On finite element analysis of compressible and incompressible, temperature-dependent fluid flow

A finite element formulation for analysis of low Reynolds number, temperature-dependent fluid flow is presented. The independent state variables used are the density, temperature and velocities. The formulation includes the compressibility of the fluid, but reduces naturally to the incompressible response prediction when the fluid behaves physically as an incompressible medium. The formulation has been implemented for the 9-node Lagrangian element and the solutions to two problems are reported: the wall driven cavity problem and the problem of natural convection in an enclosed box.