About penalty-duality methods in fluid-structure interactions

TL;DR

This paper analyzes penalty methods in fluid-structure interactions, highlighting numerical issues and proposing the penalty-duality method as a promising alternative to improve accuracy and conditioning.

Contribution

It provides a mathematical analysis of penalty methods and introduces the penalty-duality approach as a novel solution for fluid-structure interaction problems.

Findings

Penalty methods lead to ill-conditioned operators.

Penalty-duality methods improve numerical stability.

Enhanced accuracy in force estimation on structures.

Abstract

In fluid-structure interaction problems, some 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 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 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.