Title: From granular avalanches to fluid turbulences through oozing pastes. A mesoscopic physically-based particle model
ArXiv ID: 1005.3190
Date: 2010-05-18
Authors: Annie Luciani
📝 Abstract
In this paper, we describe how we can precisely produce complex and various dynamic morphological features such as structured and chaotic features which occur in sand pilings (piles, avalanches, internal collapses, arches) , in flowing fluids (laminar flowing, Kelvin-Helmholtz and Von Karmann eddies), and in cohesive pastes (twist-and-turn oozing and packing) using only a single unified model, called "mesoscopic model". This model is a physically-based particle model whose behavior depends on only four simple, but easy to understand, physically-based parameters : elasticity, viscosity and their local areas of influence. It is fast to compute and easy to understand by non-physicist users.
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Deep Dive into From granular avalanches to fluid turbulences through oozing pastes. A mesoscopic physically-based particle model.
In this paper, we describe how we can precisely produce complex and various dynamic morphological features such as structured and chaotic features which occur in sand pilings (piles, avalanches, internal collapses, arches) , in flowing fluids (laminar flowing, Kelvin-Helmholtz and Von Karmann eddies), and in cohesive pastes (twist-and-turn oozing and packing) using only a single unified model, called “mesoscopic model”. This model is a physically-based particle model whose behavior depends on only four simple, but easy to understand, physically-based parameters : elasticity, viscosity and their local areas of influence. It is fast to compute and easy to understand by non-physicist users.
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Since the first use of physically-based modeling in Computer Animation and Simulation in the middle of the 80's [1][2], many works have been supported by physically-based particle models. But only few focus on changes in matter states. Most of these developed models for specific categories of natural phenomena. Several concern the simulation of fluid features [3][4] [5][6] [7] [8]. Others concern the simulation of amorphous materials [9] and a very few concern the simulation of granular materials [10]. For the majority of these studies, the classical continuous formulation was chosen.
However, studying the changes in matter form is probably the best way to evaluate the level of genericity of a modeling method. It is also an efficient way of evaluating the perceptual quality of the motion by allowing the user to compare categories of commonly observed but nevertheless complex dynamic forms.
Many authors point out that the purpose of Computer Graphics in physically-based modeling is quite different from Physics. Particularly, two other qualities are required:
Computer Graphics tools must be available to nonphysicist users. The main challenge for these tools is to allow to the non-physicist user to model himself the phenomenon he wants, through a single method.
Computer Graphics look for a high perceptual and cognitive quality of motion. Visual perception is probably the most adapted sensor to distinguish, evaluate, categorize, or compare fine and accurate complex dynamic morphological features: the consistency of a syrupy elastic paste; the difference between sand, sugar, and volcanic lava; and between steam or smoke particles.
If particle methods are the most generic methods, they are often seen as quite rough in the restitution of motion of accurate categories of complex phenomena.
Thus, our purpose is to design a single physically-based particle model capable of synthesizing fine dynamic characters of well-known complex phenomena, according to a clear specification of their main pertinent figures, such as:
• Granular materials and their well-shaped piles, avalanches and collapses; fluids and their stable and turbulent states; oozing pastes with their flowing twists and turns.
• states changes between them : from solid (rigid or deformable), to pure kinetic gas through granular collapsing, pastes, stable laminar and turbulent fluid.
In 1989-1991, soon after the introduction of physical modeling in Computer Animation, four founding works were performed : Miller and Pearce [11], Terzopoulos and al. [12], Tonnesen [13 ], and Luciani and al. [14][15]. These studies differ on some aspects but they all point to a common issue: the need for a single unified model to simulate the different states of matter, and the need for a generic computer animation modeler.
At that time, these works explored only rough, simple figures of matter states and changes. Though these studies seem to be dated, they remain relevant because they are based on fundamental theories. They contain a large amount of potentialities for Computer Graphics and continue to play the role of pioneer on the non-solved question of genericity. It is surprising that they have not been more widely noted. It is probably the search for complex motions that has pushed computer graphics researchers to develop specific methods for categories of phenomena. The wide use of Navier-Stokes equation to simulate fluids is the most spectacular example.
The works referenced before were inspired by a common theory, investigated by Greenspan since 1973 [16][17]. But they adopt different solutions in adapting this theory. We analyze first the main ideas of these works. After, in the next paragraph ( §3), we discuss their fundamentals in relation to basic concepts in Physics and we outline the basis of our approach.
The Greenspan approach assumes that all physical behavior emerges from the microscopic level and that it is possible to reproduce this behavior by considering only the laws which play at this level. Physical objects are described as set of interacting particles interacting one to another through a potential conservative law. This interaction function supports not only the simple molecular collision as in pure kinetic gas, but a cohesion interaction, like the well-known experimental Lennard-Jones interaction function.
International Conference Graphicon 2000, Moscow, Russia, http://www.graphicon.ru/
Its general expression is then
,drawing three important features:
It presents three zones: a pure attractive zone for large distances, a pure repulsive zone for very short distances, and an intermediate zone in which the combination of the attractive and repulsive effects causes the cohesion effect.
It is mathematically expressed by a sum of two terms: the attractive term and the repulsive term.
Each term is a non-linear function of the interparticle distance.
To simulate the granular or finer states (liquid or powder), the four works referenced befo
