A 5D concept for space-time optimal control problems with application to simplified Carreau flow

TL;DR

This paper introduces a 5D finite element framework for optimizing non-Newtonian Carreau fluid flows, combining space-time discretization with an innovative approach to solving the KKT system.

Contribution

It proposes a novel 5D space-time finite element method for non-Newtonian flow optimization, moving beyond traditional time-stepping techniques.

Findings

Efficiently approximates solutions to the KKT system in a 5D framework.

Demonstrates the applicability to simplified Carreau flow models.

Provides a new computational approach for non-Newtonian fluid optimization.

Abstract

This work presents a 5D concept to optimizing non-Newtonian fluid flows through a simplified Carreau flow model. We solve the optimization problem by approximating the solution of the KKT System with fully space-time finite element methods instead of the more traditional time-stepping technique combined with spatial finite element discretization. Therein, the finite element method is formulated in 3D in space, 1D in time, and 1D in the optimization loop, yielding a 5D overall framework.