A few remarks on penalty and penalty-duality methods in fluid-structure interactions

Philippe Destuynder (1) , Erwan Liberge (1)

1 LaSIE - Laboratoire des Sciences de l'Ingénieur pour l'Environnement - UMR 7356

In fluid-structure interaction problems, many people use a penalty method for positioning the structure inside the fluid. This is usually performed by considering that the fluid is very stiff or/and very heavy at the place occupied by the structure. These methods are very convenient for the programming point of view but can lead to ill conditioned operators. This is a drawback in the numerical solution methods. In particular the forces applied to the structure by the surrounding flow are not always accurately estimated because the penalty parameter-which is a very large number-appears in their expressions. We suggest in this paper a mathematical analysis of the difficulties encountered and we discuss how the penalty-duality method of D. Bertsekas can be an interesting alternative to overcome them.

Domaines: Equations aux dérivées partielles [math.AP]

Philippe Destuynder, Erwan Liberge. A few remarks on penalty and penalty-duality methods in fluid-structure interactions. Applied Numerical Mathematics, 2021, 167, pp.1 - 30. ⟨10.1016/j.apnum.2021.04.017⟩. ⟨hal-03320890⟩