A Scheme for Conservative Interpolation on Overlapping Grids

Abstract

This paper describes how to interpolate in a conservative manner when solving systems of conservative laws on overlapping grids. Overlapping grids are a flexible and efficient way to create grids for complicated regions. Before now, however, no general method had been developed for conservative interpolation. The basic idea consists of assuming that the interpolation coefficients are free parameters and then deriving constraints to ensure that the interpolation is conservative. A system of equations is then solved to determine the coefficients. A two-dimensional viscous Burger’s equation is solved to demonstrate the conservative nature of the scheme.