Computer Implementation of SPH and a 3D SPH Code

Abstract

Two main purposes of developing meshfree methods are 1. to relieve the users or the analysts from the trivial and time-consuming task of meshing, and 2. to solve problems with extremely large deformation and even breakage. The computer implementations of meshfree methods are, in general, more difficult than that in a grid/mesh-based method, simply because there is no predefined grid/mesh to use in establishing the discrete system equations. Among the meshfree methods, SPH method is relatively simple to code. A detailed discussion on issues and techniques related to computer implementation of a meshfree method has been given by Liu (2002) in his recent monograph.In this chapter, issues related to the computer implementation of meshfree particle methods are discussed. Computer implementations of meshfree particle method over serial and parallel computers are also briefly addressed. The source code of a standard serial 3D SPH code is provided. The main features of the SPH code, detailed descriptions and the source code of the related subroutines are also provided.The programs demonstrate most of the concepts and techniques related to the SPH method. The code can be easily extended to other corrective or modified versions of SPH with proper treatment either on the kernel approximation or the particle approximation. The 3D SPH code can solve compressible flows with real viscosity, and can be readily modified for applications to hydrodynamics with material strength with a proper constitutive model and an equation of state. As a structured code, it can be readily modified or imported to other user-application subroutines according to users' specific requirements. Two benchmark problems, a ID shock tube and a 2D shear driven cavity are provided to test the accuracy and efficiency of the attached SPH source code.The purpose of releasing the source code is to save readers' time in 365 Smoothed Particle Hydrodynamics Downloaded from www.worldscientific.com by MONASH UNIVERSITY on 10/09/15. For personal use only. Smoothed Particle Hydrodynamics Downloaded from www.worldscientific.com by MONASH UNIVERSITY on 10/09/15. For personal use only. Smoothed Particle Hydrodynamicsapproaches such as the direct all-pair search, linked-list search algorithm, tree search algorithm, and bucket search algorithm can be employed (see, Section 4.5). 2.3 Calculating the smoothing function (for the summation density approach) and its derivatives from the generated information of interaction particle pairs. 2.4 Updating density if the summation density approach is used. 2.5 Calculating the artificial viscous force. 2.6 Calculating the internal forces arising from the particle interactions.Note that the particle pressure is obtained from the density and energy through an equation of state. 2.7 Calculating the external forces if necessary. 2.8 Calculating the change of momentum, energy and density (if using the continuity density approach). 2.9 Updating smoothing length for the next time step. 2.10Updating particle momentum, energy and density; Up...