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Abstract
This course provides an introduction to particle-based methods for the numerical resolution of partial differential equations describing continuum phenomena or for the simulation of particulate flows. Details are given for the Material Point Method (MPM) and the Discrete Element Method (DEM).
Objective
By the end of the course, the student must be able to: - Describe the difference between the Eulerian and Lagrangian approaches - Identify and apply the different steps in a numerical simulation (e.g. geometry and mesh generation, computation, post-processing) and integrate all the essential basic concepts in a numerical flow simulation - Describe different methods used to discretize differential equations, such as finite differences, finite elements, MPM, SPH, PFEM - Perform a numerical simulation with appropriate software; understand the limits of each software in terms of its application domain and accuracy of the results obtained
Content
Particle-based computational methods are being increasingly employed for solving a variety of problems in engineering and applied science. While such methods can yield significant advantages compared to traditional mesh-based methods, their accurate and efficient implementation also provides a number of challenges. This course presents the fundamental aspects of two methods: Material Point Method (MPM) is a hybrid Eulerian-Lagrangian numerical scheme for solving continuum mechanics problems. It is particularly well suited to simulate problems involving large deformations, collisions, fractures and the interaction between different materials (solids, fluids and gases). Material points are used to track the motion and carry information while a background mesh is used to compute spatial gradients. Discrete Element Method (DEM) is used for simulating granular and particulate flows and tracks particle motions and detects and models collisions between particles and with their environment. It relies on the equations of Newton and a variety of contact models. The course provides an introduction to these two methods and their domains of application (e.g. fluid and solid mechanics, computer graphics). The theoretical basis of each method is presented in introductory lectures. Following a literature search, students give oral presentations on a specific article about DEM or MPM and explain more advanced aspects. Mini-project using open-source softwares provide practical experience in the application of these methods. Illustrations of the use of particle-based methods is also provided by researchers from industry and other universities.
General Information
- Language
- English
- Levels
- MSC
- Frequency
- Yearly recurring
Examination
- Type
- graded semester performance
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise |
Particle-Based Methods (EPFL)
**Course at EPFL**
|
No time listed | 4 h weekly |
Offered In
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Nuclear Engineering Master (MSc Nuclear Engineering is a joint program of EPF Lausanne and ETH Zurich. The first semester takes place in Lausanne. Students therefore have to enroll at EPFL. For more information about the curriculum and courses see: )
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