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A Leray regularized ensemble-proper orthogonal decomposition method for parameterized convection-dominated flows

Journal Article · · IMA Journal of Numerical Analysis
 [1];  [2];  [3]
  1. Department of Scientific Computing, Florida State University, Tallahassee, FL, USA; OSTI
  2. Department of Mathematics, Virginia Tech, Blacksburg, VA, USA
  3. Department of Scientific Computing, Florida State University, Tallahassee, FL, USA
+ Show Author Affiliations
Abstract

Partial differential equations (PDEs) are often dependent on input quantities that are uncertain. To quantify this uncertainty PDEs must be solved over a large ensemble of parameters. Even for a single realization this can be a computationally intensive process. In the case of flows governed by the Navier–Stokes equations, an efficient method has been devised for computing an ensemble of solutions. To further reduce the computational cost of this method, an ensemble-proper orthogonal decomposition (POD) method was recently proposed. The main contribution of this work is the introduction of POD spatial filtering for ensemble-POD methods. The POD spatial filter makes possible the construction of the Leray ensemble-POD model, which is a regularized-reduced order model for the numerical simulation of convection-dominated flows of moderate Reynolds number. The Leray ensemble-POD model employs the POD spatial filter to smooth (regularize) the convection term in the Navier–Stokes equations, and diminishes the numerical inaccuracies produced by the ensemble-POD method in the numerical simulation of convection-dominated flows. Specifically, for the numerical simulation of a convection-dominated two-dimensional flow between two offset cylinders, we show that the Leray ensemble-POD method better reflects the dynamics of the benchmark results than the ensemble-POD scheme. The second contribution of this work is a new numerical discretization of the variable viscosity ensemble algorithm in which the average viscosity is replaced with the maximum viscosity. It is shown that this new numerical discretization is significantly more stable than those in current use. Furthermore, error estimates for the novel Leray ensemble-POD algorithm with this new numerical discretization are also proven.

Research Organization:
Florida State Univ., Tallahassee, FL (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
DOE Contract Number:
SC0009324
OSTI ID:
1801902
Journal Information:
IMA Journal of Numerical Analysis, Journal Name: IMA Journal of Numerical Analysis Journal Issue: 2 Vol. 40; ISSN 0272-4979
Publisher:
Oxford University Press/Institute of Mathematics and its Applications
Country of Publication:
United States
Language:
English

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Related Subjects

Mathematics