The one-shot method for a pressure correction Navier-Stokes solver: An example where optimization can be faster than simulation

Rückelt, Johanesn, Bärwolff, Günter and Slawig, Thomas (2013) The one-shot method for a pressure correction Navier-Stokes solver: An example where optimization can be faster than simulation International Journal of Mathematical Modelling and Numerical Optimisation, 4 (2). pp. 114-135. DOI 10.1504/IJMMNO.2013.055201.

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Abstract

We show an exemplary optimisation problem for a fluid flow where a numerical optimisation run can be as fast as and even faster than a pure simulation. In this example, the optimisation parameter is the upper boundary value in a two-dimensional driven cavity flow, mathematically described by the stationary incompressible Navier-Stokes equations. The stationary solution of the equations is computed by pseudo-time stepping, i.e., by running a transient solver into a steady state, using additional inner pressure correction steps. We compare optimisation methods of Newton and quasi-Newton type that use the fully converged state and derivative with an alternating algorithm that performs a parameter update already after a few steps of the state and derivative iterations. All derivatives are computed via automatic differentiation. The alternating algorithm is able to produce the mentioned fast optimisation results. A second example configuration shows that this phenomenon is problem-dependent and cannot be generalised.

Document Type: Article
Keywords: automatic differentiation; one-shot optimisation; fixed point solver; pressure-correction solver; Navier-Stokes equations; fluid flow
Research affiliation: OceanRep > The Future Ocean - Cluster of Excellence
Kiel University
Refereed: Yes
DOI etc.: 10.1504/IJMMNO.2013.055201
ISSN: 2040-3607
Date Deposited: 11 Sep 2019 13:40
Last Modified: 11 Sep 2019 13:40
URI: http://eprints.uni-kiel.de/id/eprint/47704

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