Abstract
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.
Highlights
Classical problems in fluid structure interaction (FSI) require a long computational time
On a fixed domain, the Navier Stokes equations are projected on the Proper Orthogonal Decomposition (POD) vectors, and thanks to the orthonormality of POD modes, a low order dynamical system whose size is equal to the number of POD vector selected is obtained
This paper introduces an application method of the proper orthogonal decomposition for moving boundary problems, in the case of fluid rigid body interaction problem
Summary
Classical problems in fluid structure interaction (FSI) require a long computational time. In case of a very high-dimensional system, extracting eigenmodes can be computationally very expensive We use another method such as the method of balanced modes [3] or Proper Orthogonal Decomposition (POD) which will be. The second technique to determine ROM is the input/output model This method uses a transfer function, that typically receives input in structure modes and gives as output generalised forces weighted by structural modes [4]. We have chosen to study POD capacities in fluid structure interaction This method was introduced in 1967 by Lumley [5] in fluid mechanics in order to extract coherent structures in a turbulent fluid flow. A low order dynamical system in case of fluid-rigid body interaction problem is proposed and tested on differents cases
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