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.

Keywords

• hybridized discontinuous galerkin method
• non-newtonian fluid (oldroyd-b model)
• shape optimization problem
• snapshot pod
• two-dimensional cavity flow