Conservation form, in general non steady coordinates, of the NavierStokes equations and boundary conditions for a moving boundary problem
Abstract
The conservative form of the complete set of NavierStokes equations and of the 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 nonsteady general coordinates. The boundary fitted coordinate systems in space and spacetime are stated, and a brief list of the main relations between the corresponding matrix tensors is given. The conservative form of the NavierStokes equations is derived from the corresponding relativistic balance equations by assuming small relative velocities. This method is also applied to derive a strong conservative form of the boundary conditions at the interface. The set of boundary conditions is analyzed and discussed, and the possible application of the method to treat different kinds of surfaces of discontinuity is suggested.
 Publication:

Meccanica
 Pub Date:
 March 1983
 Bibcode:
 1983Mecc...18....8S
 Keywords:

 Boundary Conditions;
 Boundary Value Problems;
 Computational Fluid Dynamics;
 Conservation Equations;
 NavierStokes Equation;
 Flow Distribution;
 Mass Balance;
 Space Commercialization;
 Thermal Energy;
 Fluid Mechanics and Heat Transfer