Topological sensitivity analysis of a time-dependent nonlinear problem

Abstract

Abstract We are interested in the optimization of the pipe shape allowing minimization of the dissipated energy in time-dependent Navier–Stokes Darcy flow. The used technique is based on the topological gradient method. In the theoretical part, we present an analysis of the topological sensitivity for the dissipated energy function. Some numerical tests are presented to illustrate the developed approach.

Keywords

• Shape optimization
• Topological sensitivity
• Calculus of variations
• Time-dependent Navier–Stokes equation
• Darcy equation