CONSERVATIVE AND NONCONSERVATIVE INTERPOLATION BETWEEN OVERLAPPING GRIDS FOR FINITE-VOLUME SOLUTIONS OF HYPERBOLIC PROBLEMS

We consider the Euler equations of gas dynamics. To solve the problem numerically we use finite volume methods on regions covered by overlapping structured grids. Using overlapping grids makes the discretization of complicated domains possible and is an effective method for vectorized and multitasking computers. We study some different ways of obtaining the interface boundary conditions, concentrating on flows which contain slowly moving shocks. Analysis and numerical computations show that the choice of the boundary conditions is critical for the accuracy and stability of the entire approximation. The use of non-conservative cell value interpolation leads to poor accuracy. The numerical results show that the shock is slowed down or stopped at the overlapping grid interface. When conservative flux interpolation is used, the numerical solution have large errors at the interface. We explain the errors by showing that this procedure is only weakly stable. We present a new, strongly stable, conservative treatment of the interface conditions, in which the interpolated fluxes are decomposed characteristically, followed by a filter to remove unwanted oscillations.