Shape optimization problem for transient Non-Newtonian fluid in hybridized discontinuous Galerkin method

Abstract

This paper presents a shape optimazation method for transient Non-Newtonian fluid which is playing important roles of calculating blood flow, oil flow and so on. So far, the author constructed a shape optimization problem for suppressing transient Newtonian fluid by using Snapshot POD, and extends it toward to Non-Newtonian fluid, here. For such the suggested shape optimization, the eigenvalue in Snapshot POD is defined as a cost function, where the constraint functions are the Oldroyd-B model, and an eigenvalue equation of Snapshot POD. For numerical calculations, a two-dimensional cavity flow with a disk-shaped isolated body is adopted for an initial domain. To descritize the Oldroyd-B model spatially, Galerkin Method (GM) and Hybridized Discontinuous Galerkin Method (HDGM) are used to compare numerical accuracies. As a result, it is considered that HDGM is able to obtain better solutions than GM during numerical validations. Finally, eigenvalues of Snapshot POD are compared in the initial and optimal domains obtained by HDGM.