A Lagrangian particle-wavelet method

This paper presents a novel, multiresolution Lagrangian particle method with enhanced, wavelet-based adaptivity. The method is formulated for transport problems and combines the efficiency of wavelet collocation with the inherent numerical stability of particle methods. The accuracy and efficiency of the present method is assessed on a number of benchmark problems pertaining to interface capturing and transport. The method is compared with existing techniques demonstrating its advantages and limitations. The present approach leads to a new generation of particle methods with multiresolution capabilities.