Finite Element Technique for Solving the Stream Function Form of a Linearized Navier-Stokes Equations Using Argyris Element
F. Fairag, N. Almulla
TL;DR
The paper develops a finite element approach using Argyris elements for the stream function form of a linearized Navier–Stokes problem, enabling automatic incompressibility and a single unknown while avoiding pressure in the weak form. It implements an iterative scheme with a linear solver suitable for nonsymmetric systems and analyzes global node orderings to optimize matrix structure. Validation on a manufactured unit-square test demonstrates convergence and provides performance data, including CPU time and iteration counts, as well as qualitative streamlines. The work offers a practical FE framework for accurate and efficient solutions of stream-function formulations of incompressible flows.
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.