Reduced order modeling techniques for mesh movement as applied to fluid structure interactions

Abstract

In this thesis, the method of Proper Orthogonal Decomposition (POD) is implemented to construct approximate, reduced order models (ROM) of mesh movement methods. Three mesh movement algorithms are implemented and comparatively evaluated, namely radial basis function interpolation, mesh optimization and elastic deformation. POD models of the mesh movement algorithms are constructed using a series of system observations, or snapshots of a given mesh for a set of boundary deformations. The scalar expansion coefficients for the POD basis modes are computed in three different ways, through coefficient optimization, Galerkin projection of the governing set of equations and coefficient interpolation. It is found that using only coefficient interpolation yields mesh movement models that accurately approximates the full order mesh movement, with CPU cost savings in excess of 99%. We further introduce a novel training procedure whereby the POD models are generated in a fully automated fashion. The technology is applicable to any mesh movement method and enables potential reductions of up to four orders of magnitude in mesh movement related costs. The proposed model can be implemented without having to pre-train the POD model, to any fluid-structure interaction code with an existing mesh movement scheme. Copyright