Reduced order modeling for high-speed flows with moving shocks

The use of proper orthogonal decomposition for reduced order modeling of fluid problems is extended to high-speed compressible fluid flows. The challenge in using reduced order modeling for high-speed flows is presented by the presence of moving discontinuities in the flow field. To overcome these difficulties, a domain decomposition approach is developed that isolates the region containing the moving shock wave for special treatment. The domain decomposition approach is applied to a transonic aeroelastic problem that involves large motions of a normal shock. Two dimensional inviscid flow over an elastic panel produces transonic limit cycle oscillations under certain panel parameters and free stream conditions. Panel flutter in the transonic regime results in the large motion of a transonic normal shock across the panel surface. Previously, no reduced order modeling method has been successfully applied to this problem. Reduced order models with as large as three orders of magnitude reduction in degrees of freedom produce flow fields with maximum errors below 5 percent. One order of magnitude in computational savings for the non-Galerkin solver implementations accompanies this reduction in degrees of freedom. Finally, the robustness of the reduced order model across a wide parameter space is demonstrated.