Gradient-robustness in optimization subject to stationary Navier-Stokes equations
This work addresses numerical stability issues in fluid dynamics simulations and control, but it appears incremental as it focuses on comparing existing formulations rather than introducing a new method.
The paper tackles the problem of gradient-robust discretizations for simulating and optimally controlling incompressible Navier-Stokes flows, comparing different formulations and their impact on adjoint equations for gradient computation.
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.