Shape optimization of Navier-Stokes flows with application to optimal design of artificial heart components

Abstract: "We consider the problem of shape optimization of systems governed by the stationary incompressible Navier-Stokes equations under flow and geometric constraints. Our motivation stems from the problem of optimal design of artificial heart components. An [sic] continuation-SQP algorithm is developed to efficiently couple Newton-based optimization and flow solution. The main feature of the algorithm is to decompose the optimization problem into a sequence of subproblems characterized by increasing Reynolds numbers, and then apply continuation schemes on the design field, Hessian matrix, Lagrange multipliers, and flowfield. As an application we consider the optimum design of the shape of a two dimensional tube -- a simplification of a blood flow cannula that is a component of an artificial heart. Representative numerical results show a factor of four improvement in efficiency over a standard SQP algorithm."