Adaptive iterative linearised finite element methods for implicitly constituted incompressible fluid flow problems and its application to Bingham fluids

TL;DR

This paper presents an iterative linearised finite element method for solving Bingham fluid flow problems, demonstrating convergence properties and validating the approach through numerical experiments.

Contribution

It introduces a novel iterative linearised finite element algorithm with proven weak convergence for Bingham fluids, a class of implicit constitutive models.

Findings

Convergence of the iterative method is demonstrated.

Numerical experiments validate the effectiveness of the approach.

The method is applicable to complex Bingham fluid flow problems.

Abstract

In this work, we introduce an iterative linearised finite element method for the solution of Bingham fluid flow problems. The proposed algorithm has the favourable property that a subsequence of the sequence of iterates generated converges weakly to a solution of the problem. This will be illustrated by two numerical experiments.