The one-shot method for a pressure correction Navier-Stokes solver: an example where optimisation can be faster than simulation
by Johannes Rückelt; Günter Bärwolff; Thomas Slawig
International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO), Vol. 4, No. 2, 2013

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.

Online publication date: Sat, 26-Jul-2014

The full text of this article is only available to individual subscribers or to users at subscribing institutions.

 
Existing subscribers:
Go to Inderscience Online Journals to access the Full Text of this article.

Pay per view:
If you are not a subscriber and you just want to read the full contents of this article, buy online access here.

Complimentary Subscribers, Editors or Members of the Editorial Board of the International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO):
Login with your Inderscience username and password:

Username:        Password:          Forgotten your password?

Want to subscribe?
A subscription gives you complete access to all articles in the current issue, as well as to all articles in the previous three years (where applicable). See our Orders page to subscribe.

If you still need assistance, please email subs@inderscience.com