Abstract
This chapter covers the design and implementation of particle systems as a collection of point mass objects that can collide with each other and other rigid-body objects in the simulation. Even though this is one of the simplest models of particle systems that can be used, the computational efficiency and degree of realism that can be attained with these systems is highly attractive. This chapter also discusses in details the use of spatially dependent interaction forces to model particle-based fluid simulations including a detailed overview of Smoothed Particle Hydrodynamics (SPH).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Recall from Sect. 2.4 that the cell decomposition defines a uniform subdivision of the simulated world.
- 2.
The local-coordinate frame is defined by the collision normal and tangent plane.
- 3.
When collision becomes a contact, the collision normal will also be referred to as the contact normal.
- 4.
Notice that F t is zero if a t (t) is zero.
- 5.
Later in this section, we shall relax this assumption to show how the system of equations used in the frictionless case can be expanded to handle friction.
- 6.
These coefficients need only be computed if friction is taken into account. In the frictionless case, both F t and F k are zero.
- 7.
Here, we are already using the result of Sect. 3.5.3 that the matrix A is all zero, save for its diagonal elements.
- 8.
Notice that the contact force acting on particle O 2 because of contact C j can be \(+\vec{F}_{j}\) or \(-\vec{F}_{j}\), depending on particle O 2 having index 1 or 2 with respect to contact C j . The following derivations assume the contact force is \(+\vec{F}_{j}\).
References
Adams, B., Pauly, M., Keiser, R., Guibas, L.J.: Adaptively sampled particle fluids. Comput. Graph. (Proc. SIGGRAPH) 26 (2007)
Beer, F.P., Johnston, E.R.: Vector Mechanics for Engineers: vol. 2—Dynamics. McGraw-Hill, New York (1977)
Becker, M., Müller, M.: Weakly compressible SPH for free surface flows. In: SIGGRAPH Symposium on Computer Animation, pp. 1–8 (2007)
Borve, S., Omang, M., Truslen, J.: Regularized smoothed particle hydrodynamics with improved multi-resolution handling. J. Comput. Phys. 208, 345–367 (2005)
Brach, R.M. (ed.): Mechanical Impact Dynamics: Rigid Body Collisions. Wiley, New York (1991)
Bridson, R.: Fluid Simulation. AK Peters, Wellesley (2008)
Baraff, D., Witkin, A.: Physically based modeling. SIGGRAPH Course Notes 13 (1998)
Foster, N., Metaxas, D.: Realistic animation of liquids. In: Proceedings Graphics Interface, pp. 204–212 (1996)
Foster, N., Metaxas, D.: Modeling the motion of a hot, turbulent gas. Comput. Graph. (Proc. SIGGRAPH) 31, 181–188 (1997)
Frenkel, D., Smit, B.: Understanding Molecular Simulation from Algorithms to Applications. Academic Press, San Diego (1996)
Kipfer, P., Westermann, R.: Realistic and interactive simulation of rivers. In: Proceedings of Graphics Interface (2006)
Liu, G.R., Liu, M.B.: Smoothed Particle Hydrodynamics. World Scientific, Singapore (2003)
Müller, M., Chentanez, N.: Solid simulation with oriented particles. Comput. Graph. (Proc. SIGGRAPH) 30 (2011)
Müller, M., Charypar, D., Gross, M.: Particle-based fluid simulation for interactive applications. In: SIGGRAPH Symposium on Computer Animation (2003)
Reeves, W.T.: Particle systems—a technique for modeling a class of fuzzy objects. Comput. Graph. (Proc. SIGGRAPH) 17, 359–376 (1983)
Solenthaler, B., Bucher, P., Müller, M., Gross, M.: SPH based shallow water simulation. In: Proceedings of Virtual Reality Interaction and Physical Simulation, pp. 39–46 (2011)
Stam, J., Fiume, E.: Depicting fire and other gaseous phenomena using diffusion processes. Comput. Graph. (Proc. SIGGRAPH) 29, 129–136 (1995)
Solenthaler, B., Pajarola, R.: Predictive-corrective incompressible SPH. Comput. Graph. (Proc. SIGGRAPH) 28 (2009)
Stam, J.: Stable fluids. Comput. Graph. (Proc. SIGGRAPH) 33, 121–127 (1999)
Wilkins, M.L.: Computer Simulation of Dynamic Phenomena. Springer, Berlin (1999)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag London
About this chapter
Cite this chapter
Coutinho, M.G. (2013). Particle Systems. In: Guide to Dynamic Simulations of Rigid Bodies and Particle Systems. Simulation Foundations, Methods and Applications. Springer, London. https://doi.org/10.1007/978-1-4471-4417-5_3
Download citation
DOI: https://doi.org/10.1007/978-1-4471-4417-5_3
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4416-8
Online ISBN: 978-1-4471-4417-5
eBook Packages: Computer ScienceComputer Science (R0)