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 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.

Brachistochronous motion of a flat plate parallel to its surface immersed in a fluid

“…Accounts of how to find the adjoint and the gradients δL/δu, and descend along it, can be found elsewhere (e.g. He et al 1994;Mohammadi & Pironneau 2004;Pringle & Kerswell 2010;Pringle et al 2012;Passaggia & Ehrenstein 2013). Suppose that this process converges to u = u * , corresponding to α = α * and W = W * .…”

“…For example, animal body actuation for propulsion in a fluid medium seeks to minimize the energetic cost of aerial (Berman & Wang 2007;Pesavento & Wang 2009;Vincent, Liu & Kanso 2020) and aquatic (Pironneau & Katz 1974;Kern & Koumoutsakos 2006;Tam & Hosoi 2007;Michelin & Lauga 2010Tam & Hosoi 2011;Eloy & Lauga 2012;Alben, Miller & Peng 2013;Montenegro-Johnson & Lauga 2014;Maertens, Gao & Triantafyllou 2017) locomotion. Optimization is invoked in cardiovascular biomechanics (He et al 1994;Marsden 2014) and sports biomechanics such as rowing (Labbé et al 2019), where fluid dynamics is central to the mechanics. Optimization is also an important tool to study fundamental fluid dynamics.…”

Optimal design of paper machine headboxes

“…u =u in , on G in (12) u= u r , on G r (13) p= Dp(u n ), on G out (14) where Dp(u n ) denotes the pressure losses in the manifold tube bank, typically of the form Dp(u n )= cu n 2 , with c being a constant and u n the normal velocity component. For details, see References [1-3].…”

PEDS18: Automated CFD Shape Optimization of Stator Blades for the PediaFlow Pediatric VAD

“…Consequently, the end result is unlikely to be the truly optimal design. This imbroglio has motivated our group to incorporate automated shape optimization for VAD design, [6][7][8][9][10] inspired by the success of such methods in aerospace, automotive, and other industries. 11,12 CFD-driven optimization has been recently applied to design of several VADs with encouraging results.…”