The one-shot method for a pressure correction Navier-Stokes solver: an example where optimisation can be faster than simulation (Q391688)

Summary: 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.