CN113822000B - Flow field real-time prediction system and method based on edge calculation - Google Patents

Flow field real-time prediction system and method based on edge calculation Download PDF

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CN113822000B
CN113822000B CN202111187792.4A CN202111187792A CN113822000B CN 113822000 B CN113822000 B CN 113822000B CN 202111187792 A CN202111187792 A CN 202111187792A CN 113822000 B CN113822000 B CN 113822000B
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王卓霖
张栏
江俊扬
杨耿超
姚清河
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Sun Yat Sen University
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Abstract

A flow field real-time prediction system and method based on edge calculation, wherein the system comprises a Windows server, atlas200DK and a digital sensor. The method comprises the following steps: acquiring flow field calculation parameters; establishing a discretized particle model according to flow field parameters; calculating the intermediate speed and the intermediate displacement of the particles according to the viscosity force and the physical force in the control equation; constructing input data required by a neural network for solving a pressure poisson equation according to the intermediate displacement; transmitting the obtained input data to an Atlas200DK AI acceleration module for calculating and solving pressure data; transmitting the pressure data back to the Windows server; correcting the particle speed and position according to the pressure gradient; and entering the next time step, and re-executing the steps. Compared with the prior art, the invention has the advantages that: the system and the method of the invention combine the neural network technology and the leading edge artificial intelligent equipment to realize the instant simulation of the complex flow field, and solve the problems of long calculation time for the complex flow field and difficult realization of instant flow field analysis in the field of fluid calculation.

Description

Flow field real-time prediction system and method based on edge calculation
Technical Field
The invention relates to the technical field of edge calculation and computational fluid mechanics, in particular to a flow field real-time prediction system and method aiming at edge calculation.
Background
Currently, the main flow fluid calculating methods are mainly divided into two types: grid-based euler method and particle-based lagrangian method. The Euler method is to divide a calculation region into grids and discrete differential equations to obtain physical quantity changes at each moment of grid points; the Lagrangian method is used for researching the change of physical quantity of particles along with time and is suitable for relatively complex boundary conditions or large deformation fluid simulation scenes.
At present, the grid method is the most mature fluid simulation scheme, but the grid method has great difficulty in handling complex boundary and large deformation fluid simulation. The flow field conditions which are common in the actual life or production are quite complex, and the problems are easier to deal with by adopting a gridless Lagrange method.
Fluid computation without grid methods requires greater computational expense than grid methods. Current fast flow field simulation is typically implemented using a performance-intensive computing hardware cluster or a specialized cloud computing server. However, in practical engineering applications, expensive computing hardware or cloud computing servers render fast fluid computing difficult to achieve.
Disclosure of Invention
In order to solve the problems of high fluid calculation consumption and high calculation cost in the background technology, the invention provides a flow field real-time prediction system and a flow field real-time prediction method based on edge calculation. The system and the method solve the problems of long calculation time for complex flow fields and difficult realization of instant flow field analysis in the field of calculating fluid, and have the advantages of low cost, high speed, reliability and suitability for complex scenes.
In order to achieve the above purpose, the technical scheme of the flow field real-time prediction system based on edge calculation of the invention is as follows:
a flow field real-time prediction system based on edge calculation comprises
The server is provided with a server which, the method comprises the steps of obtaining and storing flow field calculation parameters, establishing a particle model, calculating intermediate speed and intermediate displacement of the particle model, inputting data of a neural network, transmitting the inputting data of the neural network to a developer kit to calculate pressure data, and correcting the intermediate speed and intermediate displacement of particles by using the pressure data;
the developer kit comprises an acceleration module, a server and a control module, wherein the acceleration module is used for calculating input data of the neural network, solving pressure data and transmitting the pressure data to the server;
the digital sensor comprises a digital temperature sensor and a digital flow rate sensor and is used for acquiring the temperature and the flow rate of the flow field.
The invention also provides a flow field real-time prediction method based on edge calculation, which has the technical scheme that:
a flow field real-time prediction method based on edge calculation comprises the following steps:
s1, acquiring flow field calculation parameters and storing the flow field calculation parameters in a server;
s2, establishing a discretized particle model in a server according to the flow field parameters;
s3, solving a particle model in a server according to the viscosity force and the physical strength in a control equation, and calculating the intermediate speed and the intermediate displacement of the particles;
s4, constructing input data of a neural network according to the intermediate displacement, wherein the neural network is used for solving a pressure poisson equation;
s5, transmitting the input data to a neural network of a developer kit for calculation, and solving pressure data; transmitting the pressure data back to the server;
s6, correcting the intermediate speed and the intermediate displacement of the particles according to the pressure gradient;
s7, entering the next time step, and re-executing the steps S3-S7.
Further, the flow field parameters include constants in the viscosity coefficient empirical formula, flow field boundary positions, solid wall boundary positions, density information, and temperature and flow rate of the fluid.
Further, the step S2 specifically includes the following steps:
s21, comparing the internal memory of the developer kit according to the flow field calculation parameters, and ensuring that the total internal memory is less than 70% to determine proper inter-particle distance;
s22, constructing four layers of common particles on the solid wall boundary and the outer side according to the inter-particle distance and the solid wall boundary position, and uniformly dispersing the rest into fluid particles; wherein, two layers of common particles close to the fluid are first-class solid particles, and two layers far away from the fluid are second-class solid particles; the first type solid particles and the second type solid particles do not update the speed displacement, and the second type solid particles do not participate in the pressure solution;
s23, marking fluid particles positioned at the flow field boundary according to the flow field boundary position and the fluid flow velocity, and marking the fluid particles escaping from the flow field boundary as common particles in the calculation process; judging whether fluid particles exist in the boundary position of the flow field, and if so, marking the fluid particles; if not, supplementing the fluid particles of the flow velocity into the boundary position of the flow field according to the flow velocity of the fluid.
Further, the step S3 specifically includes: decomposing a control equation into an estimated step and a correction step by using a gridless method-a moving particle semi-implicit method; in the estimating step, according to the viscous force and physical force in the control equation, solving a particle model, and calculating an estimated intermediate speed v * And intermediate displacement r *
Further, the step S4 specifically includes the following steps:
s41, calculating the particle number density n according to the intermediate displacement * The calculation formula is as follows:
wherein ,represents the intermediate displacement of the i particles, W represents the kernel function, h represents the radius of the support set, and is 2.1l 0
S42, converting the solving process of the pressure poisson equation into a regression problem, wherein the calculation formula is as follows:
wherein k represents the number from the operation to the kth step, indicating the divergence of the i particles at the intermediate velocity of the kth step.
Further, the neural network construction method comprises the following steps: to be used forAs input data of the neural network, constructing a neural network structure taking the multi-layer perceptron as a main body; the neural network with each layer of perceptrons as a main body is expressed as follows:
f(x)=H(ω*x+b)
wherein ,x(x1 ,x 2 ,…,x n ) Representing the input vector of the layer, ω represents the weight, b represents the bias, H represents the activation function, f () represents the layer output, and the neural network employs ReLU as the activation function.
Further, the step S5 specifically includes the following steps:
s51, packaging neural network input data of all fluid particles;
s52, transmitting the neural network input data to a developer kit;
s53, receiving and unpacking data by the developer suite, and then calling a neural network to solve the pressure data;
s54, packaging the solving result, then transmitting the solving result back to the server, and entering step S6.
Further, step S6 is more specifically: according to the pressure data returned by the developer kit, solving a pressure gradient term of a control equation, correcting the speed and the displacement, and calculating the formula:
wherein ,v* Representing an intermediate speed; r is (r) * Representing an intermediate displacement; v represents the speed; r represents displacement; Δt represents the time step; p represents pressure, ρ represents density;
and then outputting the calculation result of the current time step.
Compared with the prior art, the invention has the advantages that: the flow field real-time prediction system and the method based on edge calculation realize the instant simulation of the complex flow field by combining the neural network technology and the leading edge artificial intelligent equipment, and solve the problems of long calculation time and difficult realization of instant flow field analysis for the complex flow field in the field of fluid calculation. In addition, the method has the advantages of low cost, high speed, reliability and suitability for fluid instant calculation in complex scenes.
Drawings
FIG. 1 is a schematic diagram of a flow field modeling process;
FIG. 2 is a neural network architecture for use with the present invention;
FIG. 3 is a program structure of the Ubuntu/Windows server according to the present invention;
FIG. 4 is a program structure of Atlas200DK of the present invention;
fig. 5 is a schematic diagram of physical data preparation.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the present patent. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
In this embodiment, as a preferred mode, the server is a Ubuntu/Windows server, and the developer suite is an Atlas200DK developer suite of wagons, which is a developer scenario with an Atlas200AI acceleration module as a core. Wherein Atlas200AI acceleration module integrates an ascent 310AI processor. The neural network reasoning for solving the pressure poisson equation is transplanted to an Atlas200DK development board to run, the rest is completed by a Ubuntu/Windows server, and the neural network reasoning is used for realizing rapid data exchange by utilizing a Socket communication protocol through a gigabit Ethernet.
The technical scheme of the invention is further described below with reference to fig. 1 to 5 and examples.
Example 1
A flow field real-time prediction system based on edge calculation comprises a Ubuntu/Windows server, atlas200DK and a digital sensor. The Ubuntu/Windows server is used for acquiring and storing flow field calculation parameters, establishing a particle model, calculating intermediate speed and intermediate displacement of the particle model, inputting data of a neural network, transmitting the inputting data of the neural network to a developer suite to calculate pressure data, and correcting the intermediate speed and intermediate displacement of the particle by using the pressure data. The Atlas200DK comprises an acceleration module, which is used for calculating input data of the neural network, solving pressure data and transmitting the pressure data to a server. The digital sensor comprises a digital temperature sensor and a digital flow rate sensor and is used for acquiring the temperature and the flow rate of the flow field.
As a preferred way, the program structure is (corresponding flow charts are specifically shown in fig. 3-4):
Ubuntu/Windows server:
1. acquiring flow field calculation parameters;
2. calculating the intermediate speed and the intermediate displacement of the particles according to the viscosity force and the physical strength in the control equation;
3. constructing input data of a neural network for solving a pressure poisson equation according to the intermediate displacement;
4. transmitting the input data to an AI acceleration module of Atlas200DK by using a Socket communication protocol, and calculating pressure data;
5. receiving pressure data sent from Atlas200DK by using Socket communication protocol;
6. correcting the particle speed and position according to the pressure gradient;
7. judging whether the target calculation time is reached, if so, outputting a calculation result, and analyzing the calculation result; if the target calculation time is not reached, returning to the step 2, and starting the next time step.
Atlas200DK end:
1. generating a model file suitable for AIcore solving neural network;
2. initializing a computing environment;
3. receiving input data by using a Socket protocol;
4. the input data is transmitted into an AIcore solving neural network to solve the pressure data;
5. packaging the pressure data and transmitting the pressure data back to the Ubuntu/windows server;
6. returning to step 2, waiting for the next time step of reasoning.
Example 2
A flow field real-time prediction method based on edge calculation comprises the following steps:
s1, acquiring flow field calculation parameters including constants, flow field boundary positions, solid wall boundary positions, density information, fluid temperature and fluid velocity in a viscosity coefficient empirical formula, and then storing the data in a server.
The constant in the viscosity coefficient empirical formula can be obtained by selecting a table look-up mode or an experimental mode according to the difference of the empirical formula and the fluid type, and is stored in a database.
The boundary position of the flow field and the boundary position of the solid wall are obtained by adopting an engineering measurement mode, and the boundary position information is stored in a database of Atlas200DK equipment, and boundary data is directly read from the database during calculation;
fluid viscosity is calculated by adopting an empirical formula based on temperature; firstly, collecting a fluid sample, obtaining relevant parameters except temperature of an empirical formula, connecting a serial digital temperature sensor with an Atlas200DK serial port, immediately obtaining temperature data during calculation, and substituting the temperature data into the empirical formula to obtain the fluid viscosity.
The temperature and the flow rate of the fluid are measured by a digital temperature sensor and a digital flow rate sensor which are externally connected with the Atlas200DK respectively, data processing is carried out through the Atlas200DK, the viscosity coefficient of the fluid is calculated, the flow rate boundary of the flow field is determined, relevant physical data are transmitted back to a computer through a socket communication protocol for storage, and the physical data are prepared as shown in figure 5.
When a flow rate inlet exists, a digital flow rate sensor is connected to an Atlas200DK expansion GPIO interface in an instant measurement mode, and when calculation is performed, flow rate signals are read by using the Atlas200DK to obtain instant flow rate boundary information.
S2, establishing a discretized particle model in a server according to flow field parameters, namely modeling a flow field;
s21, comparing memories of Atlas200DK according to flow field calculation parameters, and ensuring that the total memory is less than 70% to determine proper inter-particle distance.
S22, constructing four layers of common particles on the solid wall boundary and the outer side according to the inter-particle distance and the solid wall boundary position, and uniformly dispersing the rest into fluid particles. Wherein, the two layers of the common particles close to the fluid are the first type of solid particles, and the two layers far away from the fluid are the second type of solid particles. The first type of solid particles and the second type of solid particles do not update the speed displacement, and the second type of solid particles do not participate in pressure solving.
S23, marking fluid particles positioned at the flow field boundary according to the position of the flow field boundary and the fluid flow velocity, and marking the fluid particles escaping from the flow field boundary as common particles in the calculation process. Judging whether fluid particles exist in the boundary position of the flow field, and if so, marking the fluid particles; if not, supplementing the fluid particles of the flow velocity into the boundary position of the flow field according to the flow velocity of the fluid. The positional relationship between the boundary particles and the fluid particles is shown in fig. 1.
S3, calculating the intermediate speed and the intermediate displacement of the particles in the server according to the viscosity force and the physical strength in the control equation;
the control equation is decomposed into a pre-estimated step and a correction step distribution solution by using a gridless Method, namely a moving particle semi-implicit Method (Moving Particle Semi-real Method, MPS). In the estimating step, according to the viscous force and physical force in the control equation, solving a particle model, and calculating an estimated intermediate speed v * And intermediate displacement r * The calculation formula is as follows:
r * =r k +Δtv *
wherein ,vk Representing the speed of the kth step (current step); r is (r) k Representing the displacement of the kth step (current step), v representing the kinematic viscosity of water; f represents the force exerted by the particles; typically only the gravitational acceleration g.
The control equation is:
wherein ,representing the satellite derivative of a certain physical quantity.
The conventional step of solving the control equation is specifically:
I. calculating intermediate speed and intermediate displacement according to the viscous force and the physical force in the control equation;
II, calculating the particle number density by using the intermediate displacement obtained in the estimating step;
thirdly, constructing a pressure poisson equation according to an incompressible principle, and solving to obtain pressure data;
wherein ,the Laplace operator, representing pressure, is developed specifically below; the right side is the source item; gamma represents a mixed source coefficient, and 0 to 0.2 is taken; n is n 0 Representing the initial population density.
IV, correcting the intermediate speed and the intermediate displacement by using the pressure gradient term of the solving control equation;
and V, entering the next time step, and solving a control equation at the next moment according to the steps III-IV.
S4, constructing input data of a neural network for solving a pressure poisson equation according to the intermediate displacement, wherein the input data comprises
S41, calculating the particle number density n according to the intermediate displacement * The calculation formula is as follows:
wherein ,represents the intermediate displacement of the i particles, W represents the kernel function, h represents the radius of the support set, and is 2.1l 0
S42, converting the solving process of the pressure poisson equation into a regression problem, wherein the calculation formula is as follows:
wherein k represents the number from the operation to the kth step, indicating the divergence of the i particles at the intermediate velocity of the kth step.
The formula of the traditional pressure poisson equation is:
wherein D represents a system dimension;w represents a weight function in the MPS; p represents pressure; n is n 0 Representing the initial population density.
S5, transmitting the input data to an Atlas200DK AI acceleration module for calculation, and solving the pressure data; the pressure data is then transferred back to the Ubuntu/Windows server.
S51, packaging neural network input data of all fluid particles;
s52, adopting a Socket communication protocol to send the neural network input data to an inference program on Atlas200 DK;
s53, the inference program receives and unpacks the input data of the neural network, and then calls the built-in AI core to solve the neural network to solve the pressure data. The neural networkAs input data of the neural network, constructing a neural network structure taking the multi-layer perceptron as a main body; the neural network with each layer of perceptrons as a main body is expressed as follows:
f(x)=H(ω*x+b)
wherein ,x(x1 ,x 2 ,…,x n ) Representing the input vector of the layer, ω represents the weight, b represents the bias, H represents the activation function, f () represents the layer output, and the neural network employs ReLU as the activation function.
Before the program is run in an inference mode, a model file suitable for solving the neural network by AIcore is generated, namely the neural network (shown in fig. 2) is converted into a form which can be used by an AI chip, and the process comprises two steps of model preparation and model conversion. The model preparation is specifically as follows: and (3) acquiring a training data set by using a traditional MPS algorithm in the S3, and constructing and training a neural network by using tensorsurface. The model transformation is specifically as follows: converting pb files of the tensorflow preservation network by using a Hua OMG tool to obtain an om model supported by an AI chip.
After generating the model file, the programming realizes reasoning, namely solving the neural network to solve the pressure data by using the built-in AI core, and specifically comprises the following steps:
I. initializing a model, wherein the model comprises a Matrix frame such as a Graph object, an Engine object and a model manager required by running an om file;
II, reconstructing input data sent by the Ubuntu/Windows server to make the input data be NNTensor objects suitable for model households;
pushing the NNTensor object into a model manager, calling an AIcore solving neural network to perform reasoning, and solving pressure data;
IV, obtaining an inference result;
v, packaging the result and sending the result back to the Ubuntu/Windows server;
and VI, returning to the step II, and waiting for receiving the next time step data.
S54, after the AIcore solving neural network is solved, the reasoning program packages the reasoning result, and the reasoning result is sent back to the Ubuntu/Windows server in a Socket communication mode.
S6, correcting the particle speed and position according to the pressure gradient;
1. solving the pressure gradient term correction speed and displacement of the control equation according to the pressure data transmitted back to the Ubuntu/Windows server; the specific calculation formula is as follows:
the Ubuntu/Windows server outputs the calculation result of the current time step, namely the result of flow field real-time prediction, including particle position, speed, pressure and the like.
S7, entering the next time step, and re-executing the steps S3-S7.
And when the calculation termination condition is reached, outputting a calculation result, and analyzing the calculation result. If the calculation termination condition is not reached, returning to the step 2, and starting the next time step.
Compared with the prior art, the beneficial effects of the embodiment are as follows: according to the flow field real-time prediction system and the flow field real-time prediction method based on edge calculation, the neural network technology and the leading edge artificial intelligent equipment are combined to realize the real-time simulation of the complex flow field, so that the problems that the calculation time of the complex flow field is long and the real-time flow field analysis is difficult to realize in the field of fluid calculation are solved. When a flood disaster is sudden, disaster development is rapidly analyzed for flood disaster scene which is easy to be subjected to the unconditional use of a professional computing server, a coping strategy is rapidly made, and loss is reduced. In addition, the system and the method thereof have the advantages of low cost, high speed, reliability and suitability for fluid instant calculation in complex scenes.
It should be noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solution of the present invention may be modified or substituted without departing from the spirit and scope of the technical solution of the present invention, and the scope of the claims of the present invention should be covered.

Claims (8)

1. A flow field real-time prediction system based on edge calculation is characterized in that: comprising
The server is provided with a server which, the method comprises the steps of obtaining and storing flow field calculation parameters, establishing a particle model, calculating intermediate speed and intermediate displacement of the particle model, inputting data of a neural network, transmitting the inputting data of the neural network to a developer kit to calculate pressure data, and correcting the intermediate speed and intermediate displacement of particles by using the pressure data;
the developer kit comprises an acceleration module, a server and a data processing module, wherein the acceleration module is used for calculating input data of the neural network by constructing a solution pressure poisson equation, solving the pressure data and transmitting the pressure data to the server;
the digital sensor comprises a digital temperature sensor and a digital flow rate sensor and is used for acquiring the temperature and the flow rate of the flow field;
the neural network is used for solving a pressure poisson equation;
the method comprises the following specific steps:
s41, calculating the particle number density n according to the intermediate displacement * The calculation formula is as follows:
wherein ,representing the intermediate displacement of the i particles; w represents a kernel function; h represents the radius of the support set, which is 2.1l 0 ;l 0 Representing inter-particle distances;
s42, converting the solving process of the pressure poisson equation into a regression problem, wherein the calculation formula is as follows:
wherein k represents the operation to the kth step; indicating the divergence of the i particles at the intermediate velocity of the kth step.
2. The flow field real-time prediction method based on edge calculation is characterized by comprising the following steps of:
s1, acquiring flow field calculation parameters and storing the flow field calculation parameters in a server;
s2, establishing a discretized particle model in a server according to the flow field parameters;
s3, solving a particle model in a server according to the viscosity force and the physical strength in a control equation, and calculating the intermediate speed and the intermediate displacement of the particles;
s4, constructing input data of a neural network according to the intermediate displacement, wherein the neural network is used for solving a pressure poisson equation;
the method comprises the following specific steps:
s41, calculating the particle number density n according to the intermediate displacement * The calculation formula is as follows:
wherein ,representing the intermediate displacement of the i particles; w represents a kernel function; h represents the radius of the support set, which is 2.1l 0 ;l 0 Representing inter-particle distances;
s42, converting the solving process of the pressure poisson equation into a regression problem, wherein the calculation formula is as follows:
wherein k represents the operation to the kth step; indicating the divergence of the i particles at the intermediate velocity of the kth step;
s5, transmitting the input data to a neural network of a developer kit for calculation, and solving pressure data; transmitting the pressure data back to the server;
s6, correcting the intermediate speed and the intermediate displacement of the particles according to the pressure gradient;
s7, entering the next time step, and re-executing the steps S3-S7.
3. The method of claim 2, wherein the flow field parameters include constants in the empirical formula of viscosity coefficients, flow field boundary locations, solid wall boundary locations, density information, and temperature and flow rate of the fluid.
4.A method according to claim 3, wherein step S2 comprises the steps of:
s21, comparing the internal memory of the developer kit according to the flow field calculation parameters, and ensuring that the total internal memory is less than 70% to determine the proper inter-particle distance l 0
S22, constructing four layers of common particles on the solid wall boundary and the outer side according to the inter-particle distance and the solid wall boundary position, and uniformly dispersing the rest into fluid particles; wherein, two layers of common particles close to the fluid are first-class solid particles, and two layers far away from the fluid are second-class solid particles; the first type solid particles and the second type solid particles do not update the speed displacement, and the second type solid particles do not participate in the pressure solution;
s23, marking fluid particles positioned at the flow field boundary according to the flow field boundary position and the fluid flow velocity, and marking the fluid particles escaping from the flow field boundary as common particles in the calculation process; judging whether fluid particles exist in the boundary position of the flow field, and if so, marking the fluid particles; if not, supplementing the fluid particles of the flow velocity into the boundary position of the flow field according to the flow velocity of the fluid.
5. The method according to claim 2, wherein step S3 is specifically: decomposing a control equation into an estimated step and a correction step by using a gridless method-a moving particle semi-implicit method; in the estimating step, according to the viscous force and physical force in the control equation, solving a particle model, and calculating an estimated intermediate speed v * And intermediate displacement r *
6. A method according to claim 2, characterized in thatIn the following steps: the neural network construction method comprises the following steps: to be used forAs input data of the neural network, constructing a neural network structure taking the multi-layer perceptron as a main body; the neural network with each layer of perceptrons as a main body is expressed as follows:
f(x)=H(ω*x+b)
wherein ,x(x1 ,x 2 ,…,x n ) Representing the input vector of the layer, ω represents the weight, b represents the bias, H represents the activation function, f () represents the layer output, and the neural network employs ReLU as the activation function.
7. The method according to claim 2, characterized in that step S5 comprises in particular the steps of:
s51, packaging neural network input data of all fluid particles;
s52, transmitting the neural network input data to a developer kit;
s53, receiving and unpacking data by the developer suite, and then calling a neural network to solve the pressure data;
s54, packaging the solving result, then transmitting the solving result back to the server, and entering step S6.
8. The method according to claim 2, characterized in that step S6 is more specific: according to the pressure data returned by the developer kit, solving a pressure gradient term of a control equation, correcting the speed and the displacement, and calculating the formula:
wherein ,v* Representing an intermediate speed; r is (r) * Representing an intermediate displacement; v represents the speedThe method comprises the steps of carrying out a first treatment on the surface of the r represents displacement; Δt represents the time step; p represents pressure, ρ represents density; wherein ∈v is nabla operator ∈p is pressure gradient;
and then outputting the calculation result of the current time step.
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