TABLE OF CONTENTS A series of numerical tests have been carried out to examine the ability and efficiency of the presented SPH formulations and the SPH code implemented in simulating fluid dynamic problems (Lam et al., 2000). As can be seen from the previous discussions, the presented SPH method with various formulations is able to simulate different dynamic fluid flow problems, such as inviscid or viscous flows, compressible or incompressible flows. The followings are some applications to incompressible flows, free surface flows and compressible flows. These applications and numerical examples not only examine the effectiveness of the SPH method, but also provide foundations for the complex explosion problems to be simulated in the next chapters. In these applications, the cubic spline function (see, Section 3.1) is used. The SPH code used to generate these examples is attached in Chapter 10 with detailed descriptions.
In the finite difference methods, the incompressible flows have been widely studied and will be studied in this section using the SPH method. In the SPH simulation of incompressible flows, the artificial compressibility technique (see, Section 4.4.7) is employed to model the incompressible fluid as slightly compressible by selecting a proper equation of state. Three standard benchmarking cases, the Poiseuille flow, Couette flow, and the shear driven cavity problem are studied. For the Poiseuille flow, Couette flow and the shear driven cavity problem, equation (4.89) is employed. For the later simulation of water discharge with free surface, equation (4.88)) is used to...
