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An Evolve-Filter-Relax Stabilized Reduced Order Stochastic Collocation Method for the Time-Dependent Navier--Stokes Equations

Journal Article · · SIAM/ASA Journal on Uncertainty Quantification
DOI:https://doi.org/10.1137/18m1221618· OSTI ID:1896786
 [1];  [2];  [3];  [4]
  1. Florida State Univ., Tallahassee, FL (United States); OSTI
  2. Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
  3. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
  4. Univ. of Pittsburgh, PA (United States)
+ Show Author Affiliations

In this paper, we propose a filter-based stabilization of reduced order models (ROMs) for uncertainty quantification (UQ) of the time-dependent Navier--Stokes equations in convection-dominated regimes. Here we propose a novel high-order ROM differential filter and use it in conjunction with an evolve-filter-relax (EFR) algorithm to attenuate the numerical oscillations of standard ROMs. We also examine how stochastic collocation methods can be combined with the EFR algorithm for efficient UQ of fluid flows. We test the new framework in the numerical simulation of a two-dimensional flow past a circular cylinder with a random viscosity that yields a random Reynolds number with mean Re = 100.

Research Organization:
Florida State Univ., Tallahassee, FL (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); US Air Force Office of Scientific Research (AFOSR); National Science Foundation (NSF); Commonwealth Fusion Systems
Grant/Contract Number:
SC0009324
OSTI ID:
1896786
Journal Information:
SIAM/ASA Journal on Uncertainty Quantification, Journal Name: SIAM/ASA Journal on Uncertainty Quantification Journal Issue: 4 Vol. 7; ISSN 2166-2525
Publisher:
Society for Industrial and Applied Mathematics (SIAM)Copyright Statement
Country of Publication:
United States
Language:
English

References (42)

Filtering techniques for complex geometry fluid flows journal January 1999
Filtered POD-based low-dimensional modeling of the 3D turbulent flow behind a circular cylinder journal March 2011
Deconvolution‐based nonlinear filtering for incompressible flows at moderately large Reynolds numbers journal December 2015
An evolve-then-filter regularized reduced order model for convection-dominated flows: EVOLVE-THEN-FILTER REGULARIZED REDUCED ORDER MODEL journal February 2017
Physically constrained data‐driven correction for reduced‐order modeling of fluid flows journal October 2018
Supremizer stabilization of POD-Galerkin approximation of parametrized steady incompressible Navier-Stokes equations: SUPREMIZER STABILIZATION OF POD-GALERKIN APPROXIMATION OF NS EQUATIONS
  • Ballarin, Francesco; Manzoni, Andrea; Quarteroni, Alfio
  • International Journal for Numerical Methods in Engineering, Vol. 102, Issue 5 https://doi.org/10.1002/nme.4772
journal November 2014
Two Comments on Filtering (Artificial Viscosity) for Chebyshev and Legendre Spectral and Spectral Element Methods: Preserving Boundary Conditions and Interpretation of the Filter as a Diffusion journal June 1998
Comments on “Filter-Based Stabilization of Spectral Element Methods” journal November 2002
Comparison Between Reduced Basis and Stochastic Collocation Methods for Elliptic Problems journal August 2013
Filter-based stabilization of spectral element methods journal February 2001
α Regularization of the POD-Galerkin dynamical systems of the Kuramoto–Sivashinsky equation journal January 2012
Learning-based robust stabilization for reduced-order models of 2D and 3D Boussinesq equations journal September 2017
A dynamically adaptive sparse grids method for quasi-optimal interpolation of multidimensional functions journal June 2016
Long-term behavior of polynomial chaos in stochastic flow simulations journal August 2006
Approximate deconvolution reduced order modeling journal January 2017
Finite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier–Stokes equations journal September 2018
Sparse grid collocation schemes for stochastic natural convection problems journal July 2007
Enablers for robust POD models journal February 2009
Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier–Stokes equations journal September 2016
A stabilized POD model for turbulent flows over a range of Reynolds numbers: Optimal parameter sampling and constrained projection journal October 2018
Spectral analysis of nonlinear flows journal November 2009
Dynamic mode decomposition of numerical and experimental data journal July 2010
Stochastic finite element methods for partial differential equations with random input data journal May 2014
Numerical analysis of modular regularization methods for the BDF2 time discretization of the Navier-Stokes equations journal April 2014
An explicit filtering method for large eddy simulation of compressible flows journal August 2003
Differential filters for the large eddy numerical simulation of turbulent flows journal January 1986
Differential filters of elliptic type journal January 1986
A posteriori analysis of low-pass spatial filters for approximate deconvolution large eddy simulations of homogeneous incompressible flows journal December 2014
Filtering in Legendre spectral methods journal September 2008
Turbulence and the dynamics of coherent structures. I. Coherent structures journal January 1987
A Stochastic Collocation Method for Uncertainty Quantification and Propagation in Cardiovascular Simulations journal February 2011
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data journal January 2007
An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data journal January 2008
Nonlinear Model Reduction via Discrete Empirical Interpolation journal January 2010
Numerical Analysis of Filter-Based Stabilization for Evolution Equations journal January 2012
Error Analysis of a Stochastic Collocation Method for Parabolic Partial Differential Equations with Random Input Data journal January 2012
Reduced Basis Collocation Methods for Partial Differential Equations with Random Coefficients journal January 2013
pyMOR -- Generic Algorithms and Interfaces for Model Order Reduction journal January 2016
Stochastic Least-Squares Petrov--Galerkin Method for Parameterized Linear Systems journal January 2018
On a Certified Smagorinsky Reduced Basis Turbulence Model journal January 2017
Data-Driven Filtered Reduced Order Modeling of Fluid Flows journal January 2018
Stabilized Weighted Reduced Basis Methods for Parametrized Advection Dominated Problems with Random Inputs journal January 2018

Figures / Tables (17)

Fig. 5.1(p. 13)figure Fig. 5.1
Fig. 5.2(p. 15)figure Fig. 5.2
Fig. 5.3(p. 15)figure Fig. 5.3
Fig. 5.4(p. 15)figure Fig. 5.4
Fig. 5.5(p. 16)figure Fig. 5.5
Fig. 5.6(p. 17)figure Fig. 5.6
Fig. 5.7(p. 17)figure Fig. 5.7
Table 5.1(p. 17)table Table 5.1
Table 5.2(p. 18)table Table 5.2
Table 5.3(p. 18)table Table 5.3
Table 5.4(p. 18)table Table 5.4
Table 5.5(p. 18)table Table 5.5
Table 5.6(p. 19)table Table 5.6
Table 5.7(p. 19)table Table 5.7
Table 5.8(p. 19)table Table 5.8
Table 5.9(p. 19)table Table 5.9
Table 5.10(p. 20)table Table 5.10

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Related Subjects

97 MATHEMATICS AND COMPUTING
differential filter
reduced order model
stabilization method
stochastic collocation method