Finite element analysis of viscous fluid flow

A finite element model for the analysis of two dimensional viscous flows is formulated using the virtual work method. The model is in part based on a finite element shell model, using the same reduced integration of quadratic interpolations for all variables1]. Differences from preceding formulations are that integration by parts is applied to the continuity equation, yielding different loading terms which are more easily defined in some problems, and a new approach is used for the convective inertia terms, giving a clearer interpretation of their effects which are distributed to both sides of the nonlinear recurrence relation. In the case of compressible flow, for which comparatively few formulations have been proposed to date, the thermal energy equation is used to form a two stage solution and here this seems the most natural and economical approach.