Open Access

ARTICLE

Polygonal Finite Element for Two-Dimensional Lid-Driven Cavity Flow

by T. Vu-Huu¹, C. Le-Thanh², H. Nguyen-Xuan^3,4, M. Abdel-Wahab^3,5,*

1 Faculty of Civil Engineering, Vietnam Maritime University, 484 Lach Tray Str., Hai Phong, Vietnam
2 Faculty of Civil Engineering and Electricity, Ho Chi Minh City Open University, Vietnam
3 CIRTech Institute, Ho Chi Minh City University of Technology (HUTECH), Ho Chi Minh City, Vietnam
4 Department of Architectural Engineering, Sejong University, 209 Neungdongro, Gwangjingu, Seoul, 05006, Republic of Korea
5 Soete Laboratory, Faculty of Engineering and Architecture, Ghent University, Technologiepark Zwijnaarde, 903, B-9052, Zwijnaarde, Belgium

* Corresponding Authors: M. Abdel-Wahab. Email: ,

Computers, Materials & Continua 2022, 70(3), 4217-4239. https://doi.org/10.32604/cmc.2022.020889

Received 12 June 2021; Accepted 14 July 2021; Issue published 11 October 2021

Abstract

This paper investigates a polygonal finite element (PFE) to solve a two-dimensional (2D) incompressible steady fluid problem in a cavity square. It is a well-known standard benchmark (i.e., lid-driven cavity flow)-to evaluate the numerical methods in solving fluid problems controlled by the Navier–Stokes (N–S) equation system. The approximation solutions provided in this research are based on our developed equal-order mixed PFE, called Pe₁Pe₁. It is an exciting development based on constructing the mixed scheme method of two equal-order discretisation spaces for both fluid pressure and velocity fields of flows and our proposed stabilisation technique. In this research, to handle the nonlinear problem of N-S, the Picard iteration scheme is applied. Our proposed method’s performance and convergence are validated by several simulations coded by commercial software, i.e., MATLAB. For this research, the benchmark is executed with various Reynolds numbers up to the maximum . All results then numerously compared to available sources in the literature.

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