Finite Element Technique for Solving the Stream Function Form of a Linearized Navier-Stokes Equations Using Argyris Element

TL;DR

This paper presents a finite element method using Argyris elements to solve the stream function form of linearized Navier-Stokes equations, analyzing node orderings and matrix structures for efficient fluid flow computation.

Contribution

It introduces an implementation of the finite element method with Argyris elements for linearized Navier-Stokes equations and evaluates node ordering strategies for optimal matrix structure.

Findings

Optimal node ordering improves matrix sparsity

The method accurately captures fluid flow patterns

Visualization aids in understanding flow and matrix structure

Abstract

The numerical implementation of finite element discretization method for the stream function formulation of a linearized Navier-Stokes equations is considered. Algorithm 1 is applied using Argyris element. Three global orderings of nodes are selected and registered in order to conclude the best banded structure of matrix and a fluid flow calculation is considered to test a problem which has a known solution. Visualization of global node orderings, matrix sparsity patterns and stream function contours are displayed showing the main features of the flow.