**SPH Source Code**

The SPH code is associated with the book titled "Smoothed particle hydrodynamics: a meshfree particle method" by Liu and Liu (2003). The detailed programs and explanations can also be found in the book.

SPH code in the SPH book

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 1D 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 developing their own SPH code. Readers are free to use in part or the entire code at their own risks, as long as a proper reference and acknowledgement are given. The authors apologize for not being able to provide technical support, but welcome comments and suggestions from the users. We will try to improve the code in the future, whenever there is a chance.

You can download the SPH code and unzip it.

The installation of the software requires a serial number. You may email liugr@uc.edu for the serial number, by providing your basis information: Name, Address, Contacts, Affiliations etc.

For the theoretical background of the software development, please refer to the publications authored by Dr. G. R. Liu and co-workers. Following lists are most relevant.

**Book**

Liu G. R. and Liu M. B., Smoothed particle hydrodynamics: a meshfree particle method, World Scientific, 3rd printing, 2003.

**Book Chapters**

Liu M. B., Liu G. R., Zong Z. and Lam K. Y., Numerical simulation of underwater explosion by SPH, In S. N. Atluri & F. W. Brust (eds.): Advances in Computational Engineering & Science 2000, Tech Science Press, pp. 1475-1480, 2000.

Liu G. R., Liu M. B., Lam K. Y. and Zong Z., Simulation of the explosive detonation process by using SPH methodology, In K. J. Bathe (ed.): Computational Fluids and Solid Mechanics, Elsevier Science Ltd, pp. 323-326, 2001.

Liu M. B., Liu G. R. and Lam K. Y., A new technique to treat material interfaces for smoothed particle hydrodynamics, In S. Valliappan and N. Khalili (eds.): Computational Mechanics ? New Frontiers for New Millennium, Elsevier Science Ltd, pp. 977-982, 2001.

Liu M. B., Liu G. R. and Lam K. Y., Coupling molecular dynamics with meshfree particle method: a novel approach for multi-scale simulations, In G. R. Liu (ed.) Advances in meshfree and X-FEM methods, World Scientific, pp. 211-216, 2002.

**Peer-reviewed Journal papers**

Liu M. B., Liu G. R. and Lam K. Y., Investigations into water mitigations using a meshless particle method, Shock Waves 12(3):181-195, 2002.

Liu M. B., Liu G. R., Zong Z. and Lam K. Y., Computer simulation of the high explosive explosion using smoothed particle hydrodynamics methodology, Computers & Fluids, 32(3): 305-322, 2003.

Liu M. B., Liu G. R., Lam K. Y. and Zong Z., Meshfree particle simulation of the explosion process for high explosive in shaped charge, Shock Waves 12 (6): 509-520, 2003.

Liu M. B., Liu G. R., Lam K. Y. and Zong Z., Computer simulation of shaped charge detonation using meshless particle method, International Journal for Blasting and Fragmentation, 7(3):181-202, 2003.

Liu M. B., Liu G. R., Zong Z. and Lam K. Y., Smoothed particle hydrodynamics for numerical simulation of underwater explosions, Computational Mechanics, 30(2):106-118, 2003.

Liu M. B., Liu G. R., Lam K. Y. and Zong Z., Comparative study of the real and artificial detonation models in underwater explosions, Engineering Simulation, 25(2):113-124, 2003.

Liu M. B., Liu G. R., Lam K. Y., Constructing smoothing functions in smoothed particle hydrodynamics with applications, Journal of Computational and Applied Mathematics, 155(2):263-284, 2003.

Liu M. B., Liu G. R., Lam K. Y., A one dimensional meshfree particle formulation for simulating shock waves, Shock Waves, 13(3):201 ? 211, 2003.

Liu M. B., Liu G. R., Lam K. Y., Computer simulation of flip-chip underfill encapsulation process using the meshfree particle method, International Journal of Computational Engineering Science, 4(2): 405-408, 2003.

**Peer-reviewed Conference papers**

Lam K. Y., Liu G. R., Liu M. B. and Zong Z., Numerical simulation of underwater shock using SPH methodology, Computational Mechanics and Simulation of Underwater Explosion Effects- US/Singapore workshop, pp. 1-6, November 2000, Washington D.C.

Lam K. Y., Liu G. R., Liu M. B. and Zong Z., Smoothed particle hydrodynamics for fluid dynamic problems, Proceedings of International Symposium on Supercomputing and Fluid Science, pp. 1-16, August 2000, Institute of fluid Science, Tohoku University, Sendai, Japan.

Liu M. B., Liu G. R., Zong Z. and Lam K. Y., Numerical simulation of incompressible flows by SPH, International Conference on Scientific & Engineering Computing, pp. 72, March 2001, Beijing, China.

Liu G. R., Liu M. B. and Lam K. Y., Smoothed particle hydrodynamics for numerical simulation of high explosive explosions, The first international symposium on advanced fluid information (AFI-2001), pp. 1-7, Oct. 2001, Institute of fluid Science, Tohoku University, Sendai, Japan.

Liu G. R., Liu M. B. and Lam K. Y., A general approach for constructing smoothing function for meshfree methods, Proceedings of the Ninth International Conference on Computing in Civil and Building Engineering, pp. 431-436, April 2002, Taipei, Taiwan.

We appreciate very much your comments and suggestions. We will be constantly improve the code to incorporate your valuable comments and suggestions.