Finite element solution algorithm for incompressible fluid dynamics

Abstract

A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the transient motion of a viscous incompressible fluid, i.e., hydrodynamics. Dependent variable transformation renders the differential equation description uniformly elliptic. The finite element algorithm is established using the Galerkin criterion on a local basis within the Method of Weighted Residuals. It is unconstrained with respect to system linearity, computational mesh uniformity or solution domain closure regularity. The finite element matrices are established using a linear 'natural coordinate function' description. Computational solutions using the COMOC computer program illustrate the various features of the algorithm including recirculating flows.