A Finite Element Implementation of the SRTD Algorithm for an Oldroyd 3-Parameter Viscoelastic Fluid Model

TL;DR

This paper presents a finite element implementation of the SRTD algorithm for Oldroyd 3-parameter viscoelastic fluids, comparing its stability and speed to the EVSS method through benchmark problems.

Contribution

It introduces a finite element implementation of the SRTD algorithm for Oldroyd 3-parameter models and compares it to the EVSS method in terms of stability and computational efficiency.

Findings

SRTD implementation is stable with mesh refinement.

SRTD is generally faster than EVSS.

SRTD cannot reach as high Weissenberg numbers as EVSS.

Abstract

In this paper, we discuss a finite element implementation of the SRTD algorithm described by Girault and Scott for the steady-state case of a certain 3-parameter subset of the Oldroyd models. We compare it to the well-known EVSS method, which, though originally described for the upper-convected Maxwell model, can easily accommodate the Oldroyd 3-parameter model. We obtain numerical results for both methods on two benchmark problems: the lid-driven cavity problem and the journal-bearing, or eccentric rotating cylinders, problem. We find that the resulting finite element implementation of SRTD is stable with respect to mesh refinement and is generally faster than EVSS, though is not capable of reaching as high a Weissenberg number as EVSS.