Goal-Oriented Mesh Adaptivity for Fluid-Structure Interaction with Application to Heart-Valve Settings
We apply a fluid-structure interaction method to simulate prototypical dynamics of the aortic heart-valve. Our method of choice is based on a monolithic coupling scheme for fluid-structure interactions in which the fluid equations are rewritten in the ‘arbitrary Lagrangian Eulerian’ (ALE) framework....
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Polish Academy of Sciences |
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| Abstract | We apply a fluid-structure interaction method to simulate prototypical dynamics of the aortic heart-valve. Our method of choice is based on a monolithic coupling scheme for fluid-structure interactions in which the fluid equations are rewritten in the ‘arbitrary Lagrangian Eulerian’ (ALE) framework. To prevent the backflow of structure waves because of their hyperbolic nature, a damped structure equation is solved on an artificial layer that is used to prolongate the computational domain. The increased computational cost in the presence of the artificial layer is resolved by using local mesh adaption. In particular, heuristic mesh refinement techniques are compared to rigorous goal-oriented mesh adaption with the dual weighted residual (DWR) method. A version of this method is developed for stationary settings. For the nonstationary test cases the indicators are obtained by a heuristic error estimator, which has a good performance for the measurement of wall stresses. The results for prototypical problems demonstrate that heart-valve dynamics can be treated with our proposed concepts and that the DWR method performs best with respect to a certain target functional.
W artykule przedstawiono analizę zagadnienia oddziaływania płyn-struktura (FSI) w komputerowej symulacji pracy zastawki serca. Przedstawiono monolityczne sformułowanie tego zagadnienia, w którym równania dla struktury i płynu rozwiązywane są w pełnym sprzężeniu, przy czym do opisu ruchu płynu stosowane jest podejście typu Arbitrary Lagrangian-Euelerian (ALE). Zaproponowano metodę eliminacji zjawiska niefizycznego odbicia fal odkształceń struktury, polegającą na wprowadzeniu sztucznej dyssypacji energii tych fal w części brzegu obszaru położonej za zastawkami. W celu zwiększenia efektywności obliczeniowej wprowadzono lokalną adaptację siatki. W szczególności, porównano heurystyczne techniki adaptacji siatki z techniką opartą na wykorzystaniu ważonego residuum sprzężonego (Dual Weighted Residual, DWR). Przedstawiono wyniki obliczeń testowych demonstrujące poprawność zaproponowanego podejścia oraz skuteczność metody adaptacyjnej DWR. |
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| AbstractList | We apply a fluid-structure interaction method to simulate prototypical dynamics of the aortic heart-valve. Our method of choice is based on a monolithic coupling scheme for fluid-structure interactions in which the fluid equations are rewritten in the ‘arbitrary Lagrangian Eulerian’ (ALE) framework. To prevent the backflow of structure waves because of their hyperbolic nature, a damped structure equation is solved on an artificial layer that is used to prolongate the computational domain. The increased computational cost in the presence of the artificial layer is resolved by using local mesh adaption. In particular, heuristic mesh refinement techniques are compared to rigorous goal-oriented mesh adaption with the dual weighted residual (DWR) method. A version of this method is developed for stationary settings. For the nonstationary test cases the indicators are obtained by a heuristic error estimator, which has a good performance for the measurement of wall stresses. The results for prototypical problems demonstrate that heart-valve dynamics can be treated with our proposed concepts and that the DWR method performs best with respect to a certain target functional.
W artykule przedstawiono analizę zagadnienia oddziaływania płyn-struktura (FSI) w komputerowej symulacji pracy zastawki serca. Przedstawiono monolityczne sformułowanie tego zagadnienia, w którym równania dla struktury i płynu rozwiązywane są w pełnym sprzężeniu, przy czym do opisu ruchu płynu stosowane jest podejście typu Arbitrary Lagrangian-Euelerian (ALE). Zaproponowano metodę eliminacji zjawiska niefizycznego odbicia fal odkształceń struktury, polegającą na wprowadzeniu sztucznej dyssypacji energii tych fal w części brzegu obszaru położonej za zastawkami. W celu zwiększenia efektywności obliczeniowej wprowadzono lokalną adaptację siatki. W szczególności, porównano heurystyczne techniki adaptacji siatki z techniką opartą na wykorzystaniu ważonego residuum sprzężonego (Dual Weighted Residual, DWR). Przedstawiono wyniki obliczeń testowych demonstrujące poprawność zaproponowanego podejścia oraz skuteczność metody adaptacyjnej DWR. Goal-Oriented Mesh Adaptivity for Fluid-Structure Interaction with Application to Heart-Valve Settings We apply a fluid-structure interaction method to simulate prototypical dynamics of the aortic heart-valve. Our method of choice is based on a monolithic coupling scheme for fluid-structure interactions in which the fluid equations are rewritten in the 'arbitrary Lagrangian Eulerian' (ALE) framework. To prevent the backflow of structure waves because of their hyperbolic nature, a damped structure equation is solved on an artificial layer that is used to prolongate the computational domain. The increased computational cost in the presence of the artificial layer is resolved by using local mesh adaption. In particular, heuristic mesh refinement techniques are compared to rigorous goal-oriented mesh adaption with the dual weighted residual (DWR) method. A version of this method is developed for stationary settings. For the nonstationary test cases the indicators are obtained by a heuristic error estimator, which has a good performance for the measurement of wall stresses. The results for prototypical problems demonstrate that heart-valve dynamics can be treated with our proposed concepts and that the DWR method performs best with respect to a certain target functional. We apply a fluid-structure interaction method to simulate prototypical dynamics of the aortic heart-valve. Our method of choice is based on a monolithic coupling scheme for fluid-structure interactions in which the fluid equations are rewritten in the ‘arbitrary Lagrangian Eulerian’ (ALE) framework. To prevent the backflow of structure waves because of their hyperbolic nature, a damped structure equation is solved on an artificial layer that is used to prolongate the computational domain. The increased computational cost in the presence of the artificial layer is resolved by using local mesh adaption. In particular, heuristic mesh refinement techniques are compared to rigorous goal-oriented mesh adaption with the dual weighted residual (DWR) method. A version of this method is developed for stationary settings. For the nonstationary test cases the indicators are obtained by a heuristic error estimator, which has a good performance for the measurement of wall stresses. The results for prototypical problems demonstrate that heart-valve dynamics can be treated with our proposed concepts and that the DWR method performs best with respect to a certain target functional. |
| Author | Wick, Thomas |
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| Snippet | We apply a fluid-structure interaction method to simulate prototypical dynamics of the aortic heart-valve. Our method of choice is based on a monolithic... Goal-Oriented Mesh Adaptivity for Fluid-Structure Interaction with Application to Heart-Valve Settings We apply a fluid-structure interaction method to... |
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| SubjectTerms | 35Q74 65M60 65N30 74B20 arbitrary Lagrangian Eulerian method elastic waves finite element method fluid-structure interaction goal-oriented mesh adaption 2010 MSC: 74F10 heart-valve dynamics |
| Title | Goal-Oriented Mesh Adaptivity for Fluid-Structure Interaction with Application to Heart-Valve Settings |
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