The development and use of Reduced Order Models (ROMs) has attracted lots of attention among the engineering and scientific community in the past decades. Indeed, these models are able to significantly reduce the original complexity of a system, without severely affecting the accuracy. A crucial point to consider when elaborating Reduced Order Models (ROMs) for unsteady (e.g. transient) nonlinear problems in fluid dynamics is the definition of a proper set of dominant features, alias modes or basis functions, that can project the fluid system behaviour in a low-dimensional space without losing essential dynamics. To ensure that this is the case, a quantitative assessment is often necessary to define how well the low-dimensional space is approximating the underlying dynamics. For transient nonlinear flows, elaborating such a ROM, equipped with an efficient and reliable measure of its accuracy, can be a rather challenging task. To address these aspects, the present work reports a heuristic study of ROM performance, targeted for transient nonlinear fluid flows, when using different low-dimensional spaces, that are defined using different algorithms for the extraction of dominant features and different sorting of dominant features within each algorithm. An analysis is also performed to assess quantitatively such ROMs. In particular, the reliability of an error measure is investigated, namely the residual error, based on a specific discretisation of the initial set of equations of the fluid system, as opposed to an error measure that requires the computation of high-fidelity reference solution to obtain information about the accuracy of the ROM. The results of these analyses have shown that different linear low-dimensional spaces, identified by a specific set of global basis functions, are able to solve for different dynamic features with a good degree of accuracy. Moreover the residual error has demonstrated to be a reliable means to assess the relative performance of the various ROMs considered. As a consequence, a Model-Based Adaptive ROM Framework has been introduced. The novel framework combines the strengths of several linear ROMs in a unique monolithic structure by selecting the best low-dimensional space, among a collection of available ones, based on the specific time window where the low-dimensional reconstruction is needed. The term Model-Based refers to the residual error that is used to drive the selection of the basis. The performance of the Model-Based Adaptive ROM has been finally assessed on a set of test-cases relevant for the aeronautical field, that exhibit transient nonlinear dynamics with advection-diffusion and interaction of flow structures. Namely, a multielement airfoil, also in a 3D wing-body configuration, an isolated delta wing and three delta wing geometries in a formation flight configuration have been considered. The Adaptive ROM has shown promising capabilities in promoting strong dimensionality reduction (degrees of freedom less than 10-15, compared to the¬ 106 - 108 degrees of freedom (DOFs) of a common three dimensional CFD problem), while preserving good accuracy and physical consistency. Such a reduction in terms of DOFs will have a substantial impact on the reduction in computational cost to achieve any low-dimensional solution within the time window where the ROM has been trained. It is worth noting that, being the method data driven, the overall advantage in terms of computational cost has to be filtered with the upfront cost of generating the training dataset. The Adaptive ROM has demonstrated to be able to solve more details in terms of ow structures present in the field, which can be of advantage when design and/or flow control problems are addressed.
|Date of Award||1 Jun 2021|
- University Of Strathclyde
|Sponsors||University of Strathclyde|
|Supervisor||Marco Fossati (Supervisor) & Gabriel Barrenechea (Supervisor)|