Goal-oriented mesh adaptivity for fluid-structure interaction with application to heart-valve settings

• Autorzy: Wick T.

Warianty tytułu

PL

Metody adaptacji siatki w zagadnieniu oddziaływania płyn-struktura (FSI) w zastosowaniu do symulacji przepływu przez zastawkę serca

• Języki publikacji: EN

Abstrakty

EN

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.

PL

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.

Słowa kluczowe

EN

heart-valve dynamics; elastic waves; arbitrary Lagrangian Eulerian method; ALE; finite element method; fluid-structure interaction; FSI; goal-oriented mesh adaption

PL

dynamika zastawki serca; fale elastyczne; metoda arbitrary Lagrangian-Eulerian; ALE; metoda elementów skończonych; oddziaływanie płyn-struktura; FSI; zorientowana na cel adaptacja siatki

• Wydawca: Komitet Budowy Maszyn PAN
• Czasopismo: Archive of Mechanical Engineering
• Rocznik: 2012
• Tom: Vol. LIX, nr 1
• Strony: 73--99
• Opis fizyczny: Bibliogr. 45 poz., rys., tab.

Twórcy

autor

Wick T.

• Institute of Applied Mathematics, University of Heidelberg, INF 293/294, 69120 Heidelberg, Germany,

Bibliografia

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