Smoothed Particle Hydrodynamics (SPH) with PySPH

This comprehensive course is designed to guide you from the fundamental principles of Smoothed Particle Hydrodynamics (SPH) to the development and execution of complete SPH simulations using PySPH, an open-source, Python-based SPH framework developed at IIT Bombay. Whether you are new to meshless methods or an experienced CFD engineer looking to expand your skill set, this course offers a structured and practical pathway to mastering SPH-based simulations.

You will begin by developing a solid understanding of the mathematical foundations of SPH, including particle approximation, kernel interpolation, and gradient formulations. The course carefully explains how SPH replaces traditional mesh-based discretization with particle interactions, making it especially powerful for problems involving large deformations, free surfaces, and complex physics. Concepts such as interpolation methods, kernel functions, and density formulations are introduced step by step and directly connected to their implementation in code.

A major focus of this course is hands-on implementation using PySPH. You will learn how to install and configure PySPH along with its supporting libraries, including Compyle and Cyarray, using Conda. To ensure a smooth learning experience across platforms, the course also demonstrates how to run PySPH using Docker, allowing you to work without complex local installations. Throughout the course, you will write real SPH codes in Python, create particle arrays, define physical fields, group equations, and configure solver structures from scratch.

As you progress, you will implement core SPH equations such as momentum, energy, and density summation, explore Gaussian kernels and their properties, and build custom time integrators, including an explicit Euler scheme. These concepts are reinforced through classic benchmark problems such as the Shock Tube and Dam Break simulations, giving you practical insight into solver behavior, numerical stability, and physical interpretation of results.

By the end of this course, you will be able to independently build, run, and analyze SPH simulations using PySPH. You will also gain experience exporting simulation results and visualizing them using tools such as ParaView and Mayavi. This course equips you with both the theoretical understanding and practical workflow needed to apply SPH methods to real-world engineering and research problems using a fully open-source toolchain.