normal direction of the solid structure, and the imaginary particle density is calculated through the equation of state. Accordingly, the interaction forces and acting on a solid particle are given by and The anti-symmetric property of the derivative of the kernel function will ensure the momentum conservation for each pair of interacting particles and . Others The discrete element method, used for simulating granular materials, is related to SPH. Variants of the method References Further reading Hoover, W. G. (2006). Smooth Particle Applied Mechanics: The State of the Art, World Scientific. Impact Modelling with SPH Stellingwerf, R. F., Wingate, C. A., Memorie della Societa Astronomia Italiana, Vol. 65, p. 1117 (1994). Amada, T., Imura, M., Yasumuro, Y., Manabe, Y. and Chihara, K. (2004) Particle-based fluid simulation on GPU, in proceedings of ACM Workshop on General-purpose Computing on Graphics Processors (August, 2004, Los Angeles, California). Desbrun, M. and Cani, M-P. (1996). Smoothed Particles: a new paradigm for animating highly deformable bodies. In Proceedings of Eurographics Workshop on Computer Animation and Simulation (August 1996, Poitiers, France). Hegeman, K., Carr, N.A. and Miller, G.S.P. Particle-based fluid simulation on the GPU. In Proceedings of International Conference on Computational Science (Reading, UK, May 2006). Proceedings published as Lecture Notes in Computer Science v. 3994/2006 (Springer-Verlag). M. Kelager. (2006) Lagrangian Fluid Dynamics Using Smoothed Particle Hydrodynamics, M. Kelagar (MS Thesis, Univ. Copenhagen). Kolb, A. and Cuntz, N. (2005). Dynamic particle coupling for GPU-based fluid simulation. In Proceedings of the 18th Symposium on Simulation Techniques (2005) pp. 722–727. Liu, G.R. and Liu, M.B. Smoothed Particle Hydrodynamics: a meshfree particle method. Singapore: World Scientific (2003). Monaghan, J.J. (1992). Smoothed Particle Hydrodynamics. Annu. Rev. Astron. Astrophys. (1992). 30 : 543–74. Muller, M., Charypar, D. and Gross, M. Particle-based Fluid Simulation for Interactive Applications, In Proceedings of Eurographics/SIGGRAPH Symposium on Computer Animation (2003), eds. D. Breen and M. Lin. Vesterlund, M. Simulation and Rendering of a Viscous Fluid Using Smoothed Particle Hydrodynamics, (MS Thesis, Umea University, Sweden). Violeau, D., Fluid Mechanics and the SPH method. Oxford University Press (2012). External links First large simulation of star formation using SPH SPHERIC (SPH rEsearch and engineeRing International Community) ITVO is the web-site of The Italian Theoretical Virtual Observatory created to query a database of numerical simulation archive. SPHC Image Gallery depicts a wide variety of test cases, experimental validations, and commercial applications of the SPH code SPHC. A derivation of the SPH