scholarly journals Equal-Order Polygonal Analysis for Fluid Computation in Curved Domain

2020 ◽  
pp. 2040003
Author(s):  
T. Vu-Huu ◽  
C. Le-Thanh ◽  
H. Nguyen-Xuan ◽  
M. Abdel Wahab
Keyword(s):  
Finite Element ◽  
Fluid Flow ◽  
Stokes System ◽  
Shape Function ◽  
Incompressible Fluid Flow ◽  
Local Projection ◽  
Mixed Scheme ◽  
Pressure Fields ◽  
Order Scheme ◽  
High Flexibility

Our research introduces a novel advanced method for fluid computation in complicated domain. It makes use of an advanced polygonal finite element applying equal-order scheme; within each element. Both velocity and pressure fields are represented by a polygonal basis shape function system. This technique is based on a combination of the equal-order mixed scheme method, the polygon finite element method (PFEM) and the adapted local projection method that is used to stabilize the pressure. In order to simulate the fluid flow, MATLAB is utilized for coding and programming. A numerical example of an incompressible fluid flow governed by Stokes system in curved domain is performed to demonstrate the applicability of our developed polygon element. Besides, through the numerical analysis, we show the high flexibility of PFEM for curved domains.

scholarly journals A Convergent three Field Quadrilateral Finite Element Method for Simulating Viscoelastic Flow on Irregular Meshes

1992 ◽  
pp. 391-406
Author(s):  
Victoriano Ruas
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fluid Flow ◽  
Stokes System ◽  
Viscoelastic Flow ◽  
Flow Problems ◽  
Extra Stress Tensor ◽  
Irregular Meshes ◽  
Quadrilateral Finite Element ◽  
Extra Stress

In a recent paper a finite elemenJ method for solving the three field Stokes system as a basis for the numerical solution of viscoelastic fluid flow problems was introduced. The method constructed upon a biquadratic velocity, a discontinuous linear pressure and a bilinear extra stress tensor interpolation in quadrilaterals, enriched with fifteen bubble tensors, has been proved to yield second order approximations of these variables, in the case of rectangular meshes. In this work equivalent results are proven to hold in the case of irregular meshes.  

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