KR101319996B1 - Method for simulating fluid - Google Patents

Abstract

The present invention comprises the steps of (a) modeling a fluid into sphere particles; (b) converting the sphere particles into elliptical sphere particles; (c) converting the elliptical sphere particle into a global coordinate system; And (d) rendering the surface of the fluid using the determined particles in the global coordinate system, wherein step (b) is performed with neighboring particles within a predetermined distance from each of the elliptic sphere particles. In consideration of the interaction, the interpolated physical quantity is obtained based on each particle, and the step (d) calculates the surface mesh of the elliptic sphere particles to render the surface of the fluid determined by the particles. And reducing the curvature of the surface mesh by changing the potential value of the ellipsoidal sphere particle to a signed distance function.

Description

Fluid simulation method {METHOD FOR SIMULATING FLUID}

The present invention relates to a fluid simulation method and a recording medium thereof.

Fluid simulation plays a big role in various contents production fields such as movies, animations, and games. In the past, it used a method of overlaying a texture on a three-dimensional figure, which consumed a lot of time and effort, but decreased the realism. However, with the development of technology, a fluid simulation method based on real physics has been used much more recently. It creates realistic movements.

There are two methods for simulating fluids: the lattice based method based on Euler's method and the particle based method based on Lagrange's method. Grid-based methods can produce realistic motion, but they are often used in movie production because they require a lot of computation. Particle-based methods are used for game production that requires real-time calculation.

The Navier-Stoke's equation, the fluid motion equation, is the basis of fluid simulation. Smooth Particle Hydrodynamics (SPH), a method of representing fluids as sphere particles, discretizes this equation to calculate the physical quantities required by the interaction of each sphere particle.

The number of particles depends on the resolution, which affects the realism and physical accuracy of the fluid's movement. Increasing the number of particles, however, increases the cost of computation and must be compromised on an appropriate basis. Accordingly, the present invention proposes a method for realistically and delicately expressing the motion of a fluid without increasing the number of particles by using elliptical particles instead of spherical particles.

In addition, by reducing the number of particles used to calculate the physical quantity, the computational cost is greatly reduced, and a method of expressing the surface more realistically when rendering is proposed.

In this regard, Korean Patent Laid-Open Publication No. 10-2010-0066976 ("Method for simulating fluid in uncompressed state, recording medium, apparatus, system") discloses a configuration for simulating a fluid in an uncompressed state.

In addition, Korean Patent No. 10-0568563 ("Real-time fluid flow simulation and rendering method using particle dynamics analysis and volume rendering techniques") discloses a configuration that represents the motion and three-dimensional feeling of the fluid.

SUMMARY OF THE INVENTION The present invention has been made to solve the above problems, and an object thereof is to provide a fluid simulation method that realistically expresses the motion of a fluid at low cost.

A fluid simulation method according to the first aspect of the present invention for achieving the above object comprises the steps of (a) modeling a fluid as a sphere particle; (b) converting the sphere particles into elliptical sphere particles; (c) converting the elliptical sphere particle into a global coordinate system; And (d) rendering the surface of the fluid using the determined particles in the global coordinate system, wherein step (b) is performed with neighboring particles within a predetermined distance from each of the elliptic sphere particles. In consideration of the interaction, the interpolated physical quantity is obtained based on each particle, and the step (d) calculates the surface mesh of the elliptic sphere particles to render the surface of the fluid determined by the particles. And reducing the curvature of the surface mesh by changing the potential value of the ellipsoidal particle to a signed distance function.

The recording medium according to the second aspect of the present invention for achieving the above object is a computer-readable recording medium on which a program for performing the fluid simulation method according to the first aspect is recorded.

In the fluid simulation method, the present invention obtains the effect of more realistically representing the motion of a fluid.

In particular, in expressing the motion of a fast-moving fluid, detailed motion can be depicted without significantly increasing computational costs.

Specifically, the resolution of fluid motion can be increased without significantly increasing the number of particles required for modeling.

In addition, the calculation cost is reduced by limiting the number of particles used to calculate the physical quantity.

It also reduces curvature when rendering fluid surfaces.

1 shows a flow of a fluid simulation method according to the present invention.
2 shows the conversion of sphere particles into elliptical sphere particles.
Figure 3 shows how particles affect each other's physical quantities.
Figure 4 shows how to limit the number of other particles affecting the physical quantity of the particles.
5 shows the appearance of creating a surface mesh.
6 shows the appearance of reducing the curvature of the surface mesh.
7 shows an embodiment of a fluid simulation method according to the present invention.
8 shows an embodiment of a fluid simulation method according to the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings, which will be readily apparent to those skilled in the art. The present invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. In the drawings, parts irrelevant to the description are omitted in order to clearly describe the present invention, and like reference numerals designate like parts throughout the specification.

Throughout the specification, when a part is referred to as being "connected" to another part, it includes not only "directly connected" but also "electrically connected" with another part in between . Also, when an element is referred to as "comprising ", it means that it can include other elements as well, without departing from the other elements unless specifically stated otherwise.

1 shows the flow of a fluid simulation method according to the present invention.

First, briefly, the fluid is modeled as a sphere particle (S110), the elliptic sphere particles are converted (S120), and then converted into a global coordinate system (S130). After the location of each particle is derived, surface particles are generated using each particle, and the fluid is rendered by reducing the curvature of the surface mesh (S140).

Each fluid particle has a physical quantity such as mass m, density p, viscosity μ, pressure p, external force f, position r, and velocity u that affect each other. These physical quantities are expressed based on the Navier-Stokes' equation, which is a fluid motion equation as described above. The Navier-Stoke equation, which shows the law of conservation of momentum and mass of a fluid, shows the change of velocity u with the flow of fluid as

<Equation 1>

<Equation 2>

Modeling the fluid as a sphere particle (S110) is a step of discretizing the Navier-Stoke equation, which is a continuous function expressed as above, and expressing it as a sphere particle. If W is a smoothing kernel function of a sphere particle, the physical quantity A (r) interpolated as the sum of the physical quantities of particles having a distance less than h from the position r can be expressed by the following equation. .

&Quot; (3) &quot;

In the fluid simulation method according to the present invention, a curved kernel function is defined and used for each physical quantity. The following equations are kernels for calculating density, pressure, and viscosity, respectively.

&Lt; Equation 4 &

<Equation 5>

<Equation 6>

Let's look at the step (S120) of converting the spherical particles into elliptical sphere particles through FIG. The drawings show circles and ellipses in a two-dimensional plane for ease of explanation.

As described above, the use of elliptical particles in which the spherical particles are deformed by increasing the speed of the spherical particles in the direction of movement in the moving direction can improve the accuracy and the realism of the fluid movement without increasing the number of particles. This is because the weight increases according to the direction and receives more force. Therefore, a large number of particles, such as rain or shower water, can be effectively simulated.

To this end, the fluid simulation method according to the present invention sets the distance the sphere particles move for a unit time as shown in FIG. 2 as the distance between two focal points of the ellipse. When the length of the major axis is a and the length of the minor axis is b, the ellipse can be expressed by the following equation.

<Equation 7>

In addition, the fluid simulation method according to the present invention limits the length a of the long axis of the ellipse not to exceed the threshold. That is, a may be represented as follows, where a is set to a smaller value of the maximum value of a predetermined value and a value derived by the following equation.

<Equation 8>

<Equation 9>

This is to reduce the number of neighboring particles affecting each particle. Let's look through Figures 3 and 4.

3 shows how particles affect each other's physical quantities. Here is the reason why the equation for obtaining the interpolated physical quantity using particles in the above description can be derived. However, the greater the distance between particles, the less the impact, so it is a waste of computation to consider all the particles that make up a fluid when calculating the physical quantities around a particle.

However, in the prior art, the distance between all particles had to be calculated to determine the physical force, so that the calculation time greatly increased as the number of particles increased. That is, when n particles were required, it took O (n ² ) time since all particles had to be searched for each particle.

On the other hand, as shown in Figure 4 showing the limit of the number of other particles affecting the physical quantity of particles, in the fluid simulation method according to the present invention by dividing the search space into a lattice tailored to the ellipsoid particles You only need to calculate the distance between the ellipsoid particles within a specified number of grids. This greatly reduces the computation time to O (kn) because the physical quantities need only be searched for and reflected in the calculation for k particles located within a predetermined number of lattice. Here, dividing the search space into a lattice tailored to ellipsoid particles means that the lattice is set in consideration of the length of the long axis of the elliptical sphere.

After deforming the particle model of the fluid into an elliptic sphere to obtain all the necessary physical quantities (S120), the final position is determined by converting to a global coordinate system (S130). The conversion to the global coordinate system is performed by the product of the rotation matrix and the size transformation matrix, which is a diagonal matrix having the lengths of the major and minor axes of the ellipse.

If the position of each particle in the fluid model has been determined, it is necessary to actually render the fluid with this position data (S140). The fluid simulation method according to the present invention represents the surface of the fluid in a mesh. Let's look through Figures 5 and 6.

FIG. 5 illustrates the creation of a surface mesh, and FIG. 6 illustrates the reduction of the curvature of the surface mesh.

Conventional technologies, such as metaballs, have the disadvantage that the surface is curved. In contrast, the fluid simulation method according to the present invention divides the space into a lattice and sets the potential (kernel) value of the elliptical sphere particle at the vertex of the lattice to express the surface of the fluid as a mesh, and based on the value, Create If the potential value is negative, it is judged into water, if it is positive, it is judged out of water, and if it is zero, it is determined as water surface. An embodiment of the mesh thus created is shown in the second drawing of FIG. 5.

The surface mesh thus produced has a smaller curvature compared to conventional metabols. However, when the number of gratings is small, or when the phase change is severe, such as when the fluid merges or splits, the curvature may still be awkward as shown in the first drawing of FIG. 6.

In order to compensate for this and create a smooth surface mesh, the fluid simulation method according to the present invention converts the potential value into a signed distance function and reduces the curvature to make it flat. Then, the surface can be visualized more realistically as shown in the second drawing of FIG. 6.

는 표면의 위치이고,

은

에서의 표면 법선이며,

은 표면 장력 계수이다.

이 부호가 있는 거리 함수,

은 속도의 법선 방향 요소라고 하면, 이는 다음 수식들로 나타낼 수 있다.For this purpose it is assumed that any surface tension acts on the fluid surface and quickly converges to dynamic equilibrium.

Is the position of the surface,

silver

Is the surface normal at,

Is the surface tension coefficient.

This signed distance function,

If is a normal component of velocity, it can be expressed by the following equation.

<Equation 10>

<Equation 11>

<Equation 12>

Therefore, the fluid simulation method according to the present invention can control the degree of sharpness of the fluid surface by adjusting the surface tension coefficient.

7 and 8 illustrate an embodiment of a fluid simulation method according to the present invention.

FIG. 7 shows the results of a three-dimensional dam destruction experiment using 144,000 particles. It took 91.246 seconds to derive one frame from a 30fps animation.

8 shows the results of a shower experiment using 830,000 particles. The upper figures show the experimental results of the basic sphere particle based simulation method, and the lower figures show the experimental results of the elliptic sphere particle based simulation method according to the present invention. As shown, the fluid simulation method according to the present invention represents more realistic and detailed movement.

The foregoing description of the present invention is intended for illustration, and it will be understood by those skilled in the art that the present invention may be easily modified in other specific forms without changing the technical spirit or essential features of the present invention. will be. It is therefore to be understood that the above-described embodiments are illustrative in all aspects and not restrictive. For example, each component described as a single entity may be distributed and implemented, and components described as being distributed may also be implemented in a combined form.

The scope of the present invention is shown by the following claims rather than the above description, and all changes or modifications derived from the meaning and scope of the claims and their equivalents should be construed as being included in the scope of the present invention. do.

Claims (9)

In the fluid simulation method,
(a) modeling the fluid as sphere particles having one or more physical quantities;
(b) converting the sphere particles into ellipsoid particles;
(c) converting a coordinate system of the ellipsoid particles into a global coordinate system; And
(d) rendering the surface of the fluid using the particles having their positions determined in the global coordinate system;
The step (b)
Obtaining an interpolated physical quantity by the sum of physical quantities possessed by neighboring particles within a predetermined distance from each of the ellipsoid particles;
The step (d)
Simulating the effect of surface tension on the surface mesh of the fluid expressing the potential value of the ellipsoid particles as a signed distance function to reduce the curvature of the surface mesh from that when the surface mesh was created,
The surface tension is modeled using surface tension coefficients. The method of claim 1,
At least one physical quantity possessed by the sphere particles and the ellipsoid particles is an external force, mass, density, pressure, viscosity, velocity, or position. The method of claim 1,
The step (a)
The modeling is a fluid simulation method that is made by discretizing the Navier-Stoke equation. The method of claim 1,
The step (b)
And converting the sphere particles into ellipsoid particles according to the velocity and direction of movement of the sphere particles. The method of claim 1,
The step (b)
The focal length of the ellipsoid particles is equal to the moving distance per unit time of the spherical particles. The method of claim 1,
The step (b)
Wherein the length of the long axis of the ellipsoid particles is set not to exceed a predetermined threshold. The method of claim 1,
The step (b)
Dividing the space into a lattice according to the length of the long axis of the ellipsoidal particles, and selecting only the neighboring particles located within a predetermined number of lattice to reflect the calculation in the physical quantity. The method of claim 1,
The step (c)
Convert coordinates using the product of a magnitude transformation matrix and a rotation transformation matrix,
And the magnitude transformation matrix is a diagonal matrix having elements of long and short axes of ellipses as elements. A computer-readable recording medium having recorded thereon a program for performing the method according to any one of claims 1 to 8.

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