Component-wise Interpolation of Solenoidal Vector Fields: A Comparative Numerical Study

Abstract

Vector-field interpolation is a fundamental task in flow simulation and visualization. The common practice is to interpolate the vector field in a component-wise fashion. When the vector field of interest is solenoidal (divergencefree), such an approach is not conservative and gives rise to artificial divergence. In this work, we numerically compare some recently proposed scalar interpolation methods on the Cartesian and body-centered cubic lattices, and investigate their ability to conserve the solenoidal nature of the vector field. We start with a sampled version of a synthetic solenoidal vector field and use an interpolative component-wise reconstruction method to approximate the vector field and its divergence at arbitrary locations. Our results show that an improved scalar interpolation method does not necessarily lead to a more conservative vector field approximation.