Method for calculating force acting on interface between immiscible fluids in fluid simulation

1. A method for calculating a force acting on an interface between immiscible fluids in an SPH (Smoothed Particle Hydrodynamics) based fluid simulation, the method comprising:

calculating a force caused by viscosities of the fluids;

calculating a force caused by pressures of the fluids;

calculating an external force applied to the fluids from outside; and calculating an interactive force caused by interaction between the fluids,

wherein the force acting on the interface between the immiscible fluids are obtained by a computer by using a sum of the force caused by the viscosities, the force caused by the pressures, the external force and the interactive force,

wherein the interactive force is a surface tensional force calculated based on a pressure acting on the interface between the fluids at a contact surface of the fluids, and

wherein the interactive force is calculated by using parameters representing scattering properties of the fluids, normal vectors of particles in the fluids, a magnitude of the force caused by the pressure acting on the interface between the fluids and an angle between a direction of the force caused by the pressure acting on the interface between the fluids and the interface of the fluids,

wherein the interactive force is calculated by using the following formula:

∑

k

⁢

⁢

(

a

i

+

a

k

2

)

×

(

1

-

cos

⁢

⁢

θ

ik

)

×



f

ik

pressure



×

N

ik

_

,

wherein N ik denotes an average normal vector of particles of i and k; N ik denotes a unit vector of N ik ; f ik pressure the force caused by the pressure acting on the interface between the fluids; a i and a k denote the scattering properties of the particles of i and k, respectively; and θ ik denotes the angle between the force f ik pressure and the interface of the fluids.

2. The method of claim 1 , wherein the angle between the direction of the force caused by the pressure acting on the interface between the fluids and the interface of the fluids is calculated by using the normal vectors of the particles.

3. The method of claim 1 , wherein the normal vectors' of the particles are calculated by using variations of color fields assigned to the particles.

4. The method of claim 1 , wherein each of the parameters representing the scattering properties has a value in a range from 0 to 0.5.

5. The method of claim 1 , wherein a magnitude of the interactive force is determined by the magnitude of the force caused by the pressure acting on

the interface between the fluids and a difference between the direction of the force caused by the pressure acting on the interface between the fluids and a direction of an average normal vector of the normal vectors of the particles.

6. A non-transitory computer-readable storage medium for storing therein computer-readable programs to execute on a computer the method of claim 1 .

7. A method for calculating a force acting on an interface between immiscible fluids in an SPH (Smoothed Particle Hydrodynamics) based fluid simulation, the method comprising:

calculating a force caused by viscosities of the fluids;

calculating a force caused by pressures of the fluids;

calculating an external force applied to the fluids from outside; and calculating an interactive force caused by interaction between the fluids,

wherein the force acting on the interface between the immiscible fluids are obtained by a computer by using a sum of the force caused by the viscosities, the force caused by the pressures, the external force and the interactive force,

wherein the interactive force is a surface tensional force calculated based on a pressure acting on the interface between the fluids, and

wherein the interactive force is calculated by using parameters representing scattering properties of the fluids, normal vectors of particles in the fluids, a magnitude of the force caused by the pressure acting on the interface between the fluids and an angle between a direction of the force caused by the pressure acting on the interface between the fluids and the interface of the fluids,

wherein the interactive force is calculated by using the following formula:

∑

k

⁢

⁢

(

a

i

+

a

k

2

)

×

(

1

-

cos

⁢

⁢

θ

ik

)

×



f

ik

pressure



×

N

ik

_

,

wherein N ik denotes an average normal vector of particles of i and k; N ik denotes a unit vector of N ik ; f ik pressure denotes the force caused by the pressure acting on the interface between the fluids; a i and a k denote the scattering properties of the particles of i and k, respectively; and θ ik denotes the angle between the force f ik pressure and the interface of the fluids.