Smoothed Particle Hydrodynamics numerical methods

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This is a short course on Smoothed Particle Hydrodynamics (SPH) numerical schemes that will cover basic and theoretical concepts, as well as latest innovations. This course is primarily aimed at the beginners with a Master and/or a PhD degree 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 SPH practitioners.

The course will combine lectures on the basic theory and numerical methods.
It will also include a final tutorial using the open source code DualSPHysics, an international collaboration between five institutions: The University of Manchester (UK), The University of Vigo (Spain), Universitat Politècnica de Catalunya (Spain), University of Lisbon (Portugal), the University of Parma (Italy), and New Jersey Institute of Technology (United States):


The SPH method

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


Course detailed Programme (19/10/2020 – 22/10/2020)

 Day 1
Intro (0.5 hours) Welcome and course introduction
Lecture 1 (4 hours Fundamentals of meshless spatial interpolations
(SPH, Moving Least Square, Radial Basis Functions)
and consistency of the SPH interpolation.
Day 2
Lecture 2 (2 hours) SPH discretization of continuity and Euler equations
for compressible fluids
Lecture 3 (4 hours) Second-order SPH operators, time integration schemes,
boundary conditions
 Day 3
Lecture 4 (2 hours) Arbitrary Eulerian – Lagrangian SPH schemes
Lecture 5 (2 hours) SPH through Lagrangian, introduction to data structures
for SPH numerical schemes
 Day 4
Lecture 6 (4 hours) Introduction to the open-source software DualSPHysics



The course will be virtual, a link will be provided to people registered to attend the online classes.


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

renaDr. Renato Vacondio 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 is a member of the Steering Committee of SPHERIC as well as the newsletter editor.

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