Smoothed particle Hydrodynamics numerical methods

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This is a short course on the Smoothed Particle Hydrodynamics (SPH) numerical schemes and it will cover basic and theoretical concepts, latest innovations.  This course is primarily aimed at the beginners with Master and PhD students in mathematics, engineering, computer science, physics, environmental disciplines, astrophysics and biomedicine, amongst others. The contents will also be of interest to post-doctoral fellows in academia and industry, as well as to academics and practitioners.

The course will combine lectures on the basic theory and numerical methods, with practical activities involving computer-based experimentation using the DualSPHysics open-source software provided with the course material.


The course will include a practical hands-on session using the open source code DualSPHysics, an international collaboration between five institutions: The University of Manchester (UK), The University of Vigo (Spain), Flanders Hydraulics (Belgium), University of Lisbon (Portugal) and the University of Parma (Italy):


The SPH method

Developed originally for astrophysics, the method Smoothed Particle Hydrodynamics (SPH) has seen rapid development in the last decade for application to engineering problems for both fluids and solids. The meshless and Lagrangian nature of SPH makes it perfect for applications where there is very large deformation with arbitrarily complex moving boundaries. The method is now attracting considerable interest from industry for solving a range of difficult problems where conventional Computational Fluid Dynamics (CFD) methods and Computational Mechanics have great difficulty.


Course detailed Programme

 Day 1 – Tuesday 19/02/2019
8:30 – 9:00 Welcome ceremony and course introduction
9:00 – 11:00             Fundamentals of meshless spatial interpolations (SPH, Moving Least Square, Radial Basis Functions) and consistency of SPH interpolation
11:00 – 13:00 SPH discretization of continuity and Euler equations for compressible fluids
Day 2 – wednesday 20/02/2019
9:00 – 11:00 second-order SPH operators, time integration schemes, boundary conditions
11:00 – 13:00 SPH through Lagrangian, introduction to data structures for SPH numerical schemes
 Day 3 – Thursday 21/02/2019
9:00 – 11:00 High Performance Computing applied to Smoothed particle Hydrodynamics
11:00 – 13:00 Latest achievements and Current Challenges
14:30 – 18:30 Practical training for DualSPHysics – exercises in the computer lab



The course will take place at the Engineering and Architecture department of University of Parma:


Dipartimento di Ingegneria e Architettura

Parco Area delle Scienze, 59,

43124 Parma PR



Contact person



Please register here:

Registration is free of charge.


Course Lecturer:

Prof. Benedict Rogers

benProfessor Benedict Rogers is the Chair of Computational Hydrodynamics at the School of Mechanical, Aerospace and Civil Engineering (MACE) in the University of Manchester. With his doctoral studies in numerical simulation of free-surface flow for shallow water, he has more than 15 years of experience of SPH research having published over 55 journal papers on SPH investigating fundamental formulations, hardware acceleration and engineering applications such as wave breaking, wave impact and multi-phase flows. He is the current Chair (2015-2020) of the Smoothed Particle Hydrodynamics rEsearch and engineeRing International Community (SPHERIC), the international organization representing developers, users and researchers of SPH.

Dr. Renato Vacondio

renaRenato is an SIR (Scientific independence of Young Researchers) Research Fellow at the University of Parma. He obtained his PhD from the University of Parma in Italy on SPH developing a new methodology for solving shallow water flows. His research focuses on the development of variable resolution for SPH including particle splitting and merging within DualSPHysics for the Navier-Stokes equations. He organised the 2015 SPHERIC International SPH workshop at the University of Parma, is a member of the Steering Committee of SPHERIC.

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