Inverse distance interpolation for used in unstructured mesh finite volume solver

Abstract

This article discusses adjusting inverse distance interpolation for use in unstructured mesh finite volume solutions. The adjustment was made on the weight function of the inverse distance interpolation using the Laplacian of the flow variable inside a Voronoi-dual of finite volume cells. We tested the accuracy of the adjusted inverse distance interpolation on two-dimensional potential flows. It was found that the adjusted and standard inverse distance interpolations have a similar degree of accuracy when used in unstructured, Delaunay based, finite volume mesh. However, the L1 norm error of the adjusted version of the inverse distance interpolation was much smaller than the L1 norm error of the standard version.