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arXiv · 1709.06422

A higher-order ensemble/proper orthogonal decomposition method for the nonstationary Navier-Stokes equations

Max Gunzburger·Nan Jiang·Michael Schneier
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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.

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Max Gunzburger, Nan Jiang, Michael Schneier. 2017-09-16. A higher-order ensemble/proper orthogonal decomposition method for the nonstationary Navier-Stokes equations. https://arxiv.org/abs/1709.06422

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