2 NASA Langley Research Center 3 University of Southern California SciTech 2023 Jan 25 2023 Quantifying Emergent Fluid Dynamics Using ReynoldsInterpolated Fluid ReducedOrder Models Chris Edwards ID: 1044591
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1. 1North Carolina State University, 2NASA Langley Research Center, 3University of Southern CaliforniaSciTech 2023Jan. 25, 2023Quantifying Emergent Fluid Dynamics Using Reynolds-Interpolated Fluid Reduced-Order ModelsChris Edwards1, Michael W. Lee2, Donya Ramezanian3, Ralph C. Smith1
2. OverviewMotivationGeneral approachDerivation and comparison of methodsSpanning Reduced-order ModelBasis ConcatenationBasis InterpolationConclusion2
3. MotivationPlanetary entry, descent, and landingUncertainty Quantification (UQ):Bayesian Markov Chain Monte Carlo techniquesRequires numerous model evaluations O(104)High-Fidelity computational fluid dynamics (CFD) simulations are computationally expensive –> Reduced-order Models (ROMs)Parametric ROMs:Goal: Accurately simulate fluid physics at parameter points not included in the reference data3
4. Collect high-fidelity data at few parameter points (Reynolds no.)Extract coherent structures (POD)Use reduced-order model to predict flow physics at any intermediate parameter pointGeneral Approach4
5. Incompressible ROM Formulation5Consider the incompressible conservation equations:Linearly decompose the velocity field:
6. Incompressible ROM Formulation6Assume satisfies the boundary conditionsGalerkin projection yields (matrices defined in paper):Pressure term vanishes where Matrices are not Reynolds-dependentOrthonormal modes make the identity matrix
7. Methodology: Spanning ROM7Form collection of snapshotsUse ROM to predict flow physicsat any intermediate parameter pointHigh-fidelity Data: Snapshots from different parameter points (Reynolds no.)Extract coherent structures (POD)…Construct Reduced-Order Model (ROM)
8. Snapshots from Re = [15k | 16k | 17k | 18k]ROMs at Re = [15.5k | 16.5k | 17.5k]Bifurcation at Re=15.5k is well capturedResults: Spanning ROM8First iterations, Re = 15.5kFinal iterations, Re = 15.5k
9. Results: Spanning ROM9Snapshot Re = [15k | 16k | 17k | 18k]Snapshot Re = [15k | 16.5k | 18k]ROM Solution is stable with high snapshot parameter resolutionFirst iterations, Re = 16.5kFinal iterations, Re = 16.5kFirst iterations, Re = 16kFinal iterations, Re = 16k
10. Methodology: Basis Concatenation10Extract coherent structures (POD)High-fidelity Data: Snapshots from different parameter points (Reynolds no.)Concatenate POD basesConstruct Reduced-Order Model (ROM)…Use ROM to predict flow physicsat any intermediate parameter point
11. Snapshots from Re = [15k | 16k | 17k | 18k]ROMs at Re = [15.5k | 16.5k | 17.5k]Bifurcation at Re=15.5k is well capturedResults: Basis Concatenation11First iterations, Re = 15.5kFinal iterations, Re = 15.5k
12. Results: Basis Concatenation12Snapshot Re = [15k | 16k | 17k | 18k]Snapshot Re = [15k | 16.5k | 18k]Less accurate than Spanning ROMFirst iterations, Re = 16.5kFinal iterations, Re = 16.5kFirst iterations, Re = 16kFinal iterations, Re = 16k
13. Methodology: Basis Interpolation13Interpolate Bases…Use ROM to predict flow physicsat any intermediate parameter pointConstruct Reduced-Order Model (ROM)Univariate InterpolationMultivariate InterpolationHigh-fidelity Data: Snapshots from different parameter points (Reynolds no.)Extract coherent structures (POD)
14. Results: Basis Interpolation14General Basis interpolation more stableGeneral Interp. Re = [16k | 17.5k] Univariate Interp. [16.5k | 17.5k]First iterations, Re = 17kFinal iterations, Re = 17kFirst iterations, Re = 17kFinal iterations, Re = 17k
15. Results: Basis Interpolation152 Univariate Interpolation ROMsDifferent target ReSame Re separationROM performance decreases as disparity in relative size of bases increases[15.5k | 17.5k] Univar. Basis Interp., Re = 16.5k[16.5k | 18.5k] Univar. Basis Interp., Re = 17.5k
16. Comparison of Methods16Spanning ROMBasis Concat.Univar. Basis Interp.Gen. Basis Interp.stabilityneeds high resolutionneeds high resolutionunpredictableneeds high resolutionmode creation costhighmidmidmidsmall basisyesnoyesyeshandles implicit parametersnonoyesyesOverall Performancebestgoodunpredictablegood
17. ConclusionWe can inexpensively and accurately simulate flow physics at intermediate Reynolds numbers using only high-fidelity data from other Reynolds numbersBifurcations can be captured with high snapshot resolution near critical pointChanges in dominant frequencies can be capturedWill next extend to multiple parameters:Computational concerns will limit the effectiveness of Spanning and Basis Concatenation ROM techniques for moderate and large sized basesGeneral Basis Interpolation naturally extends with multivariate interpolation17