A Second-Order Time-Stepping Scheme for Simulating Ensembles of Parameterized Flow Problems
We consider settings for which one needs to perform multiple flow simulations based on the Navier-Stokes equations, each having different initial condition data, boundary condition data, forcing functions, and/or coefficients such as the viscosity. For such settings, we propose a second-order time accurate ensemble-based method that to simulate the whole set of solutions, requires, at each time step, the solution of only a single linear system with multiple right-hand-side vectors. Rigorous analyses are given proving the conditional stability and establishing error estimates for the proposed algorithm. Numerical experiments are provided that illustrate the analyses.
M. Gunzburger et al., "A Second-Order Time-Stepping Scheme for Simulating Ensembles of Parameterized Flow Problems," Computational Methods in Applied Mathematics, vol. 19, no. 3, Walter de Gruyter GmbH, Jul 2019.
The definitive version is available at https://doi.org/10.1515/cmam-2017-0051
Mathematics and Statistics
Keywords and Phrases
Linear systems; Viscous flow; Conditional stability; Ensemble methods; Ensemble-based method; Initial conditions; Multiple right-hand sides; Numerical experiments; Parameterized; Time-stepping schemes; Navier Stokes equations; Navier-Stokes Equations; Parameterized Flow
International Standard Serial Number (ISSN)
Article - Journal
© 2017 Walter de Gruyter GmbH, All rights reserved.
01 Jul 2019
This research was partially supported by the U.S. Department of Energy under grants DE-SC0009324 and DE-SC0016540, the U.S. Air Force Office of Scientific Research grant FA9550-15-1-0001, a Defense Advanced Projects Agency contract administered under the Oak Ridge National Laboratory subcontract 4000145366, the U.S. National Science Foundation grants DMS-1522672 and DMS-1720001, and a University of Missouri Research Board grant.