Decoupled Scheme for Non-Stationary Viscoelastic Fluid Flow

Decoupled Scheme for Non-Stationary Viscoelastic Fluid Flow

Year:    2018

Author:    Md. Abdullah Al Mahbub, Shahid Hussain, Nasrin Jahan Nasu, Haibiao Zheng

Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 5 : pp. 1191–1226

Abstract

In this paper, we present a decoupled finite element scheme for two-dimensional time-dependent viscoelastic fluid flow obeying an Oldroyd-B constitutive equation. The key idea of our decoupled scheme is to divide the full problem into two subproblems, one is the constitutive equation which is stabilized by using discontinuous Galerkin (DG) approximation, and the other is the Stokes problem, can be computed parallel. The decoupled scheme can reduce the computational cost of the numerical simulation and implementation is easy. We compute the velocity $u$ and the pressure $p$ from the Stokes like problem, another unknown stress $σ$ from the constitutive equation. The approximation of stress, velocity and pressure are respectively, $P_1$-discontinuous, $P_2$-continuous, and $P_1$-continuous finite elements. The well-posedness of the finite element scheme is presented and derive the stability analysis of the decoupled algorithm. We obtain the desired error bound also demonstrate the order of the convergence, stability and the flow behavior with the support of two numerical experiments which reveals that decoupled scheme is more efficient than coupled scheme.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2017-0186

Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 5 : pp. 1191–1226

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    36

Keywords:    Viscoelastic fluid decoupled scheme DG method Oldroyd-B fluid flow model.

Author Details

Md. Abdullah Al Mahbub

Shahid Hussain

Nasrin Jahan Nasu

Haibiao Zheng