ENH: Reduced-order modelling field reconstruction with DMD

Acknowledgement

OpenCFD would like to acknowledge and thank Marco Kiewat for his contributions, elaborate suggestions and help, and critical recommendations. Highly appreciated.

Problem

• OpenFOAM currently lacks one of the key advantages of DMD: 
  • the capability to generate a field based on given modes and their associated dynamics, without the need for any CFD computations at arbitrary intermediate and/or future time points.
• This functionality would allow users to condense an entire simulation into a few modes and mode dynamics, and subsequently generate fields at any desired time or predict their future states of periodic or pseudo-periodic systems, all without the need for additional CFD analyses.

Solution

Implement and verify the method proposed by Kiewat (2019) to generate time-variant field data from DMD data for a set of specified times.

Verification

Coarse mesh

coarse

Fine mesh

fine

Discussion

• The quality of results depends on the capabilities of the underlying reduced-order model, and the quality of the input data.
• To improve the reconstruction results, one needs to make sure that modes are correctly extracted from the flow.
  • The easiest method to check the quality:
    • Inspect the real part of the first mode visually.
    • Compare it with the time-mean of the operand decomposed field.
    • The real part of the first mode should always look like the time-mean of the operand decomposed field.
    • If both fields are dissimilar, expect low quality results from the createROMfields.

Risks

• No change in existing input/output.
• The tutorial $FOAM_TUTORIALS/incompressible/pimpleFoam/laminar/cylinder2D is run for a longer period.
  • Also, the parallel renumberMesh operation is removed from its existing Allrun script.

Metadata

• linux64ClangDPInt32Opt (clang15)
• linux64GccDPInt32Opt
• linux64GccSPDPInt64Debug
• Alltest: No new error/No change in existing output
• Test cases: $FOAM_TUTORIALS/incompressible/pimpleFoam/laminar/cylinder2D

applications/utilities/postProcessing/miscellaneous/createROMfields/Make/files

+ROMmodels/ROMmodel/ROMmodel.C
+ROMmodels/ROMmodel/ROMmodelNew.C
+ROMmodels/DMD/DMD.C
+
+createROMfields.C
+
+EXE = $(FOAM_APPBIN)/createROMfields