ON CONSERVATION AT GRID INTERFACES.

This paper considers the solution of hyperbolic systems of conservation laws on discontinuous girds. In particular, we consider what happens to conservation at grid interfaces. A procedure is presented to derive conservative difference approximations at the grid interfaces for two-dimensional grids which overlap in an arbitrary configuration. The same procedures are applied to compute interface formulas for grids which are refined in space and/or time, and for continuous grids where a switch in the scheme causes the discontinuity. The results are applicable to certain problems involving shock waves.