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虚拟现实

模拟方法

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Multiple-scale Simulation Method for Liquid with Trapped Air

under Particle-based Framework

Sinuo Liu

Ben Wang

†

Xiaojuan Ban

‡

Beijing Advanced Innovation Center for Materials Genome Engineering,

School of computer and communication Engineering,

University of Science and Technology Beijing

ABSTRACT

Trapped air in liquid is an important factor which affect the realism

of ﬂuid simulation. However, due to the complex physical properties,

simulating the interaction and transformation between air and liquid

is extremely challenging and time-consuming. In this paper, we

propose a multi-scale simulation method under particle-based frame-

work to achieve the realistic and efﬁcient simulation of air-liquid

ﬂuid. A uniﬁed generation rule is proposed according to the kinetic

energy and the velocity difference between ﬂuid particles. Two

velocity-based dynamic models are then established for different

size of air materials respectively. The Brownian motion of small

scale air materials is achieved by Schilk random function. The inter-

action and air transfer between large scale air materials is achieved

by inverse diffusion equation and a new high-order kernel function.

Experimental results show that the proposed method can improve

the ﬁdelity and richness of the ﬂuid simulation. The post-processing

scheme makes it able to be integrated with existing particle method

easily.

Index Terms:

Computing methodologies—Computer graphics—

Animation—Physical simulation

NTRODUCTION

Existing ﬂuid simulation methods, including particle-based meth-

ods and grid-based method, is able to describe the macroscopic

motion trend of the ﬂuid realistically [3, 8, 39], which puts higher

requirements on the detail simulation (spray [17], foams [4], turbu-

lence [22, 38], etc.). Liquid with trapped air is essentially a mixture

of a large amount of liquid and a small amount of air. Due to nucle-

ation [9, 32], trapped air [18, 31], and boiling [21, 30], air materials

with different physical properties are generated in ﬂuid. Without

these air materials, the realism of ﬂuid animation will decreased

signiﬁcantly. However, the physical laws of the generation, inter-

actions, dissipation and mass transfer are extremely complex. This

make it difﬁcult to simulate air materials in ﬂuid realistically.

The study of air-liquid ﬂuid is mainly divided into two types

according to their size. When modeling of the large-size air mate-

rials [1, 21], the ﬂuid is usually regarded as a air-liquid two-phase

ﬂuid, and a complex physical model will be established including

buoyancy force and drag force. This type of models are able to

describe the shape change of bubbles vividly, but the calculation

process is very time consuming [15]. Besides, the phenomenon of

mass transfer between bubbles cannot be well described.

As for the simulation of the small size air materials, the shape and

size of the particles is usually ignored, and only the macroscopic

motion trend is described [14]. Generally, this type of model is

e-mail: liusinuo@xs.ustb.edu.cn

†

e-mail: ben ben wang@yeah.net

‡

Corresponding author, e-mail: banxj@ustb.edu.cn

a post-processing model which can enhance visual effects with

negligible computational overhead. However, it usually focuses on

only the free surface. Since most details are lost, its advantages can

only be achieved when shooting from a long distance. Besides, if

Brownian motion is not considered, large number of air particles

will move with similar motion patterns, which result in a extremely

regular periodic distribution and affect the visual effect [18]. In

real life, air bubbles of different sizes (like large bubbles and small

foams) are usually generated at the same time. Simulating different

scales of air materials simultaneously in a uniﬁed framework can

achieve a more realistic results.

In order to combine the advantages of the above two methods,

we propose a uniﬁed multiple-scale air material simulation method

for particle-based ﬂuid. In this paper, areas where entrapped air are

determined by the kinetic energy and velocity difference of ﬂuid

particles. air materials are divided into six different types depending

on the size and coupling degree with the ﬂuid, and different dy-

namic models are designed separately. By ignoring the feedback of

small-mass air particles on large-mass ﬂuid particles, efﬁcient one-

way coupling is achieved through the velocity ﬁeld, which greatly

improves the calculation efﬁciency. The Brownian motion of air ma-

terials is simulated using a random emitter. The interaction between

the air particles is described by a new high-order kernel function

based on Lennard-Jones function to ensure their stable status con-

forms to Plateau equilibrium distance. An inverse diffusion equation

was introduced to describe the air transfer between two large-scale

air particles. The main contributions of this paper are as follows:

•

A multiple-scale air material simulation method under uniﬁed

particle-based framework, with adjustable control parameters

to achieve different visual effect.

•

A new dynamics model for large-size air material, including

air transfer model based on the inverse diffusion equation, and

interaction scheme using a new high-order kernel function.

•

A new dynamics model based on Schilk random function for

small-size air material, which solve the problem of regular

distribution of air particles by implementing Brownian motion.

2RELATED WORK

Fluid simulation is an important research topic in computer graphics.

With the development of the entertainment industry and Virtual

Reality, the demand for ﬂuid simulation is increasing [40, 41]. For

better understanding of the whole research area, we recommend the

groundbreaking work of Stam [33] and the book of Bridson [6]. In

this section, we discuss related work on ﬂuid simulation (section 2.1)

and air materials simulation (section 2.2).

2.1 Fluid Simulation

Fluid motion can be described in two forms: Euler description based

on the spatial point of the ﬂow ﬁeld and Lagrangian description

based on the ﬂuid particle. Therefore, ﬂuid simulation methods

842

2020 IEEE Conference on Virtual Reality and 3D User Interfaces (VR)

DOI 10.1109/VR46266.2020.00011

(a) real scene (b) μ = −10,σ = 1

Figure 1: Injecting water into a pool with 29k ﬂuid particles. (a) is the real scene, (b)(c)(d) are the simulation results with particle result on the left

and rendered result on the right. In particle result, small size air materials and large size air materials are marked as red dot and blue sphere,

respectively. By adjusting control parameter

in Eq.5, the occupation of large air particle is changed, and different styles are realized. The

proportion of large-sized particles in (b)(c) and (d) is 0%, 8.23% and 13.80%, respectively. The visual effect in (d) is more similar to real scene.

are also divided into two categories: grid-based Euler method and

particle-based Lagrangian method [35]. Both methods are based

on the ﬂuid’s control equations but differ in discretization process.

Since the discretization is more regular, it is easy for grid method

to derive simple formulas that are easy to calculate. However, due

to the limitations of ﬁxed grid points, its spatial ﬂexibility is not

as good as particle-based method. For intense or complex scenes,

particle-based method is able to capture details better.

Air-liquid ﬂuids are usually generated in highly deformed ﬂuids.

Therefore, the Lagrange-based method is very suitable for simulating

scenes containing air materials. In this paper, we use a classical

particel-based method, Smoothed Particle Hydrodynamics (SPH

method) [27] for ﬂuid simulation. For the latest development, we

would like to refer to two reviews [20] and [15].

2.2 Air Material Simulation

In terms of air-liquid ﬂuid simulation, it can be divided into

three categories according to the generating mechanism: trapped

air(section 2.2.1), nucleation and boiling(section 2.2.2). Our method

is illustrated in section 2.2.3.

2.2.1 Trapped Air

When moving intensely or rushing quickly, air will be trapped in

ﬂuid. This type of air materials are usually divided into two cate-

gories according to their size, and the simulation mechanisms are

also different.

Large Size Air Materials. Many researches focus on the cou-

pling of air-liquid two-phase ﬂow. Air materials, such as bubbles and

foam, are considered as air phase and be simulated as macroscopic

air bubbles in ﬂuids [10].

In 2005, Muller et al. [28] proposed a bubble generation rule

based on the color ﬁeld, which can generate bubble particles in the

SPH multi-phase ﬂow solver dynamically. Hong et al. [13] used the

SPH method to simulate non-deformable bubbles, and used a level

set method to simulate deformable bubbles and ﬂuids. Air and liquid

are coupled through a velocity ﬁeld. However, due to the limitation

of the grid resolution, this method is difﬁcult to simulate the unstable

motion when bubbles rising. Akinci et al. [1] separately processed

the air-liquid two phases, calculated the density and pressure of

the two phases using SPH method, and simulated the interaction

of the two phases through the velocity ﬁeld. This method solves

the problem of high density ratio and can simulate complex bubble

motion in water. However, since the SPH method must ensure a

certain initial particle spacing, the number of bubble particles is

limited by the resolution of the ﬂuid particles. In 2012, Busaryev

et al. [7] proposed an algorithm to simulate bubbles in dense foam.

By applying strong interactions, the arrangement and geometry of

bubbles are more in line with physics laws. Ren et al. [31] used

volume fraction representation to simulate various bubble effects in

multiphase ﬂow simulations. The deformation and dissolution of

bubbles, and accumulation of foams can be handled simultaneously.

Small Size Air Material. Some research ignored the effect of

air phase to the liquid phase, to avoid the excessive calculation cost

in multiphase ﬂow model.

Takahashi et al. [34] combined a grid-based ﬂuid solver (Con-

strained Interpolation Proﬁle, CIP method) with a particle-based air

material solver and proposed a splash and foam simulation method.

Air particles are added at area with larger curvatures over free surface.

In 2007, Th

urey et al. [36] proposed a bubble and foam simulation

method based on shallow water equations. This method can simu-

late scene with millions of air particles, but the simpliﬁed equation

makes it difﬁcult to describe the interaction of the ﬂuid. Onderik et

al. [29] used particle emitter to simulate waves in the ocean. Bubble

particles concentrated on the peaks of the waves can be modeled real-

istically. In order to speed up the simulation, the interaction between

bubble particles is ignored. Inspired by the work of Onderik [29]

and Takahashi [34], Ihmsen et al. [14] proposed to simulate the air

materials (bubble, foam, and spray) in the waves using a uniﬁed

particle system. Through a post-processing velocity-based coupling,

the motion of the air materials can be efﬁciently simulated. However,

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