1122 words - 4 pages

1 Introduction

Surface Tension is one of the many forces that shape the behavior of water and other fluids when they interact among themselves leading to an interface between them. In computer based simulations, especially in Computer Graphics field, this force is usually omited because it is considered that there is no significant effect when applying it. This is speccialy true when the object of the simulation is a large scale volume of fluid, in the opposite case, low scale fluid simulations show and need surface tension to achive realistic results.

Afer presenting the physical background and context needee for our simulation we will present our method to improve the quality of the simulation through the inclusion of Surface Tension.

In this work we apply Surface Tension force to a fluid solver. We describe how to modify the fluid solver to included this new force, and analize the numerical and visual results obteined from the experiment. We apply the new force is a coarse grid to improve the lack of quality due to the lack of detail in the datasctucture. Finally we present our results and conclusions.

2 Related Work

Surface Tension simulations have been studied by several related fields (e.g. Physics, Chemestry, Scientific Computing, Computer Graphics, etc.) each one with its own emphasis and goals.

Physics wants 100% accurate results and a deeper understanding of the phenomena.

Scientific Computing is usually more concerned about the underneath algorithms and the numerical precision.

In the other hand Computer Graphics, as most of the time, is concerned about getting the closest result possible in the minimum time. For this regard most of the time it has to sacrifice some information. In fluids simulations it often is surface tension.

In computer based simulations there two different scenarios when simulating fluids. The first one is when whe simulation large scale amounts of the fluid and the second one is when we simulate small-scale amoutns of the fluids. In the former case you can review [wang2005water, rousseau2006realistic, zhang2012deformable].

For small-scale fluid simulations the reader could read . Small-scale basically mean simulation of drops which size is not beger that 3mm in most cases.

3 Physical Background

In this section we briefly review the most important concepts we need to undestand our fluid simulation, and refer the reader the the appropiate documentation available. The problem is model using Navier-Stokes equations. The difference and relationship with Young equations.

The Navier-Stokes equations are:

\frac{\partial\vec{u}}{\partial t}+\vec{u}\cdot\nabla\vec{u}+\frac{1}{\rho}\nabla p=\vec{g}+\nu\nabla\cdot\nabla\vec{u}

\nabla\cdot\vec{u}=0

The Young equations is:

\gamma_{SG}=\gamma_{SL}+\gamma_{LG}\cos\theta

For the interpretation of the presented equations refer to [tab:Nomenclature].

Nomenclature

For a method of simulation equation [eq:young] the reader can refer to[wang2005water].

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