Chapter 14 - Smoothed Particle Hydrodynamics

Abstract

Chapter 14 Mesh-free particle methods are presented with emphasis on smoothed particle hydrodynamics (SPH). The integral representation of fluid properties is discussed by introduction of the smoothing kernel. Integral representation expressions for partial and material derivatives are introduced, and the Lagrangian equations of hydrodynamics are derived. A propagation equation for SPH particles is constructed, and the concept of variable smoothing length is explained. The application of the SPH method to sharp discontinuities is discussed, and the need for artificial viscosity is justified. Boundary conditions for the free surface are formulated, ghost particles are introduced, and the SPH method is applied to the problem of surge propagation in a dry channel.