Low order dynamical system for fluid-rigid body interaction problem using POD method

This paper describes the Reduced Order Modeling (ROM) for fluid rigid body interaction problem and discusses Proper Orthogonal Decomposition (POD) utilisation. The principal difficulty for using POD being the moving domains, a referenced fixed domain is introduced. The POD is applied for the velocity field obtained on the fixed domain. Then a method to reduce dynamical system in rigid body fluid interaction is developed. This method uses the fictitious domain method approach, which consists in treating the entire fluid-solid domain as a fluid. The rigid body is considered as a fluid, by using a high viscosity which can play the role of a penalisation factor of the rigidity constraint, and by adding a distributed Lagrange multiplied associated to this constraint in the weak formulation. The fluid flow problem is then formulated on the reference domain and POD modes are used in the weak formulation. The results are compared with computational solution and discussed.