Abstract: A method of numerical simulation of fluid flow past a body. The physics of stationary flow is formulated in terms of a potential functional of at most four scalar fields: three Clebsch scalar fields and a density field. The physics of non-stationary flow is formulated in terms of an action that includes an action integral of a Lagrangian functional of the same four scalar fields and an initial and a final integral of a function of the same four scalar fields. The values of the fields are varied to extremize the potential functional or the action, under the constraint of appropriate boundary conditions. Potential functionals and Lagrangian functionals for compressible and incompressible flows with zero velocity normal to the surface of the body, and for potential flows, are described.