Ritz-Galerkin Approximations in Fluid Dynamics

The paper considers the variational formulation of boundary value problems in fluid dynamics, and particular cases are studied where approximations can be derived by Galerkin's method. The basic method is illustrated for potential flow, after which several approaches for incompressible viscous flow are examined. The basic equations to be integrated are set up for an approximation in which the pressure is taken as the primary variable. The solenoidal approach, however, ensures satisfaction of the momentum equation identically and eliminates the pressure from the equation of motion. Pressure can also be eliminated by the vorticity transport approach. The numerical approximation schemes by which resulting equations of these various approaches may be solved are indicated.