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

Constanze Neutsch, Winnifried Wollner

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.

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

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.
Paper Structure (4 sections, 24 equations, 1 figure, 2 tables)

This paper contains 4 sections, 24 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Navier-Stokes equation
  3. Discretization
  4. Numerical studies

Figures (1)

  • Figure 1: Magnitude and flow field of $\mathbf{z}_h$ for three different viscosities, considering the non-robust (top row) and robust modification (bottom row) of the convective scheme.