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In fluid-structure interaction problems, some people use a penalty method forpositioning the structure inside the fluid. This is usually performed byconsidering that the fluid is very stiff or/and very heavy at the placeoccupied by the structure. These methods are very convenient for theprogramming point of view but lead to ill conditioned operators. This is adrawback in the numerical solution methods. In particular the forces applied tothe structure by the surrounding flow are not accurately estimated because thepenalty parameter -- which is a very large number -- appears in theirexpressions. We suggest in this paper a mathematical analysis of thedifficulties encountered and we discuss how the penalty-duality method of D.Bertsekas can be an interesting alternative to overcome them.

About penalty-duality methods in fluid-structure interactions