POD-based reduced order model for flows induced by rigid bodies in forced rotation

Abstract

This paper deals with the construction of reduced order models (ROMs) for the simulation of the interaction between a fluid and a rigid body with imposed rotation velocity. The approach is a follows. First, we derive a monolithic description of the fluid–structure interaction by extending the Navier–Stokes equations from the fluid domain to the solid domain (rotor) similarly to the fictitious-domain approach. Second, we build a ROM by a proper orthogonal decomposition (POD) of the resulting multi-phase flow. This method consists in (i) constructing an optimal albeit empirical spatial basis for a very small subspace of the solution space, and (ii) projecting the governing equations on this reduced basis. Third, we cope with the reconstruction of the high-dimensional velocity field needed to evaluate the imposed velocity constraint by a POD of the rigid body membership function. This provides a substantial computation time saving compared to existing approaches. Fourth, we use a novel approach to interpolate between available POD bases to build the proposed POD-ROM for a range of parameters values. The complete procedure is applied to a simple configuration and proves efficient in the reconstruction of the velocity in both the fluid domain and the solid domain, while substantially reducing the computational cost.