SHAPE SENSITIVITY ANALYSIS FOR STABILIZED NAVIER-STOKES EQUATIONS

Abstract eng:
The paper contributes to solving optimal flow 3D problems in the context of laminar incompressible flows of Newtonian fluid in rigid ducts. A stabilization of the finite element solution is required in case of problems of low viscosity (air) flows. Analytical sensitivity formulae for extra terms originating from the stabilization of the finite element discretized Navier-Stokes equations are presented, since the analysis of flow sensitivity to shape changes of a fluid domain has a crucial influence on efficiency of a shape optimization algorithm. Preliminary numerical examples are shown, employing our theoretical results within a steepest descent optimization algorithm.

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