TABLE OF CONTENTS Smoothed particle hydrodynamics has a number of advantages over the conventional grid-based numerical methods, and is an effective technique for solving fluid dynamic problems. This chapter presented the SPH implementations based on the Navier-Stokes equations for general dynamic fluid flows. The resultant SPH equations of motion can simulate different flow problems such as inviscid or viscous flows, compressible or incompressible flows. The standard artificial viscosity is used to model the inviscid flow problems in resolving shock waves. A SPH expression of physical viscosity constructed from the viscous shear force is employed for viscous flow problems. For incompressible flow problems, the concept of artificial compressibility is applied by selecting a special equation of state to model the incompressible fluid as quasi-incompressible. Extra virtual particles (type I and/or type II) are used to treat the solid boundary condition. This treatment can prevent real particles from penetrating outside the boundary and can also improve the accuracy of numerical results.
A series of numerical tests have been carried out for different dynamic fluid flow problems. For incompressible flows such as the Poiseuille flow, Couette flow and the shear driven cavity problem, the presented SPH method can obtain satisfactory results. The advantages of the SPH method in treating free surface flows can be clearly seen in the simulation of the water discharge problems with the gate partially opened and the dam collapsing, as well as the problems of water clump impacting on a solid step. The SPH method has also simulated the...
