Nitsche's method combined with space–time finite elements for ALE fluid–structure interaction problems
We propose a weak method for handling the fluid–structure interface in finite element fluid–structure interaction based on Nitsche's method [Abh. Math. Univ. Hamburg 36 (1971) 9]. We assume transient incompressible Newtonian flow and, for the structure, undamped linear elasticity. For the time-...
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| Vydáno v: | Computer methods in applied mechanics and engineering Ročník 193; číslo 39; s. 4195 - 4206 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
01.10.2004
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| ISSN: | 0045-7825, 1879-2138, 1879-2138 |
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| Abstract | We propose a weak method for handling the fluid–structure interface in finite element fluid–structure interaction based on Nitsche's method [Abh. Math. Univ. Hamburg 36 (1971) 9]. We assume transient incompressible Newtonian flow and, for the structure, undamped linear elasticity. For the time-discretization, we use the time-continuous (energy conserving) Galerkin method for the structure, and for the fluid we employ the time-discontinuous Galerkin method. This means that the velocity becomes piecewise constant on each timestep for the fluid, matching the time-derivative of the displacements in the solid which is also piecewise constant over a time step. We formulate the method and report some numerical examples using space–time oriented elements for the fluid in order to mimic Lagrangian or ALE-type simulations. |
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| AbstractList | We propose a weak method for handling the fluid–structure interface in finite element fluid–structure interaction based on Nitsche's method [Abh. Math. Univ. Hamburg 36 (1971) 9]. We assume transient incompressible Newtonian flow and, for the structure, undamped linear elasticity. For the time-discretization, we use the time-continuous (energy conserving) Galerkin method for the structure, and for the fluid we employ the time-discontinuous Galerkin method. This means that the velocity becomes piecewise constant on each timestep for the fluid, matching the time-derivative of the displacements in the solid which is also piecewise constant over a time step. We formulate the method and report some numerical examples using space–time oriented elements for the fluid in order to mimic Lagrangian or ALE-type simulations. |
| Author | Hansbo, Peter Hermansson, Joakim Svedberg, Thomas |
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| Cites_doi | 10.1016/0045-7825(92)90039-M 10.1006/jcph.2000.6436 10.1007/s007910100057 10.1006/jcph.2002.7185 10.1007/s00466-003-0467-7 10.1016/S0045-7825(00)00383-2 10.1016/S0045-7825(00)00378-9 10.1051/m2an:2003023 10.1002/cnm.458 10.1016/0010-4655(92)90031-S 10.1002/cnm.639 10.1016/S0045-7825(97)00216-8 10.1016/0021-9991(90)90173-X 10.1002/nme.749 10.1007/BF02995904 10.1016/S0045-7949(02)00259-6 10.1016/j.cma.2003.12.041 |
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| Title | Nitsche's method combined with space–time finite elements for ALE fluid–structure interaction problems |
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