformation of the elastic body, induced by the aerodynamical force on the interface between the gas and the elastic structure. The domain occupied by the fluid depends on time. It is taken into account in the Navier-Stokes equations rewritten with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. The resulting coupled system is discretized by the STDGM using piecewise polynomial approximations of the sought solution both in space and time. The developed method can be applied to the solution of the compressible flow for a wide range of Mach numbers and Reynolds numbers. For the simulation of elastic deformations two models are used: the linear elasticity model and the nonlinear neo-Hookean model. The main goal is to show the robustness and applicability of the method to the simulation of the air flow in a simplified model of human vocal tract and the flow induced vocal folds vibrations. It will also be shown that in this case the linear elasticity model is not adequate and it is necessary to apply the nonlinear model.</description><identifier>ISSN: 0862-7940</identifier><identifier>EISSN: 1572-9109</identifier><identifier>DOI: 10.21136/AM.2018.0139-18</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Air flow ; ALE (numerical method) ; Analysis ; Applications of Mathematics ; Classical and Continuum Physics ; Compressible flow ; Computational fluid dynamics ; Computer simulation ; Elastic bodies ; Elastic deformation ; Elasticity ; Fluid flow ; Fluid-structure interaction ; Galerkin method ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematical models ; Mathematics ; Mathematics and Statistics ; Navier-Stokes equations ; Optimization ; Polynomials ; Robustness (mathematics) ; Spacetime ; Theoretical ; Vocal tract</subject><ispartof>Applications of Mathematics, 2018-12, Vol.63 (6), p.739-764</ispartof><rights>Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018</rights><rights>Applications of Mathematics is a copyright of Springer, (2018). All Rights Reserved.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c308t-dbf85d742925aa124cc0938cab6ce9af8970963c213c968b991ab5e6675216903</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.21136/AM.2018.0139-18$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.21136/AM.2018.0139-18$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Balázsová, Monika</creatorcontrib><creatorcontrib>Feistauer, Miloslav</creatorcontrib><creatorcontrib>Horáček, Jaromír</creatorcontrib><creatorcontrib>Hadrava, Martin</creatorcontrib><creatorcontrib>Kosík, Adam</creatorcontrib><title>Space-time discontinuous Galerkin method for the solution of fluid-structure interaction</title><title>Applications of Mathematics</title><addtitle>Appl Math</addtitle><description>The paper is concerned with the application of the space-time discontinuous Galerkin method (STDGM) to the numerical solution of the interaction of a compressible flow and an elastic structure. The flow is described by the system of compressible Navier-Stokes equations written in the conservative form. They are coupled with the dynamic elasticity system of equations describing the deformation of the elastic body, induced by the aerodynamical force on the interface between the gas and the elastic structure. The domain occupied by the fluid depends on time. It is taken into account in the Navier-Stokes equations rewritten with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. The resulting coupled system is discretized by the STDGM using piecewise polynomial approximations of the sought solution both in space and time. The developed method can be applied to the solution of the compressible flow for a wide range of Mach numbers and Reynolds numbers. For the simulation of elastic deformations two models are used: the linear elasticity model and the nonlinear neo-Hookean model. The main goal is to show the robustness and applicability of the method to the simulation of the air flow in a simplified model of human vocal tract and the flow induced vocal folds vibrations. It will also be shown that in this case the linear elasticity model is not adequate and it is necessary to apply the nonlinear model.</description><subject>Air flow</subject><subject>ALE (numerical method)</subject><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Classical and Continuum Physics</subject><subject>Compressible flow</subject><subject>Computational fluid dynamics</subject><subject>Computer simulation</subject><subject>Elastic bodies</subject><subject>Elastic deformation</subject><subject>Elasticity</subject><subject>Fluid flow</subject><subject>Fluid-structure interaction</subject><subject>Galerkin method</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Navier-Stokes equations</subject><subject>Optimization</subject><subject>Polynomials</subject><subject>Robustness (mathematics)</subject><subject>Spacetime</subject><subject>Theoretical</subject><subject>Vocal 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discontinuous Galerkin method for the solution of fluid-structure interaction</title><author>Balázsová, Monika ; Feistauer, Miloslav ; Horáček, Jaromír ; Hadrava, Martin ; Kosík, Adam</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c308t-dbf85d742925aa124cc0938cab6ce9af8970963c213c968b991ab5e6675216903</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Air flow</topic><topic>ALE (numerical method)</topic><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Classical and Continuum Physics</topic><topic>Compressible flow</topic><topic>Computational fluid dynamics</topic><topic>Computer simulation</topic><topic>Elastic bodies</topic><topic>Elastic deformation</topic><topic>Elasticity</topic><topic>Fluid flow</topic><topic>Fluid-structure interaction</topic><topic>Galerkin method</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Navier-Stokes equations</topic><topic>Optimization</topic><topic>Polynomials</topic><topic>Robustness (mathematics)</topic><topic>Spacetime</topic><topic>Theoretical</topic><topic>Vocal tract</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Balázsová, Monika</creatorcontrib><creatorcontrib>Feistauer, Miloslav</creatorcontrib><creatorcontrib>Horáček, Jaromír</creatorcontrib><creatorcontrib>Hadrava, Martin</creatorcontrib><creatorcontrib>Kosík, Adam</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Access via ABI/INFORM (ProQuest)</collection><collection>ABI/INFORM 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Basic</collection><jtitle>Applications of Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Balázsová, Monika</au><au>Feistauer, Miloslav</au><au>Horáček, Jaromír</au><au>Hadrava, Martin</au><au>Kosík, Adam</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Space-time discontinuous Galerkin method for the solution of fluid-structure interaction</atitle><jtitle>Applications of Mathematics</jtitle><stitle>Appl Math</stitle><date>2018-12-01</date><risdate>2018</risdate><volume>63</volume><issue>6</issue><spage>739</spage><epage>764</epage><pages>739-764</pages><issn>0862-7940</issn><eissn>1572-9109</eissn><abstract>The paper is concerned with the application of the space-time discontinuous Galerkin method (STDGM) to the numerical solution of the interaction of a compressible flow and an elastic structure. The flow is described by the system of compressible Navier-Stokes equations written in the conservative form. They are coupled with the dynamic elasticity system of equations describing the deformation of the elastic body, induced by the aerodynamical force on the interface between the gas and the elastic structure. The domain occupied by the fluid depends on time. It is taken into account in the Navier-Stokes equations rewritten with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. The resulting coupled system is discretized by the STDGM using piecewise polynomial approximations of the sought solution both in space and time. The developed method can be applied to the solution of the compressible flow for a wide range of Mach numbers and Reynolds numbers. For the simulation of elastic deformations two models are used: the linear elasticity model and the nonlinear neo-Hookean model. The main goal is to show the robustness and applicability of the method to the simulation of the air flow in a simplified model of human vocal tract and the flow induced vocal folds vibrations. It will also be shown that in this case the linear elasticity model is not adequate and it is necessary to apply the nonlinear model.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.21136/AM.2018.0139-18</doi><tpages>26</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Air flow ALE (numerical method) Analysis Applications of Mathematics Classical and Continuum Physics Compressible flow Computational fluid dynamics Computer simulation Elastic bodies Elastic deformation Elasticity Fluid flow Fluid-structure interaction Galerkin method Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical models Mathematics Mathematics and Statistics Navier-Stokes equations Optimization Polynomials Robustness (mathematics) Spacetime Theoretical Vocal tract |
| title | Space-time discontinuous Galerkin method for the solution of fluid-structure interaction |
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