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    Item type:Publication, Access status: with files ,
    Parameter-free shape optimization: Various shape updates for engineering applications
    (Multidisciplinary Digital Publishing Institute (MDPI), 2023-08-25)
    Radtke, Lars
    ;
    Bletsos, Georgios
    ;
    Kühl, Niklas
    ;
    Suchan, Tim
    ;
    Rung, Thomas
    In the last decade, parameter-free approaches to shape optimization problems have matured to a state where they provide a versatile tool for complex engineering applications. However, sensitivity distributions obtained from shape derivatives in this context cannot be directly used as a shape update in gradient-based optimization strategies. Instead, an auxiliary problem has to be solved to obtain a gradient from the sensitivity. While several choices for these auxiliary problems were investigated mathematically, the complexity of the concepts behind their derivation has often prevented their application in engineering. This work aims to explain several approaches to compute shape updates from an engineering perspective. We introduce the corresponding auxiliary problems in a formal way and compare the choices by means of numerical examples. To this end, a test case and exemplary applications from computational fluid dynamics are considered.
    Publicationtype: Journal Article
    Scopus© Citations 2  61  179
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    Item type:Publication, Access status: with files ,
    Adjoint shape sensitivities of blood flows considering non-newtonian properties
    (Wiley, 2023-01-13)
    Bletsos, Georgios
    ;
    Kühl, Niklas
    ;
    Rung, Thomas
    This article discusses the derivation and numerical implementation of an adjoint system, to the primal Navier–Stokes equations, for the computation of shape sensitivities of ducted blood flows considering non-Newtonian fluid properties. The ever-growing advancements in blood flow simulations are, naturally, accompanied by an increased interest in the optimization of related medical devices. In the majority of the computational studies, the Newtonian assumption is used to describe the rheology of blood. While this assumption has been shown to satisfactorily capture the flow when it is governed by high shear rates, it falls short at low shear rates. A rich variety of viscosity models has been proposed to tackle this shortcoming. In this article we show how such models can be incorporated into an adjoint system targeting to produce the shape sensitivity which can be used by a gradient-based optimization method for the minimization of an objective functional. A general formulation of the adjoint equations is proposed, in which contributions of the non-Newtonian properties explicitly occur. The numerical implementation is discussed and the validity of the method is assessed by means of numerical experiments of steady blood flows in a 2D stenosed duct, where results are compared against second-order finite-difference (FD) studies. The proposed methodology is then applied to CAD-free, gradient-based shape optimizations of an idealized 3D arterial bypass-graft operating at three relevant Reynolds numbers. It is observed that the impact of the adjoint viscosity treatment is amplified in low shear-rate flow regimes while fades for higher shear-rates, analogous to its primal counterpart.
    Publicationtype: Journal Article
    Scopus© Citations 1  46  197