Gradient-robustness in optimization subject to stationary Navier-Stokes equations

TL;DR

This paper investigates gradient-robust discretizations for simulating incompressible Navier-Stokes flows and their impact on optimal control, comparing different formulations and their effects on gradient computation.

Contribution

It introduces and compares various gradient-robust discretizations for Navier-Stokes equations and analyzes their influence on adjoint equations in optimal control.

Findings

Different formulations affect the gradient robustness of discretizations.

Gradient-robust discretizations improve the accuracy of adjoint-based gradient computations.

Comparison results guide the choice of formulations for better control optimization.

Abstract

In this article, we discuss gradient robust discretizations for the simulation of non-linear incompressible Navier-Stokes problem and the optimal control of such flow. We consider several formulations of the flow problem that are equivalent for the continuous non-linear forward problem and compare their gradient robust discretization. We will then discuss the influence of the chosen formulation on the adjoint equations needed for gradient computation in the solution of the optimal control problem.