Volume 10, Issue 5
Decoupled Scheme for Non-Stationary Viscoelastic Fluid Flow

Adv. Appl. Math. Mech., 10 (2018), pp. 1191-1226.

Published online: 2018-07

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• 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.

• Keywords

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

65N12, 65N30, 76A10, 76M10

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• RIS
• TXT
@Article{AAMM-10-1191, author = {Md. Abdullah Al Mahbub , and Shahid Hussain , and Nasrin Jahan Nasu , and Zheng , Haibiao}, title = {Decoupled Scheme for Non-Stationary Viscoelastic Fluid Flow}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {5}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2017-0186}, url = {http://global-sci.org/intro/article_detail/aamm/12595.html} }
TY - JOUR T1 - Decoupled Scheme for Non-Stationary Viscoelastic Fluid Flow AU - Md. Abdullah Al Mahbub , AU - Shahid Hussain , AU - Nasrin Jahan Nasu , AU - Zheng , Haibiao JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1191 EP - 1226 PY - 2018 DA - 2018/07 SN - 10 DO - http://doi.org/10.4208/aamm.OA-2017-0186 UR - https://global-sci.org/intro/article_detail/aamm/12595.html KW - Viscoelastic fluid, decoupled scheme, DG method, Oldroyd-B fluid flow model. AB -

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.

Md. Abdullah Al Mahbub, Shahid Hussain, Nasrin Jahan Nasu & Haibiao Zheng. (1970). Decoupled Scheme for Non-Stationary Viscoelastic Fluid Flow. Advances in Applied Mathematics and Mechanics. 10 (5). 1191-1226. doi:10.4208/aamm.OA-2017-0186
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