A higher-order ensemble/proper orthogonal decomposition method for the nonstationary Navier-Stokes equations
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Publication:5374417
zbMATH Open1402.35207arXiv1709.06422MaRDI QIDQ5374417
Author name not available (Why is that?)
Publication date: 14 September 2018
Abstract: Partial differential equations (PDE) often involve parameters, such as viscosity or density. An analysis of the PDE may involve considering a large range of parameter values, as occurs in uncertainty quantification, control and optimization, inference, and several statistical techniques. The solution for even a single case may be quite expensive; whereas parallel computing may be applied, this reduces the total elapsed time but not the total computational effort. In the case of flows governed by the Navier-Stokes equations, a method has been devised for computing an ensemble of solutions. Recently, a reduced-order model derived from a proper orthogonal decomposition (POD) approach was incorporated into a first-order accurate in time version of the ensemble algorithm. In this work, we expand on that work by incorporating the POD reduced order model into a second-order accurate ensemble algorithm. Stability and convergence results for this method are updated to account for the POD/ROM approach. Numerical experiments illustrate the accuracy and efficiency of the new approach.
Full work available at URL: https://arxiv.org/abs/1709.06422
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