On the Accuracy of Impulse Methods for Fluid Flow

A Lagrangian numerical method based on impulse variables is analyzed. The relation between discrete impulse vectors and vortex dipoles with a prescribed dipole moment is presented and used to adapt the high-accuracy cutoo functions of vortex methods for use in impulse-based methods. The long-time implementation of the impulse method is shown to contain a source of error whose growth in time leads to a severe loss of accuracy in interior ows. Applications for which impulse methods are well suited are identiied.