Conservation form, in general non steady coordinates, of the Navier-Stokes equations and boundary conditions for a moving boundary problem

Abstract

The conservative form of the complete set of Navier-Stokes equations and boundary conditions for the flow field of two immiscible fluids separated by a moving interface of unknown shape, is obtained with reference to a boundary fitted system of non steady general coordinates. The method applied in this paper to obtain the set of equations as the limit, in the case of small relative velocities, of the corresponding set in the frame of relativistic fluid mechanics, seems particularly direct and appropriate to express the boundary conditions on the moving interface. The immediate extension of the method to treat different kinds of interfaces of discontinuity is also discussed.