Fluid structure interaction by means of reduced order models

The standard Fluid Structure Interaction coupling (velocity--pressure/displacement) is compared against two novel types of coupling, a Two Field coupling (velocity--pressure/displacement--pressure) and a Three Field coupling (velocity--pressure--stress/displacement--pressure--stress) in this way completing our set of, what we call, field to field equations, all stabilized by means of the VMS method using dynamic and orthogonal sub-scales. The solid Two field fluid structure interaction coupling formulation is benchmarked statically and dynamically. POD is applied to all three fluid structure interaction formulations to obtain reduced basis and asses their performance in a reduced space. Usual numerical benchmarks are shown comparing all three formulations. The three field fluid structure interaction coupling proves to provide very accurate results in both FOM and ROM spaces, making it a reliable formulation. Field to field pairing appears to be beneficial providing more accurate results in all cases shown. A reduced order model designed by means of a variational multi-scale method stabilized formulation has been applied successfully to fluid structure interaction problems in a strongly coupled partitioned solution scheme. Details of the formulation and the implementation both for the interaction problem and for the reduced models, for both the off-line and on-line phases, are shown. Results are obtained for cases in which both domains are reduced at the same time. Numerical results are presented for a semi-stationary and a fully transient case. El acople estandar para casos de Interacción Fluido Estructura (Velocidad-Presión/Desplazamiento) se compara contra dos nuevas formas de acople, el primero de Dos Campos (Velocidad-Presión/Desplazamiento-Presión) y el segundo de Tres Campos (Velocidad-Presión-Esfuerzo/Desplazamiento-Presión-Esfuerzo) de esta forma completando lo que se ha llamado acoplamiento de Campo a Campo, todo estabilizado por medio del método VMS usando sub-escalas dínamicas y ortogonales. Se hacen comprobaciones estáticas y dínamicas para las dos nuevas formulaciones de sólidos (Dos y Tres campos). Se utiliza POD para obtener una base reducida y verificar el comportamiento de dichas formulaciones en el espacio reducido. La formulacion de Tres Campos resulta ser la mas precisa produciendo los resultados mas exactos tanto para los espacios FOM y ROM. La formulacion de Campo a Campo resulta ser beneficiosa al producir los resultados mas exactos