CFD methods derived from simplified variational principles

In previous papers^1-4 we have described how by minimizing the fluid action numerically one can obtain a solution of the fluid steady state equations. The action which was used was the four function action of Seliger & Whitham.⁵ In a recent paper⁶ we describe how one can improve upon previous art by reducing the number of variables in the action. Three independent functions variational formalism for stationary and non-stationary barotropic flows is introduced. This is less than the four variables which appear in the standard equations of fluid dynamics which are the velocity field v→ and the density ρ. In this paper we will discuss some issues related to the usage of the new action principles as basis for CFD algorithms.