TABLE OF CONTENTS Chapter 4 has formulated the SPH method for general CFD problems that have very large deformations. The capability of the SPH method has also been demonstrated via a number of example problems of fluid flows.
In this chapter, a SPH formulation is presented for simulating physical phenomena with discontinuities. As the formulation allows discontinuity of field functions in the support domain, it is, therefore, termed in this book as discontinuous SPH or DSPH for the convenience of description.
The DSPH formulation was initially presented by Liu et al. (2003e) for handling shock waves using the SPH method. The formulation is based on the Taylor series expansion in the piecewise continuous regions on both sides of the discontinuity. The formulation is originated from an existing improved version of the SPH method called corrective smoothed particle method (CSPM). The DSPH not only improves the boundary deficiency problem in the traditional SPH method, but also restores the kernel consistency of the corrective smoothed particle method (CSPM) in the discontinuous regions. The resultant kernel and particle approximations consist of a primary part similar to that in the CSPM, and an additional part derived from the discontinuity treatment.
A numerical study is carried out to examine the performance of the DSPH formulation. The results show that the DSPH not only remedies the boundary deficiency problem but also well simulates the discontinuity that may exist in the field variable functions. The DSPH formulation is also applied to simulate the one-dimensional shock tube problem with fairly...
