Lecturers Prof. Petros Koumoutsakos, Shilpa Khatri 
Class Room ETZ H91 (Lecture)
ETZ H91 (Exercise) 
Class Times Fridays, 08.00 – 10.00 (Lecture)
Fridays, 10.00 – 11.00 (Exercise)
Wim van Rees, CAB F84, wvanrees_AT_inf.ethz.ch 
Grading Homework: 35%
Final Exam: 65% 





Mechanics principles can be used to model phenomena ranging from turbulent fluid flows to biological cell motion. The simulation of such systems requires the development and implementation of numerical methods capable of resolving complex, multi-scale phenomena that evolve in multiscale deforming geometries. In recent years advances in particle methods have lead to the formulation of particle methods capable of simulating such systems across several scales. 

Particle simulations can be formulated by following the motion of interacting particles that carry the mechanical properties of the system under consideration. The simplicity of the method enables modeling of diverse phenomena ranging from deforming tissue to granular flows. In this class we present the fundamental aspects of simulations using particles leading to the development of a multi-scale framework for computational mechanics. 

The course will cover, but will not be limited, to the following: Particle simulations of continuum and discrete systems, fast summation algorithms, time integrators, constraints, and multi-resolution. We will present a unifying framework for various particle methods and discuss in this context common elements and differences of techniques such as Smoothed Particle Hydrodynamics, Discrete Element Methods and Molecular Dynamics. 


Lecture 1: Time Integrators for Particle Methods: notes, handout
Lecture 2: Introduction and Time Integrators for Particle Methods
Lecture 3: Constrained Mechanical Systems: notes, handout
Lecture 4: Point particle approximations: notes, handout
Lecture 5: Smooth particle approximations: notes

Lecture 6: Eulerian and Lagrangian description of transport equations and smoothed particle hydrodynamics (SPH) (Additonal resources 4 and 5 are relevant): notes
Lecture 7: Golden Rules of SPH and Derivative Approximations in SPH: notes
Lecture 8: Kernels in SPH, RKPM, Continuum Mechanics (Additonal resources 8, 9, 10, and 11 are relevant): notes
Lecure 9: RKPM and Conservation Laws (Additional Resources 9, 10, 11, 12, and 13 are relevant): notes
Lecture 10: Particle Mesh Simulations (Suggested Text 1, Chapter 7 is relevant): notes, handout
Lecture 11: Particle Mesh Simulations continued
(Suggested Text 1, Chapter 7 is relevant): notes, handout

Homework 1 (NOTE: this is a two-week homework, it is due March 19th)
    Example of making an animation with Paraview: demonstration, data format.

Homework 2
Homework 3 (NOTE: this homework is due April 16th)
Homework 4
Homework 5 (Burgers’ equation exact solution: mov, Matlab files for SPH solution: zip)
Homework 6
Homework 7 (Plots of solution: zip)
Homework 8
Homework 9 (Plots of solution: zip)

Suggested Texts:
1. Cottet, GH and Koumoutsakos, PD – Vortex Methods, Theory and Practice
2. Hockney, RW and Eastwood, JW – Computer simulation using particles

Additional Resources:
1. Hairer, E., Lubich, C. and Wanner, G. – Geometric Numerical Integration: Structure-Preserving Algorithms for ODEs (only accessible from within ETH domain)
2. Werder, T. et al. – On the Water-Carbon Interaction for Use in Molecular Dynamics Simulations of Graphite and Carbon Nanotubes

3. Pöschel, T. and Schwager, T. – Computational Granular Dynamics (only accessible from within ETH domain)
4. Roulstone, I. – Lagrangian Dynamics
5. Monaghan, J. J. – Simulating Free Surface with SPH
6. Monaghan, J.J. – Smooth Particle Hydrodynamics (2005)
7. Brookshaw, L. – A method of calculating radiative heat diffusion in particle simulations (1985)
8. Liu, M.B., Liu, G.R., and Lam, K.Y. – Constructing smoothing functions in smoothed particle hydrodynamics with applications (2003)
9. Liu, W.K., Sukky, J., Li, S. Adee, J, and Belytschko, T. – Reproducing Kernel Particle Methods for Structural Dynamics (1995)
10. Panton, R.L., Incompressible Flow
11. Acheson, D.J., Elementary Fluid Dynamics
12. Franke, R. – Scattered Data Interpolation: Tests of Some Methods (1983)
13. Lancaster, P. and Salkauskus, K. Surfaces Generated by Moving Least Squares Methods (1981)