Non-intrusive reduced order models and their applications

Reduced order models (ROMs) have become prevalent in many fields of physics as they offer the potential to simulate dynamical systems with substantially increased computation efficiency in comparison to standard techniques. Among the model reduction techniques, the proper orthogonal decomposition (POD) method has proven to be an efficient means of deriving a reduced basis for high-dimensional flow systems. The intrusive ROM (IROM) is normally derived by the POD and Galerkin projection methods. The IROM is appealing for non-linear and linear model reductions and has been successfully applied to numerous research fields. However, IROMs suffer from instability and non-linearity efficiency issues. In addition, they can be complex to code because they are intrusive. In most cases the source code describing the physical system has to be modified in order to generate the reduced order model. These modifications can be complex, especially in legacy codes, or may not be possible if the source code is not available (e.g. in some commercial software). To circumvent these shortcomings, non-intrusive approaches have been introduced into ROMs. The Non-Intrusive ROM (NIROM) is independent of the original physical system. The key contribution of this thesis are: Firstly, three novel NIROMs have been presented in this thesis: POD/Taylor series, POD-Smolyak and POD-RBF (radial basis function). Secondly, two NIROMs with varying material properties have been presented. Thirdly, these newly developed NIROMs were implemented and tested under the framework of an unstructured mesh finite element model (FLUIDITY) and a combined finite-discrete element method based solid model (Y2D). Fourthly, these NIROMs have been used to construct ROMs for multi-scale 3-D free surface flows, multi-phase porous media flows, fluid-structure interaction and blasting problems.Open Acces