Practical Aspects of the Implementation of Reduced-Order Models Based on Proper Orthogonal Decomposition
Brenner, Thomas Andrew
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This work presents a number of the practical aspects of developing reduced- order models (ROMs) based on proper orthogonal decomposition (POD). ROMS are derived and implemented for multiphase ?ow, quasi-2D nozzle ?ow and 2D inviscid channel ?ow. Results are presented verifying the ROMs against existing full-order models (FOM). POD is a method for separating snapshots of a ?ow ?eld that varies in both time and space into spatial basis functions and time coe?cients. The partial di?erential equations that govern ?uid ?ow can then be pro jected onto these basis functions, generating a system of ordinary di?erential equations where the unknowns are the time coe?cients. This results in the reduction of the number of equations to be solved from hundreds of thousands or more to hundreds or less. A ROM is implemented for three-dimensional and non-isothermal multiphase ?ows. The derivation of the ROM is presented. Results are compared against the FOM and show that the ROM agrees with the FOM. While implementing the ROM for multiphase ?ow, moving discontinuities were found to be a ma jor challenge when they appeared in the void fraction around gas bubbles. A point-mode POD approach is proposed and shown to have promise. A simple test case for moving discontinuities, the ?rst order wave equation, is used to test an augmentation method for capturing the discontinuity exactly. This approach is shown to remove the unphysical oscillations that appear around the discontinuityin traditional approaches. A ROM for quasi-2D inviscid nozzle ?ow is constructed and the results are com- pared to a FOM. This ROM is used to test two approaches, POD-Analytical and POD-Discretized. The stability of each approach is assessed and the results are used in the implementation of a ROM for the Navier-Stokes equations. A ROM for a Navier-Stokes solver is derived and implemented using the results of the nozzle ?ow case. Results are compared to the FOM for channel ?ow with a bump. The computational speed-up of the ROM is discussed. Two studies are presented with practical aspects of the implementation of POD- based ROMs. The ?rst shows the e?ect of the snapshot sampling on the accuracy of the POD basis functions. The second shows that for multiphase ?ow, the cross- coupling between ?eld variables should not be included when computing the POD basis functions.