A multimesh finite element method for the Navier–Stokes equations based on projection methods
The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche’s method. Since the non-matching meshes can result in arbitrarily cut cells, additional stabilization terms are needed to obta...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Dokken, Jørgen S. [verfasserIn] Johansson, August [verfasserIn] Massing, André [verfasserIn] Funke, Simon W. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
Multimesh finite element method |
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| Übergeordnetes Werk: |
Enthalten in: Computer methods in applied mechanics and engineering - Amsterdam [u.a.] : Elsevier Science, 1972, 368 |
|---|---|
| Übergeordnetes Werk: |
volume:368 |
| DOI / URN: |
10.1016/j.cma.2020.113129 |
|---|
| Katalog-ID: |
ELV004534840 |
|---|
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| 100 | 1 | |a Dokken, Jørgen S. |e verfasserin |0 (orcid)0000-0001-6489-8858 |4 aut | |
| 245 | 1 | 0 | |a A multimesh finite element method for the Navier–Stokes equations based on projection methods |
| 264 | 1 | |c 2020 | |
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| 520 | |a The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche’s method. Since the non-matching meshes can result in arbitrarily cut cells, additional stabilization terms are needed to obtain a stable method. In this contribution we extend the multimesh finite element method to the Navier–Stokes equations based on the incremental pressure-correction scheme. For each step in the pressure-correction scheme, we derive a multimesh finite element formulation with suitable stabilization terms. The proposed scheme is implemented for arbitrary many overlapping two dimensional domains, yielding expected spatial and temporal convergence rates for the Taylor–Green problem, and demonstrates good agreement for the drag and lift coefficients for the Turek–Schäfer benchmark (DFG benchmark 2D-3). Finally, we illustrate the capabilities of the proposed scheme by optimizing the layout of obstacles in a two dimensional channel. | ||
| 650 | 4 | |a Navier–Stokes equations | |
| 650 | 4 | |a Multimesh finite element method | |
| 650 | 4 | |a Incremental pressure-correction scheme | |
| 650 | 4 | |a Nitsche’s method | |
| 650 | 4 | |a Projection method | |
| 700 | 1 | |a Johansson, August |e verfasserin |0 (orcid)0000-0001-6950-6016 |4 aut | |
| 700 | 1 | |a Massing, André |e verfasserin |4 aut | |
| 700 | 1 | |a Funke, Simon W. |e verfasserin |0 (orcid)0000-0003-4709-8415 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Computer methods in applied mechanics and engineering |d Amsterdam [u.a.] : Elsevier Science, 1972 |g 368 |h Online-Ressource |w (DE-627)306715848 |w (DE-600)1501322-4 |w (DE-576)094531285 |7 nnns |
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| 936 | b | k | |a 50.03 |j Methoden und Techniken der Ingenieurwissenschaften |
| 936 | b | k | |a 50.31 |j Technische Mechanik |
| 936 | b | k | |a 51.32 |j Werkstoffmechanik |
| 936 | b | k | |a 54.80 |j Angewandte Informatik |
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10.1016/j.cma.2020.113129 doi (DE-627)ELV004534840 (ELSEVIER)S0045-7825(20)30314-5 DE-627 ger DE-627 rda eng 004 DE-600 50.03 bkl 50.31 bkl 51.32 bkl 54.80 bkl Dokken, Jørgen S. verfasserin (orcid)0000-0001-6489-8858 aut A multimesh finite element method for the Navier–Stokes equations based on projection methods 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche’s method. Since the non-matching meshes can result in arbitrarily cut cells, additional stabilization terms are needed to obtain a stable method. In this contribution we extend the multimesh finite element method to the Navier–Stokes equations based on the incremental pressure-correction scheme. For each step in the pressure-correction scheme, we derive a multimesh finite element formulation with suitable stabilization terms. The proposed scheme is implemented for arbitrary many overlapping two dimensional domains, yielding expected spatial and temporal convergence rates for the Taylor–Green problem, and demonstrates good agreement for the drag and lift coefficients for the Turek–Schäfer benchmark (DFG benchmark 2D-3). Finally, we illustrate the capabilities of the proposed scheme by optimizing the layout of obstacles in a two dimensional channel. Navier–Stokes equations Multimesh finite element method Incremental pressure-correction scheme Nitsche’s method Projection method Johansson, August verfasserin (orcid)0000-0001-6950-6016 aut Massing, André verfasserin aut Funke, Simon W. verfasserin (orcid)0000-0003-4709-8415 aut Enthalten in Computer methods in applied mechanics and engineering Amsterdam [u.a.] : Elsevier Science, 1972 368 Online-Ressource (DE-627)306715848 (DE-600)1501322-4 (DE-576)094531285 nnns volume:368 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 50.03 Methoden und Techniken der Ingenieurwissenschaften 50.31 Technische Mechanik 51.32 Werkstoffmechanik 54.80 Angewandte Informatik AR 368 |
| spelling |
10.1016/j.cma.2020.113129 doi (DE-627)ELV004534840 (ELSEVIER)S0045-7825(20)30314-5 DE-627 ger DE-627 rda eng 004 DE-600 50.03 bkl 50.31 bkl 51.32 bkl 54.80 bkl Dokken, Jørgen S. verfasserin (orcid)0000-0001-6489-8858 aut A multimesh finite element method for the Navier–Stokes equations based on projection methods 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche’s method. Since the non-matching meshes can result in arbitrarily cut cells, additional stabilization terms are needed to obtain a stable method. In this contribution we extend the multimesh finite element method to the Navier–Stokes equations based on the incremental pressure-correction scheme. For each step in the pressure-correction scheme, we derive a multimesh finite element formulation with suitable stabilization terms. The proposed scheme is implemented for arbitrary many overlapping two dimensional domains, yielding expected spatial and temporal convergence rates for the Taylor–Green problem, and demonstrates good agreement for the drag and lift coefficients for the Turek–Schäfer benchmark (DFG benchmark 2D-3). Finally, we illustrate the capabilities of the proposed scheme by optimizing the layout of obstacles in a two dimensional channel. Navier–Stokes equations Multimesh finite element method Incremental pressure-correction scheme Nitsche’s method Projection method Johansson, August verfasserin (orcid)0000-0001-6950-6016 aut Massing, André verfasserin aut Funke, Simon W. verfasserin (orcid)0000-0003-4709-8415 aut Enthalten in Computer methods in applied mechanics and engineering Amsterdam [u.a.] : Elsevier Science, 1972 368 Online-Ressource (DE-627)306715848 (DE-600)1501322-4 (DE-576)094531285 nnns volume:368 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 50.03 Methoden und Techniken der Ingenieurwissenschaften 50.31 Technische Mechanik 51.32 Werkstoffmechanik 54.80 Angewandte Informatik AR 368 |
| allfields_unstemmed |
10.1016/j.cma.2020.113129 doi (DE-627)ELV004534840 (ELSEVIER)S0045-7825(20)30314-5 DE-627 ger DE-627 rda eng 004 DE-600 50.03 bkl 50.31 bkl 51.32 bkl 54.80 bkl Dokken, Jørgen S. verfasserin (orcid)0000-0001-6489-8858 aut A multimesh finite element method for the Navier–Stokes equations based on projection methods 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche’s method. Since the non-matching meshes can result in arbitrarily cut cells, additional stabilization terms are needed to obtain a stable method. In this contribution we extend the multimesh finite element method to the Navier–Stokes equations based on the incremental pressure-correction scheme. For each step in the pressure-correction scheme, we derive a multimesh finite element formulation with suitable stabilization terms. The proposed scheme is implemented for arbitrary many overlapping two dimensional domains, yielding expected spatial and temporal convergence rates for the Taylor–Green problem, and demonstrates good agreement for the drag and lift coefficients for the Turek–Schäfer benchmark (DFG benchmark 2D-3). Finally, we illustrate the capabilities of the proposed scheme by optimizing the layout of obstacles in a two dimensional channel. Navier–Stokes equations Multimesh finite element method Incremental pressure-correction scheme Nitsche’s method Projection method Johansson, August verfasserin (orcid)0000-0001-6950-6016 aut Massing, André verfasserin aut Funke, Simon W. verfasserin (orcid)0000-0003-4709-8415 aut Enthalten in Computer methods in applied mechanics and engineering Amsterdam [u.a.] : Elsevier Science, 1972 368 Online-Ressource (DE-627)306715848 (DE-600)1501322-4 (DE-576)094531285 nnns volume:368 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 50.03 Methoden und Techniken der Ingenieurwissenschaften 50.31 Technische Mechanik 51.32 Werkstoffmechanik 54.80 Angewandte Informatik AR 368 |
| allfieldsGer |
10.1016/j.cma.2020.113129 doi (DE-627)ELV004534840 (ELSEVIER)S0045-7825(20)30314-5 DE-627 ger DE-627 rda eng 004 DE-600 50.03 bkl 50.31 bkl 51.32 bkl 54.80 bkl Dokken, Jørgen S. verfasserin (orcid)0000-0001-6489-8858 aut A multimesh finite element method for the Navier–Stokes equations based on projection methods 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche’s method. Since the non-matching meshes can result in arbitrarily cut cells, additional stabilization terms are needed to obtain a stable method. In this contribution we extend the multimesh finite element method to the Navier–Stokes equations based on the incremental pressure-correction scheme. For each step in the pressure-correction scheme, we derive a multimesh finite element formulation with suitable stabilization terms. The proposed scheme is implemented for arbitrary many overlapping two dimensional domains, yielding expected spatial and temporal convergence rates for the Taylor–Green problem, and demonstrates good agreement for the drag and lift coefficients for the Turek–Schäfer benchmark (DFG benchmark 2D-3). Finally, we illustrate the capabilities of the proposed scheme by optimizing the layout of obstacles in a two dimensional channel. Navier–Stokes equations Multimesh finite element method Incremental pressure-correction scheme Nitsche’s method Projection method Johansson, August verfasserin (orcid)0000-0001-6950-6016 aut Massing, André verfasserin aut Funke, Simon W. verfasserin (orcid)0000-0003-4709-8415 aut Enthalten in Computer methods in applied mechanics and engineering Amsterdam [u.a.] : Elsevier Science, 1972 368 Online-Ressource (DE-627)306715848 (DE-600)1501322-4 (DE-576)094531285 nnns volume:368 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 50.03 Methoden und Techniken der Ingenieurwissenschaften 50.31 Technische Mechanik 51.32 Werkstoffmechanik 54.80 Angewandte Informatik AR 368 |
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10.1016/j.cma.2020.113129 doi (DE-627)ELV004534840 (ELSEVIER)S0045-7825(20)30314-5 DE-627 ger DE-627 rda eng 004 DE-600 50.03 bkl 50.31 bkl 51.32 bkl 54.80 bkl Dokken, Jørgen S. verfasserin (orcid)0000-0001-6489-8858 aut A multimesh finite element method for the Navier–Stokes equations based on projection methods 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche’s method. Since the non-matching meshes can result in arbitrarily cut cells, additional stabilization terms are needed to obtain a stable method. In this contribution we extend the multimesh finite element method to the Navier–Stokes equations based on the incremental pressure-correction scheme. For each step in the pressure-correction scheme, we derive a multimesh finite element formulation with suitable stabilization terms. The proposed scheme is implemented for arbitrary many overlapping two dimensional domains, yielding expected spatial and temporal convergence rates for the Taylor–Green problem, and demonstrates good agreement for the drag and lift coefficients for the Turek–Schäfer benchmark (DFG benchmark 2D-3). Finally, we illustrate the capabilities of the proposed scheme by optimizing the layout of obstacles in a two dimensional channel. Navier–Stokes equations Multimesh finite element method Incremental pressure-correction scheme Nitsche’s method Projection method Johansson, August verfasserin (orcid)0000-0001-6950-6016 aut Massing, André verfasserin aut Funke, Simon W. verfasserin (orcid)0000-0003-4709-8415 aut Enthalten in Computer methods in applied mechanics and engineering Amsterdam [u.a.] : Elsevier Science, 1972 368 Online-Ressource (DE-627)306715848 (DE-600)1501322-4 (DE-576)094531285 nnns volume:368 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2008 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 50.03 Methoden und Techniken der Ingenieurwissenschaften 50.31 Technische Mechanik 51.32 Werkstoffmechanik 54.80 Angewandte Informatik AR 368 |
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004 DE-600 50.03 bkl 50.31 bkl 51.32 bkl 54.80 bkl A multimesh finite element method for the Navier–Stokes equations based on projection methods Navier–Stokes equations Multimesh finite element method Incremental pressure-correction scheme Nitsche’s method Projection method |
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A multimesh finite element method for the Navier–Stokes equations based on projection methods |
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Dokken, Jørgen S. |
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Dokken, Jørgen S. Johansson, August Massing, André Funke, Simon W. |
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a multimesh finite element method for the navier–stokes equations based on projection methods |
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A multimesh finite element method for the Navier–Stokes equations based on projection methods |
| abstract |
The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche’s method. Since the non-matching meshes can result in arbitrarily cut cells, additional stabilization terms are needed to obtain a stable method. In this contribution we extend the multimesh finite element method to the Navier–Stokes equations based on the incremental pressure-correction scheme. For each step in the pressure-correction scheme, we derive a multimesh finite element formulation with suitable stabilization terms. The proposed scheme is implemented for arbitrary many overlapping two dimensional domains, yielding expected spatial and temporal convergence rates for the Taylor–Green problem, and demonstrates good agreement for the drag and lift coefficients for the Turek–Schäfer benchmark (DFG benchmark 2D-3). Finally, we illustrate the capabilities of the proposed scheme by optimizing the layout of obstacles in a two dimensional channel. |
| abstractGer |
The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche’s method. Since the non-matching meshes can result in arbitrarily cut cells, additional stabilization terms are needed to obtain a stable method. In this contribution we extend the multimesh finite element method to the Navier–Stokes equations based on the incremental pressure-correction scheme. For each step in the pressure-correction scheme, we derive a multimesh finite element formulation with suitable stabilization terms. The proposed scheme is implemented for arbitrary many overlapping two dimensional domains, yielding expected spatial and temporal convergence rates for the Taylor–Green problem, and demonstrates good agreement for the drag and lift coefficients for the Turek–Schäfer benchmark (DFG benchmark 2D-3). Finally, we illustrate the capabilities of the proposed scheme by optimizing the layout of obstacles in a two dimensional channel. |
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The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche’s method. Since the non-matching meshes can result in arbitrarily cut cells, additional stabilization terms are needed to obtain a stable method. In this contribution we extend the multimesh finite element method to the Navier–Stokes equations based on the incremental pressure-correction scheme. For each step in the pressure-correction scheme, we derive a multimesh finite element formulation with suitable stabilization terms. The proposed scheme is implemented for arbitrary many overlapping two dimensional domains, yielding expected spatial and temporal convergence rates for the Taylor–Green problem, and demonstrates good agreement for the drag and lift coefficients for the Turek–Schäfer benchmark (DFG benchmark 2D-3). Finally, we illustrate the capabilities of the proposed scheme by optimizing the layout of obstacles in a two dimensional channel. |
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A multimesh finite element method for the Navier–Stokes equations based on projection methods |
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