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.

在流固耦合问题中，许多人使用惩罚方法将结构定位在流体内部。通常通过考虑在该结构所占据的位置处流体非常硬或/和非常重来执行此操作。这些方法从编程的角度来看非常方便，但是会导致条件不佳的运算符。这是数值求解方法中的一个缺点。特别是，由于周围的流向结构施加的力并不总是准确地估计出来，因为惩罚参数-一个很大的数字-出现在它们的表达式中。我们建议在本文中对遇到的困难进行数学分析，并讨论D. Bertsekas的惩罚对偶方法如何成为克服这些困难的有趣替代方法。