AbstractDeveloping suitable interpolation methods to simulate dynamic motions of continuous materials such as fluids is an important problem. In this paper, we propose a novel method to enforce the divergence condition to the interpolated velocity field by moving least squares (MLS), by means of the diffusive derivatives and moving divergence constraints that allow the practical use and easy implementation. As results, we present the velocity interpolation examples and a fluid‐like particle simulation method to show the meaningful potential of our method as a tool of physical interpolation for fluid simulations. Copyright © 2008 John Wiley & Sons, Ltd.