Reduced Order Modeling For High Speed Flows with Moving Shocks

Abstract : The use of Proper Orthogonal Decomposition (POD) for reduced order modeling (ROM) of fluid problems is extended to high-speed compressible fluid flows. The challenge in using POD for high-speed flows is presented by the presence of moving discontinuities in the flow field. To ovecome these difficulties, a domain decomposition approach is developed that isolates the region containing the moving shock wave for special treatment. The domain decomposition implementtion produces internal boundaries between the various domain sections. The domains are linked using optimization-based solvers which employ constraints to ensure smoothness in overlapping portions of the internal boundary. This approach is applied to three problems with increasing difficulty. The accuracy and order reduction of the domain decomposition POD/ROM approach is quantified for each application. ROMs with as large as three orders of magnitude reduction in degrees of freedom (DOFs) produce flow fields with maximum errors below 5%. One order of magnitude in computational savings for the non-Galerkin solver implementations accompanies this reduction in DOFs. Finally, the robustness of the reduced order models across a wide parameter space is demonstrated.

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