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.
Highlights
1 Introduction This research, instead of using widely used numerical approaches such as the finite difference method (FDMfinite volume method (FVM)), finite element method (FEM), e.g., [1,2,3], etc., proposes an advanced polygonal finite element (PFE) method (PFEM) to solve the 2D lid-driven cavity problem controlled by the incompressible steady N-S equations
The fact is that developments of PFEM in the fluid field is still too modest compared to the enormous potential of the method
In this article, we successfully address the Picard iteration technique for our proposed PFE to deal with the nonlinear convection term of N-S equations
Summary
This research, instead of using widely used numerical approaches such as the finite difference method (FDMfinite volume method (FVM)), finite element method (FEM), e.g., [1,2,3], etc., proposes an advanced PFE method (PFEM) to solve the 2D lid-driven cavity problem controlled by the incompressible steady N-S equations. The primary advantage of our developed element is the computational ability for fluid flows on all kinds of mesh families, e.g., triangular, quadrilateral, hexagonal, random and centroidal Voronoi meshes It is constructed by the mixed scheme between two equal-order discretisation spaces for both fluid pressure and velocity fields of flows. This research executes our novel stabilisation technique to eliminate the instability of the equal-order mixed scheme [9,10,11,12] It is an innovation of the local polynomial pressure projection method introduced by Bochev et al [13] in 2004. This study, applies the 2D lid-driven cavity benchmark with various Reynolds numbers (i.e., Re = 100, 400 and 1000) to assess the performance of our developed PFE (i.e., Pe1Pe1, [10]) in solving the incompressible steady N-S equations.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
