The partial differential equations governing fluid flow and heat transfer include the continuity equation, the Navier-Stokes equations and the energy equation. These equations are intimately coupled and non-linear making a general analytic solution impossible except for a limited number of special problems, where the equations can be reduced to yield analytic solutions.
Because most practical problems of interest do not fall into this limited category, approximate methods are used to determine the solution to these equations. There are numerous methods available for doing so. The following sections briefly describe the method used by Autodesk Simulation CFD.
References
1. White, F.M., Viscous Fluid Flow, McGraw-Hill, New York, 1974
2. Schnipke, R.J., “A Streamline Upwind Finite Element Method For Laminar And Turbulent Flow”, Ph.D. Dissertation, University of Virginia, May 1986
3. Bakir, F., Rey, R., Gerber, A.G., Belamri, T., Hutchinson, B., “Numerical and Experimental Investigations of the Cavitating Behavior of an Inducer”, International Journal of Rotating Machinery, vol 10, pp 15-25, 2004