Incompressible Flows as a System of Conservation Laws with a Constraint

Some inadequacies of conventional formulations of inviscid hydrodynamics with regard to the solution of free boundary problems are analyzed. An alternative algorithmic formulation which produces the flow field incrementally in time is proposed. In this formulation paramountcy is given to the equations of mass and momentum conservation, which are solved subject to a constraint on the density. Energy decay is possible. The new formulations is examined with regard to its consistency with standard formulations when flow quantities are sufficiently smooth. Extensions to the treatment of stratified incompressible flows and transonic flows are discussed. (Author) Presented at Institut de Recherche d'Automatique in Rocquencourt, 11 May 78, France.