CN115879390A - Layered cloud fluid simulation method based on weak air particles and Lennard-Jones potential - Google Patents

Layered cloud fluid simulation method based on weak air particles and Lennard-Jones potential Download PDF

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CN115879390A
CN115879390A CN202211581605.5A CN202211581605A CN115879390A CN 115879390 A CN115879390 A CN 115879390A CN 202211581605 A CN202211581605 A CN 202211581605A CN 115879390 A CN115879390 A CN 115879390A
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cloud
lennard
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秦绪佳
李景秋
郑红波
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Zhejiang University of Technology ZJUT
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Abstract

A cloud fluid simulation method based on weak air particles and Lennard-Jones potential, comprising: step 1: layering the space according to the height, and collecting data of influence of meteorological data of each layer on the motion of cloud fluid; step 2: analyzing different meteorological data; and step 3: for each piece of layered data, lennard-Jones potential is adopted to calculate interaction force among gas particles, the Lennard-Jones potential can calculate influences of different forces among the gas particles according to distances among the gas particles so as to improve original fluid particle calculation of a Navier-Stokese equation, and the calculation speed of the fluid particles can be accelerated by means of GPU acceleration operation; and 4, step 4: aiming at the movement change of particles caused by different atmospheric pressures when the particles enter different layers, introducing a weak air particle concept, and calculating the movement change of the particles by adopting a two-phase flow concept; and 5: and accelerating the rendering rate by adopting a screen space particle rendering technology SSF.

Description

Layered cloud fluid simulation method based on weak air particles and Lennard-Jones potential
Technical Field
The invention belongs to the field of computer graphic simulation, and relates to a cloud fluid simulation method.
Background
The cloud is physically a collection of droplets in the atmosphere, and is considered as one of the important components to be simulated in outdoor scene visualization, such as: flight simulators and video games. In such applications, cloud is not the only object to be rendered, and the combination of reality and real-time rendering remains a popular research topic in the field of virtual reality.
Existing methods to generate accurate animations of clouds can be divided into physical methods and procedural methods. Physics-based methods, for example, rely on physical rules to model the macroscopic behavior of the cloud, however, these methods require high computational costs. On the other hand, procedural methods (e.g., reducing computation time), but control of cloud shape is typically performed by trial and error. The cloud may be represented as a fluid form. Therefore, the most common method of modeling cloud fluid dynamics is to solve the Navier-Stokes equation, which is dedicated to describing fluid motion on a macroscopic scale. Although solving these partial differential equations can generate true cloud animation, the time step required to simulate incompressible fluid particles is still not suitable for real-time applications. Meanwhile, in the cloud simulation process, only the influence of the collected wind speed data and temperature data on the cloud simulation motion is ignored, and other factors influencing the cloud generation, such as atmospheric pressure, are ignored. Atmospheric pressure is typically ignored in simulating cloud fluids and free surface boundary conditions at the interface are assumed so that the cloud surface does not change as a function of atmospheric pressure.
Disclosure of Invention
The present invention overcomes the above-mentioned shortcomings of the prior art and provides a layered cloud fluid simulation method based on weak air particles and Lennard-Jones potential.
In order to guarantee the rendering speed and consider the influence of as many environmental influence factors (wind speed, temperature, humidity, atmospheric pressure and the like) on the cloud fluid simulation as possible under the condition of ensuring the rendering speed, the invention provides a cloud fluid simulation method which has higher rendering speed (SSF technology), adopts Lennard-Jones potential to calculate the interaction force among cloud particles so as to reduce the inter-particle calculation complexity caused by a Navier-Stokese equation and introduces a layering concept and a weak air particle concept to solve the environmental factor change and the atmospheric pressure influence with different heights.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a method for layered cloud fluid simulation based on weak airborne particles and Lennard-Jones potential, the simulation method comprising the steps of:
step 1: the space is layered according to the height, and meteorological data of different heights corresponding to each layer are collected, such as: temperature, wind speed, barometric pressure, humidity, etc. may have an impact on cloud fluid movement.
Step 2: since the movement of cloud fluids can be affected by different meteorological elements, different analyses need to be performed for different meteorological data.
And step 3: for each of the stratification data, the interaction forces between the gas particles can be calculated by using a Lennard-Jones potential, which calculates the effect of different forces between the gas particles depending on the distance between the gas particles. Therefore, the original fluid particle calculation of the Navier-Stokese equation can be improved, and the calculation speed of the fluid particles can be accelerated by means of GPU acceleration operation.
And 4, step 4: because the space is highly layered to introduce meteorological data with different heights, aiming at the movement change of the particles caused by different atmospheric pressures when the particles enter different layers, the concept of weak air particles can be introduced, and the concept of two-phase flow is adopted to calculate the movement change of the particles.
And 5: after the specific value of the particle motion change exists, the particle motion change needs to be rendered in the screen space, the ion surface construction method of Marching Cube is not adopted, and the SSF (screen space particle rendering) technology with higher efficiency is selected to accelerate the rendering rate.
Still further, in the step 2, the influence of each type of data on the change of the cloud formation set is as follows:
(2.1) because the temperature data can have great influence on the thermal force field and the intermolecular acting force in the Lennard-Jones potential, the thermal force field has significance on maintaining and correcting the motion stability of the cloud fluid, the thermal force field needs to be constructed for the temperature data of each layer, and thermodynamic variables need to be generated to calculate the acting force of the temperature on the motion of the cloud fluid.
(2.2) the wind field data comprises wind speed and wind direction, the wind speed influences the movement speed of the cloud fluid, the wind direction influences the movement direction of the cloud fluid, and the wind speed and the wind direction at different heights are different, so that a related field needs to be constructed according to the wind field data generated in each hierarchical data to apply related speed change to the cloud fluid data.
(2.3) the humidity data can influence the density change of the cloud fluid and then have a function when being calculated through a density equation, so that different processing needs to be carried out on each layered data, and the humidity data at different heights are not the same. Meanwhile, the size of the cloud particles can be dynamically adjusted by means of humidity data, so that the cloud particles are more natural in the process of forming the cloud surface.
Further, in step 3, the calculation process of Lennard-Jones potential based on the distance between particles is as follows:
Figure BDA0003987667320000021
where α and β are the attractive and repulsive terms, respectively, which are constant terms, 12 and 6, respectively ij Then the intermolecular distance; σ is the minimum separation distance between molecules, wherein the potential energy between molecules is 0; epsilon represents the magnitude of the strength of the intermolecular potential energy.
(3.1) the interaction force between the two particles can be obtained through the intermolecular distance, and the specific calculation formula is as follows:
Figure BDA0003987667320000031
since the force applied to a particle is from the force of all particles in the smooth radius divided around the particle, the force contributed by all particles around the particle needs to be calculated, and the formula is as follows:
F i =∑ i f(r ij ) r ij <r c (3)
wherein r is c Is the maximum sampling radius.
(3.2) after the influence of the distance on the acting force among the particles is calculated, in order to ensure the stability of the whole system, thermodynamic variables are required to be set according to temperature layers with different heights, the stability of the system is ensured, and a thermodynamic variable calculation formula for each temperature layer is as follows:
Figure BDA0003987667320000032
n is the number of particles in the current layer, and m is the mass of the particles, which is generally 1 by default.
After the thermodynamic variable of each layer is available, the speed of each particle of each layer based on the thermodynamic variable needs to be readjusted, and the specific formula is as follows:
Figure BDA0003987667320000033
further, in step 4, the process of introducing weak air particles is as follows:
(4.1) for different atmospheric pressures under different layers, a weak air particle concept is introduced, interaction between the weak air particles and cloud particles is achieved, and the unstable phenomenon caused by the whole motion system due to the fact that the particle density difference is too large is avoided. Meanwhile, the size radius of the weak air particles is twice that of the cloud particles, so that the calculation cost is reduced.
(5.2) after the concept of weak air particles is available, calculating a position correction change formula of the weak air particles in each time step and each layer, wherein the specific calculation formula is as follows:
Figure BDA0003987667320000034
Ω a ,Ω l respectively, a set of weak air particles and a set of cloud particles, ρ a,0 Is the density of weak airborne particles, k l Is a positive number for ensuring the stability of the weak air particles when colliding with the cloud particles,
Figure BDA0003987667320000035
is a partial derivative function of a kernel function of radius h. Through the above formula, we can calculate the position correction value of the weak air particles, so as to add the position correction value into the Lennard-Jones potential and participate in the influence on cloud particle calculation.
(4.3) because of the introduction of weak air particles, the position of the cloud particles needs to be partially corrected, and the correction formula is as follows:
Figure BDA0003987667320000041
where ρ is i,0 Is the density size of the cloud particles. Here it can be seen that the contribution of weak air particles to the cloud particle position correction is ignored, which is also different from weak air particles.
(4.4) the weak air particles also exert a surface force on the surface formed by the cloud particles, so that a calculation needs to be carried out on the surface force on the surfaces of the cloud particles and the original tension on the surfaces of the cloud particles.
Under the action of atmospheric pressure in meteorological data, a surface pressure is applied to the surface formed by the cloud particles, and the calculation formula of the surface pressure is as follows:
Figure BDA0003987667320000042
wherein A is i Indicating the relative density of air with respect to a static state and following the compression processGradually increase, V i Representing cloud particle volume, p 0 It is the current stratified atmospheric pressure value that is input.
The invention has the following beneficial effects:
(1) The rendering time is short. The method is based on the screen space rendering technology, utilizes the form of generating textures, and accelerates the rendering by means of a GPU, so that the method is much faster than the prior Marching Cube grid construction technology and has better effect.
(2) The cloud surface changes more realistically. The method introduces weak air particle concept on the basis of the original Lennard-Jones potential, and adds data of atmospheric pressure which has great influence on the cloud surface, so that the cloud surface is more in line with the change in the real environment.
(3) Based on the height layering, the cloud is more real in the performance of different heights. The method based on the whole height spatial interpolation is abandoned, division is carried out according to the height of meteorological monitoring data, the meteorological data is more refined and imported, layered simulation is better carried out, and cloud simulation is more in line with real data driving.
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FIG. 1 is a flow chart of the method of the present invention.
Detailed description of the invention
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention.
The invention is further described below with reference to the accompanying drawings.
Step 1: the space is layered according to the height, and meteorological data of different heights corresponding to each layer are collected, such as: temperature, wind speed, barometric pressure, humidity, etc. may have an effect on cloud fluid movement.
And 2, step: since the motion of the cloud fluid is influenced by different meteorological elements, different analyses are required for different meteorological data
(2.1) because the temperature data can have great influence on the thermal force field and the intermolecular acting force in the Lennard-Jones potential, the thermal force field has significance on maintaining and correcting the motion stability of the cloud fluid, the thermal force field needs to be constructed for the temperature data of each layer, and thermodynamic variables need to be generated to calculate the acting force of the temperature on the motion of the cloud fluid.
And (2.2) the wind field data comprises wind speed and wind direction, the wind speed influences the movement speed of the cloud fluid, the wind direction influences the movement direction of the cloud fluid, and the wind speed and the wind direction at different heights are different, so that a related field needs to be constructed according to the wind field data generated in each hierarchical data to apply related speed change to the cloud fluid data.
(2.3) the humidity data can influence the density change of the cloud fluid and then have a function when being calculated through a density equation, so that different processing needs to be carried out on each layered data, and the humidity data at different heights are not the same. Meanwhile, the size of the cloud particles can be dynamically adjusted by means of humidity data, so that the cloud particles are more natural in the process of forming the cloud surface.
And 3, step 3: for each of the stratification data, the interaction forces between the gas particles can be calculated by using a Lennard-Jones potential, which calculates the effect of different forces between the gas particles depending on the distance between the gas particles. Therefore, the original fluid particle calculation of the Navier-Stokese equation can be improved, the calculation speed of the fluid particles can be accelerated by means of GPU acceleration operation, and the optimized Lennard-Jones potential calculation formula based on the distance between the particles is as follows:
Figure BDA0003987667320000051
where α and β are the attractive and repulsive terms, respectively, which are constant terms, 12 and 6, respectively ij Then the intermolecular distance; σ is the minimum separation distance between molecules, wherein the potential energy between molecules is 0; epsilon represents the magnitude of the strength of the intermolecular potential energy.
(3.1) the interaction force between the two particles can be obtained through the intermolecular distance, and the specific calculation formula is as follows:
Figure BDA0003987667320000052
since the force applied to a particle is from the force of all particles in the smooth radius divided around the particle, the force contributed by all particles around the particle needs to be calculated, and the formula is as follows:
F i =∑ i f(r ij ) r ij <r c (3)
wherein r is c Is the maximum sampling radius.
(3.2) after the influence of the distance on the acting force among the particles is calculated, in order to ensure the stability of the whole system, thermodynamic variables are required to be set according to temperature layers with different heights, the stability of the system is ensured, and a thermodynamic variable calculation formula for each temperature layer is as follows:
Figure BDA0003987667320000061
n is the number of particles in the current layer, and m is the mass of the particles, which is generally 1 by default.
After the thermodynamic variable of each layer is available, the speed of each particle of each layer based on the thermodynamic variable needs to be readjusted, and the specific formula is as follows:
Figure BDA0003987667320000062
and 4, step 4: because the space is highly layered to introduce meteorological data with different heights, aiming at the movement change of the particles caused by different atmospheric pressures when the particles enter different layers, the concept of weak air particles can be introduced, and the concept of two-phase flow is adopted to calculate the movement change of the particles.
(4.1) for different atmospheric pressures under different layers, a weak air particle concept is introduced, interaction between the weak air particles and cloud particles is achieved, and the unstable phenomenon caused by the whole moving system due to overlarge particle density difference is avoided. Meanwhile, the size radius of the weak air particles is twice that of the cloud particles, so that the calculation cost is reduced.
(4.2) after the concept of weak air particles is available, calculating a position correction change formula of the weak air particles in each time step and each layer, wherein the specific calculation formula is as follows:
Figure BDA0003987667320000063
Ω a ,Ω l respectively a weak air particle set and a cloud particle set, rho a,0 Is the density, k, of weak airborne particles l Is a positive number for ensuring the stability of the weak air particles when colliding with the cloud particles,
Figure BDA0003987667320000064
is the partial derivative function of the kernel function with radius h. Through the above formula, we can calculate the position correction value of the weak air particles, so as to add the position correction value into the Lennard-Jones potential and participate in the influence on cloud particle calculation.
(4.3) because of the introduction of weak air particles, the position of the cloud particles needs to be partially corrected, and the correction formula is as follows:
Figure BDA0003987667320000065
where ρ is i,0 Is the density size of the cloud particles. Here it can be seen that the contribution of weak air particles to the cloud particle position correction is ignored, which is also different from weak air particles.
(4.4) the weak air particles also exert a surface force on the surface formed by the cloud particles, so a calculation needs to be carried out on the surface force received by the surfaces of the cloud particles and the original tension of the surfaces of the cloud particles.
Under the action of atmospheric pressure in meteorological data, a surface pressure is applied to the surface formed by the cloud particles, and the calculation formula of the surface pressure is as follows:
Figure BDA0003987667320000071
wherein A is i Representing the relative density of air with respect to a state of rest and increasing progressively with the compression process, V i Representing cloud particle volume, p 0 It is the current stratified barometric pressure value entered.
And 5: after the specific value of the particle motion change exists, the particle motion change needs to be rendered in the screen space, the ion surface construction method of Marching Cube is not adopted, and the SSF (screen space particle rendering) technology with higher efficiency is selected to accelerate the rendering rate.
The SSF technology mainly utilizes a point sprite mode to draw all particles, the depth of the particles is recorded according to the drawn point sprite, and the point sprite is regarded as a sphere through depth calculation and is stored in a depth cache. And recording the thickness of the point sprites according to the drawn point sprites, and calculating the thickness of the point sprites to regard the point sprites as spheres and storing the spheres in a thickness cache. The thickness cannot be output simultaneously with the depth using MRT, and since the thickness needs to be accumulated, the depth test is turned off, and the thickness is accumulated by mixing with alpha addition. And carrying out surface treatment through corresponding filtering, and finally outputting the surface treatment to 2 frame caches for cloud surface rendering. Compared with Marching Cube which carries out surface calculation in cpu, SSF carries out surface reconstruction by using GPU, and greatly accelerates the rendering process.

Claims (6)

1. A cloud fluid simulation method based on weak air particles and Lennard-Jones potential is characterized by comprising the following steps: the method comprises the following steps:
step 1: the space is layered according to the height, and data of influence of meteorological data of different heights corresponding to each layer on the motion of cloud fluid are collected;
and 2, step: analyzing different meteorological data;
and 3, step 3: for each piece of layered data, lennard-Jones potential is adopted to calculate the interaction force among the gas particles, the Lennard-Jones potential can calculate the influence of different forces among the gas particles according to the distance among the gas particles so as to improve the calculation of the original fluid particles of the Navier-Stokese equation, and the calculation speed of the fluid particles can be accelerated by means of GPU accelerated operation;
and 4, step 4: the space is highly layered to introduce meteorological data with different heights, and aiming at the movement change of particles caused by different atmospheric pressures when the particles enter different layers, a weak air particle concept can be introduced, and the concept of two-phase flow is adopted to calculate the movement change of the particles;
and 5: and accelerating the rendering rate by adopting a screen space particle rendering technology SSF.
2. The method according to claim 1, wherein the cloud-fluid simulation method based on weak airborne particles and Lennard-Jones potential comprises: the meteorological data of step 1 includes: temperature, wind speed, atmospheric pressure, humidity.
3. The method of claim 1, wherein the cloud fluid simulation based on weak air particles and Lennard-Jones potential comprises: in step 2, the influence of each type of data on the change of the cloud formation set is specifically as follows:
(2.1) because the temperature data can generate great influence on the thermal force field and also has great influence on intermolecular acting force in Lennard-Jones potential, and the thermal force field has significance on maintaining and correcting the motion stability of the cloud fluid, the thermal force field needs to be constructed on the temperature data of each layer, and thermodynamic variables need to be generated at the same time to calculate the acting force of the temperature on the motion of the cloud fluid;
(2.2) the wind field data comprise wind speed and wind direction, the wind speed influences the movement speed of the cloud fluid, the wind direction influences the movement direction of the cloud fluid, and the wind speed and the wind direction at different heights are different, so that a related field needs to be constructed according to the wind field data generated in each hierarchical data to apply related speed change to the cloud fluid data;
(2.3) the humidity data can influence the density change of the cloud fluid and then has a function in calculation through a density equation, so that different processing needs to be carried out on each stratified data, and the humidity data at different heights are not the same.
4. The method of claim 1, wherein the cloud fluid simulation based on weak air particles and Lennard-Jones potential comprises: in step 3, the Lennard-Jones potential calculation process based on the inter-particle distance is as follows:
Figure FDA0003987667310000021
where α and β are the attractive and repulsive terms, respectively, which are constant terms, 12 and 6, respectively ij Then the intermolecular distance; σ is the minimum separation distance between molecules, wherein the potential energy between molecules is 0; epsilon represents the strength of intermolecular potential energy;
(3.1) the interaction force between the two particles can be obtained through the intermolecular distance, and the specific calculation formula is as follows:
Figure FDA0003987667310000022
since the force applied to a particle is from the force of all particles in the smooth radius divided around the particle, the force contributed by all particles around the particle needs to be calculated, and the formula is as follows:
F i =∑ i f(r ij ) r ij <r c (3)
wherein r is c Is the maximum sampling radius;
(3.2) after the influence of the distance on the acting force among the particles is calculated, in order to ensure the stability of the whole system, thermodynamic variables are required to be set according to temperature layers with different heights, the stability of the system is ensured, and a thermodynamic variable calculation formula for each temperature layer is as follows:
Figure FDA0003987667310000023
n is the number of particles in the current layer, m is the mass of the particles, and is generally regarded as 1 by default;
after the thermodynamic variable of each layer is available, the speed of each particle of each layer based on the thermodynamic variable needs to be readjusted, and the specific formula is as follows:
Figure FDA0003987667310000031
5. the method according to claim 1, wherein the cloud-fluid simulation method based on weak airborne particles and Lennard-Jones potential comprises: in the step 4, the process of introducing the weak air particles is as follows:
(4.1) introducing a weak air particle concept for different atmospheric pressures under different layers, so that the weak air particles and cloud particles are interacted, and the unstable phenomenon caused by the whole motion system due to overlarge particle density difference is avoided; meanwhile, the size radius of the weak air particles is twice that of the cloud particles, so that the calculation overhead is reduced;
(4.2) after the concept of weak air particles is available, calculating a position correction change formula of the weak air particles in each time step and each layer, wherein the specific calculation formula is as follows:
Figure FDA0003987667310000032
Ω a ,Ω l respectively, a set of weak air particles and a set of cloud particles, ρ a,0 Is the density of weak airborne particles, k l Is a positive number for ensuring a weak nullStability of the gas particles when they collide with the cloud particles,
Figure FDA0003987667310000033
is a partial derivative function of a kernel function of radius h; calculating the position correction value of the weak air particles through the formula, and adding the position correction value into Lennard-Jones potential to participate in the calculation of the cloud particles;
(4.3) because of the introduction of weak air particles, the position of the cloud particles needs to be partially corrected, and the correction formula is as follows:
Figure FDA0003987667310000034
where ρ is i,0 Is the density size of the cloud particles; (ii) a
(4.4) calculating the surface force to the surface of the cloud particle and the original tension of the surface;
under the action of atmospheric pressure in meteorological data, a surface pressure is applied to the surface formed by the cloud particles, and the calculation formula of the surface pressure is as follows:
Figure FDA0003987667310000035
wherein A is i Representing the relative density of air with respect to the rest state and increasing gradually with compression, V i Representing cloud particle volumes, p 0 It is the current stratified atmospheric pressure value that is input.
6. The method of claim 1, wherein the cloud fluid simulation based on weak air particles and Lennard-Jones potential comprises: the step 5 specifically comprises the following steps:
the SSF technology draws all particles by using a point sprite mode, records the depth of the particles according to the drawn point sprite, and stores the point sprite into a depth cache by taking the point sprite as a sphere through depth calculation; recording the thickness of the point sprites according to the drawn point sprites, and calculating the thickness of the point sprites to take the point sprites as spheres and storing the point sprites into a thickness cache; thickness and depth cannot be output simultaneously by using MRT, and because the thickness needs to be accumulated, the depth test is closed, and the thickness is accumulated by mixing by using an alpha addition method; carrying out surface treatment through corresponding filtering, and finally outputting the surface treatment to 2 frame caches for cloud surface rendering; compared with Marching Cube which carries out surface calculation in cpu, SSF carries out surface reconstruction by using GPU, and accelerates the rendering process.
CN202211581605.5A 2022-12-08 2022-12-08 Layered cloud fluid simulation method based on weak air particles and Lennard-Jones potential Pending CN115879390A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116824009A (en) * 2023-06-29 2023-09-29 广州市大神文化传播有限公司 Animation rendering method, system, equipment and storage medium

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116824009A (en) * 2023-06-29 2023-09-29 广州市大神文化传播有限公司 Animation rendering method, system, equipment and storage medium
CN116824009B (en) * 2023-06-29 2024-03-26 广州市大神文化传播有限公司 Animation rendering method, system, equipment and storage medium

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