With the continuous development of economic globalization and the continuous conflict between human activities and the natural environment, the human living environment is deteriorating day by day. This allows us to re-examine the relationship between human living environment and natural environment. Ecological intelligent green building is put forward under the background of comprehensively promoting the concept of sustainable development of green and low-carbon building, which urges people to start to reflect on whether they can solve the building's demand for natural resources from the root based on an ideal life . Lin J and others said that the most basic concept of green building is to maximize the use of resources, save resources and protect resources on the premise that human beings can live a healthy and comfortable life. Nowadays, construction, industry and transportation are the three main sources of energy consumption, and China is a large infrastructure country. In order to reduce building energy consumption, green buildings have developed rapidly . Therefore, it is very necessary to optimize the ventilation design of green buildings through a series of scientific means. CFD (Computational Fluid Dynamics) is an interdisciplinary subject combining modern fluid mechanics, numerical mathematics and computer science. It can optimize the ventilation design of green buildings and greatly reduce building energy consumption. Haghighinia A and others believe that green building refers to a building that provides human beings with a healthy and comfortable space for work, residence and activities, while realizing the most efficient use of energy and the lowest impact on the environment. Green building is also known as ecological building and sustainable development building . In the field of architectural economics, green building measures have brought social benefits, environmental protection benefits and economic benefits, and reduced the risk of construction projects. In the field of planning, green building first emphasizes the identification of the ecological characteristics and development positioning of the site, so as to make full use of the resources and energy of the site, reduce the impact of unreasonable construction activities on the environment, and make the building and the environment live in harmony. In the design field, the green building adopts the building integrated design method and abides by the environmental design criteria, takes the building as a complete system, and comprehensively considers the factors such as the spacing, orientation, shape, structural system and envelope of the building . In the field of construction, the goal of green building is to reduce the serious impact on the environment. By adopting green construction methods with environmental awareness, the construction process of green buildings can significantly reduce the interference to the surrounding environment, reduce the amount of landfill waste and the amount of natural resources consumed in the construction process, and minimize the adverse impact of buildings on indoor air quality. In the field of operation and maintenance, the technology and method of green building can ensure the realization of building planning and design objectives through reasonable environmental goal setting and intelligent system control. Adopt a scientific and applicable consumption mode to ensure the safe and clean operation of the building equipment system, reduce the energy consumption of the system, ensure the indoor air quality and thermal, acoustic and optical environment, reduce the generation of pollutants during operation, and improve the overall operation efficiency of the building. Therefore, green building follows the principle of sustainable development, takes high and new technology as the leading factor, and comprehensively embodies the basic concept of “saving energy, saving resources, protecting the environment and people-oriented” through scientific overall design for all links of the whole life of the building. Create a building environment with high efficiency, low consumption, no waste, no pollution, health, comfort and ecological balance, and improve the function, efficiency and comfort level of the building. Mazaheri A R and others said that digital image processing technology came into being in the last century, which means converting image signals into digital signals and processing them on computers. At present, it is used in many fields. For example, it is widely used in aerospace, industrial production, military, public security, medicine, culture and art. It is a promising new technology, which is of great significance to promote the development of technology . Kim Y K and others believe that the wide application of digital image processing technology has many advantages, such as good reproducibility. There is a difference between digital image processing and analog image processing, which means that even if the image is stored, transmitted, copied and converted, the image quality will not be very poor. It can best reproduce the original image. Now, especially the accuracy of image processing, it should have high accuracy . For the current technological development, the digital image is converted into a two-dimensional array of arbitrary size, which plays a direct role in the digitization ability of the equipment in the scanner. The gray level of each pixel can be quantified to 16 bits or more.
There are three common methods to measure the wind environment of buildings: field measurement, wind tunnel experiment and CFD numerical simulation. With the rapid development of computer performance, numerical simulation method is widely used in the measurement of wind environment. As shown in Figure 1. Firstly, the finite volume method is used to obtain the calculation grid, generate the calculation points, determine the boundary conditions of the object, establish the discrete equation, and then repeat the test until the solution converges, and finally display and output the calculation results . This is the numerical simulation of CFD.
Then, the natural ventilation optimization design of green buildings based on CFD simulation. Firstly, the wind environment of the basic site is obtained by inputting the surrounding environment of the site terrain and conducting CFD simulation experiments. This is the design basis of the overall layout, and then repeatedly carry out CFD simulation and optimization to obtain the indoor and outdoor wind environment, and then design the building shape and enclosure interface, improve the relationship between the building itself and the foundation, surrounding buildings, wind direction and building layout, make full use of natural resources, obtain better natural ventilation conditions and reduce the impact of adverse wind environment. Under unstable atmospheric conditions, the flow of air near the surface is affected by the friction of topographic relief and buildings, so that the average wind speed forms a vertical velocity profile. The closer it is to the surface, the smaller the wind speed is. Generally speaking, the distribution of pollutants in the surface layer is more affected by the so-called vertical wind direction or logarithmic dispersion index . A balanced boundary layer is usually specified at the inlet, with a distance of at least 5 times the height of the highest building. The average velocity distribution is usually obtained from the logarithm curve of windward terrain with corresponding roughness
In the boundary behind the obstacle, open boundary conditions are used, which are generally outflow or static pressure boundary conditions. Under the outlet boundary condition, the derivative of all variables is zero, which corresponds to a fully developed flow. For LES model, convective outflow boundary conditions shall be used. The gradient of all variables is zero as the outflow boundary condition. The outlet boundary shall be placed where the impact on the building can be ignored. Therefore, the outlet boundary is usually set as free outflow. It is considered that the flow on the outflow surface has been fully developed and the flow has returned to the normal flow without building obstruction, so its outlet pressure is set as atmospheric pressure . The section at the outlet is taken at the place without backflow, and the pressure outlet boundary condition is adopted. The setting of top and side boundary conditions is very important to maintain the equilibrium boundary layer distribution. It is generally considered that the boundary layer is affected by constant shear stress. This is because the top and left and right sides are far enough away from the building, and the air flow is hardly affected by the building, which can be considered as a free sliding surface. The flow velocity along the top of the turbulence domain is usually calculated at the specified position and at the top of the turbulence domain. For the setting of left and right boundary conditions, when the flow direction is parallel to the side boundary, in order to make the velocity component of the parallel flow in the normal direction of the boundary zero, the symmetrical boundary is usually used in CFD commercial software. Symmetric boundary conditions strengthen a parallel flow by forcing the normal velocity component to zero, and specify that the derivatives of all other variables are zero. If the size of the calculation domain is large enough, the side and top boundary conditions have no great influence on the calculation results around the target building. Using the non stick wall state (usually the velocity component and tangential velocity gradient are zero) and a large calculation domain will make the calculation more stable. For the building wall and underlying surface, the standard
For engineering applications, the most widely used is the two equation
Conceptual design is the stage of conceiving the whole design scheme, so there are often many different design schemes at the beginning of this stage. Conceptual design determines the basic framework of the design in the next stage. The conceptual design stage is the most innovative part of the whole design process, which basically determines the spatial function distribution of the whole building, the design method and construction method of structural equipment and so on . Conceptual design involves the refinement of architectural scheme. Its architectural volume and appearance determine the location and site orientation of the building, as well as its structure and indoor environmental quality.
Conceptual design almost completely relies on the knowledge and experience of architects in conventional design. After the scheme is formed, it is handed over to other members of the design team for refinement and analysis. If the construction objectives are not met after analysis, the scheme needs to be changed again according to the feedback. After forming an alternative scheme, analyze it again. After the scheme is finally formed, it takes a lot of time to deepen the design and draw the construction drawings. This can be clearly seen from Figure 2. In the traditional design, the payment schedule proposed by the architectural designer is generally 15% in the conceptual design stage, 30% in the design deepening stage, and 55% in the construction drawing and detailed drawing stage. It also reflects that designers spend most of their time and energy on drawing in traditional design. In the green building design based on CFD, due to the parametric design of CFD technology, the model scheme formed by conceptual design can automatically draw construction drawings, detailed drawings and other drawings according to the requirements and drawing standards. The time spent by designers on drawing making is saved, so that designers have more time and energy to spend on scheme design. In addition, the application of CFD technology has also changed the traditional design mode in the conceptual design stage. Since the scheme formed in the conceptual design stage will directly affect the performance and energy consumption of the building, in the conceptual design stage of green building based on CFD, in addition to architects, structural engineers, equipment engineers, constructors, operators and other building related parties participate in the whole process . We all worked together in an all-round way around a green goal. In the conceptual design stage, we divided the tasks through joint discussion. For example, the green building standard requires that the buildings do not produce light pollution to the surrounding buildings, and the wind speed in the pedestrian area around the buildings is less than 5m / S. Although these green requirements can also be adjusted through other technical means in the later deepening design, sometimes the improper design such as site selection in the conceptual design stage will make it difficult to make up through technical means in the later stage. In the conceptual design stage, the first step is to establish a mechanism of common consultation. Secondly, it studies and formulates specific architectural design objectives based on the needs of owners and green buildings. After the goal is formulated, all participants cooperate to complete the formulation of the conceptual design scheme according to the division of labor. In the whole process of formulating the scheme, the discussion and communication among all participants are based on the 3D model of CFD, which saves the detailed information description of each discipline for the building. Therefore, all parties can easily process the information through the processing of the model. For example, in the equipment discipline, first export the scheme model to the file format recognized by the energy-saving analysis software through the interface, and then the analysis results can be obtained quickly through the analysis software. According to the results, the designers propose to adjust the architectural design, improve the thermal resistance value of building materials and other feedback information. The supplier's plan system is discussed regularly. After several rounds of such information feedback and scheme discussion, the conceptual scheme will be formulated soon. And because the scheme is the result of multi-party discussion and analysis, there will be few changes in the later deepening design and construction stage.
Before analyzing the building performance of the project, the first thing to do is to fully understand the climate environment around the project. The most influential factor on building energy efficiency design is climate. The city where the analysis site is located has a severe cold climate. Therefore, it is necessary to clarify the basic requirements of the climate zoning of the project on the building at the early stage of the station building design of the project. Figure 3 shows the meteorological data information of the main indoor areas of the city, including solar radiation, wind direction, temperature, etc. the acquisition and analysis of these data can help architectural designers understand the basic conditions of solar radiation, wind direction, humidity and so on, and provide intuitive and accurate data navigation for designers to choose various passive strategies to improve users' thermal comfort .
Through the integration of the building and the surrounding environment, combined with the local meteorological characteristics, several passive energy-saving strategies are analyzed and optimized, and finally the best range of human thermal comfort is obtained, which has a good reference value for improving human comfort. Strive for a better wind, light and thermal environment for the building, so as to reduce the unnecessary energy consumption cost caused by the adoption of passive energy-saving measures. The human body has obvious response to the changes of air humidity, relative humidity, air velocity and average radiation temperature. Through the automatic calculation of these four indexes by software, the most comfortable area of the human body can be formed in the humidity map. The city's highest temperature in summer occurs in July, while the lowest temperature in winter occurs in January. The temperature difference is large and the air is dry. The sampling points in winter and summer hardly fall into the comfort area, so it is necessary to adopt a variety of passive and active strategies to expand the range of human comfort. The orientation and shape of buildings have a great impact on the two indicators of wind environment and sunshine. In order to obtain sufficient and good sunshine and reduce the use of air conditioning and heating equipment, the strong and cold north wind in winter should be avoided in the building ventilation design, and the warm and humid South wind in summer should be introduced indoors, which greatly reduces the waste of resources and is conducive to the sustainable development of the building; The purpose of determining the ideal orientation of the building in all architectural design is to develop strengths and avoid weaknesses, prolong the opportunity to obtain sunshine in winter and avoid excessive sunlight in summer. On the basis of considering sunshine, the determination of building orientation should also take into account the dominant wind direction in winter and the dominant wind direction in summer, because if the main facade and long side of the building form an acute angle or perpendicular to the dominant wind direction in winter, the building will be more exposed to the cold wind, resulting in increased energy consumption and increased cost due to the enhancement of building structural nodes. On the contrary, if the main facade or long side of the building is at an acute angle or perpendicular to the dominant wind direction in summer, the building will obtain better ventilation effect. The reality is that in order to form the most suitable living environment indoors, the air in all indoor areas must flow, and the orientation can not be determined through simple wind environment simulation. It is also necessary to consider subjective factors such as sunshine analysis and human comfort. Building light environment analysis is divided into two parts: outdoor light environment analysis and indoor light environment analysis. The outdoor light environment focuses on the study of the building as a whole. Due to the influence of orientation and spacing, it is blocked by the surrounding buildings or causes light blocking to the surrounding buildings. It focuses on determining the sunshine spacing to ensure that all buildings meet the minimum sunshine duration requirements on the winter solstice or cold days; The indoor light environment analysis focuses on the study of the building space layout. On the basis of the initially determined best orientation, the rooms with different zoning orientations block the light of other rooms, and study the reasonable distribution of rooms with strong and weak light demand . CFD technology can meet the needs of outdoor light environment analysis. According to the solar track changes of the building's geographical location in different seasons and months, the building shadow range can be obtained, and the light shielding of the shadow to adjacent buildings can be intuitively reflected through the model, which greatly optimizes the selection of building spacing and the auxiliary building design process. The material statistical summary table is sorted out from the material list, and it can be calculated that the research project meets the evaluation requirements of green building with the utilization rate of recyclable materials of no less than 10%, reaching 13.82%. The statistical process of energy consumption analysis also fully shows the advantages of convenient extraction and easy statistics of building material information, reflecting the unique statistical and display function. The area where the project is located is hot in summer and cold in winter. In summer, it is necessary to prevent solar radiation and ventilate and dissipate heat, while in winter, it is just the opposite. Therefore, there are more strict requirements for building energy conservation, and the shape coefficient shall be controlled at a reasonable level. According to the concept of volume and the total area in CFD, the corresponding calculation is completed automatically. With the support of this function, CFD can control the specific surface area of the conceptual scheme in the scheme stage of architectural design, select the scheme with more reasonable indicators for in-depth refinement, and avoid unnecessary design ideas, which will affect the design progress and quality. According to the above methods, the shape coefficient of the buildings in the selected scheme of the project is 0.24, which is less than the shape coefficient of the reference project of 0.26, and meets the relevant evaluation standards of the green building evaluation standards. The determination of architectural form cannot be based solely on the preferences of designers or the requirements of Party A, and multiple factors need to be comprehensively considered. In the form selection, the regular and non publicized performance style is one aspect of catering to the green building design. However, while meeting the use needs and aesthetic elements, the energy-saving norms in different regions have different requirements for the building form design, which directly affect the building energy consumption. The CFD language of the architectural form can be expressed by the architectural form coefficient. If the beauty of the form cannot be described in words, and it is impossible for each designer involved in affecting the form to achieve unanimous recognition, it is better to let the data speak and use the minimum form coefficient to determine the choice of the final architectural form. According to the research, the building energy consumption will increase by 2.5% when the shape coefficient s increases by 0.01. Choosing a smaller shape coefficient is to choose a more energy-saving design orientation. In conclusion, under the limitation of various evaluation factors of building green, CFD technology can give corresponding technical parameters as a reference for auxiliary design, which is a very persuasive index in the design process.
With the continuous development and improvement of China's construction industry system and the strong praise of CFD by the state and local governments, CFD technology has increasingly become the focus of the construction industry; Similarly, in the construction industry, the increasingly prominent problems of building energy consumption and ecological environment have also promoted the great development of green buildings. It can be seen that both CFD technology and green building are the mainstream and general trend of the current development of China's construction industry. CFD technology creates a feasible technical platform and tool for the evaluation of green buildings, and the green building evaluation runs through the whole life cycle of buildings and is also the management object of CFD technology for building creation and construction operation. They just learn from each other and complement each other. By summarizing the basic theory of CFD technology and the evaluation standard of green building, this paper analyzes the author's practice of using CFD technology to design projects that meet the green building standard, discusses the possibility of CFD technology in green building, and boldly summarizes the integration strategy of CFD in green building design and green index evaluation. This paper systematically summarizes the design strategy of CFD technology in green building design, and puts forward the design principles of energy conservation, low carbon, environmental protection, passive, active complementation and overall optimization; Strengthen the connection between building and environment, obtain parameter analysis, ensure indoor environmental quality and optimize the allocation of energy; And build a CFD design team, formulate model and component specifications, meet the CFD plan of green building evaluation standards, and conduct a comprehensive and collaborative design process led by the architecture specialty. Integrate the advantages of CFD into the evaluation of green building design to provide a more reasonable, effective, scientific and realistic design method, clarify the complex situation of multi-professional, multi-platform and multi-technology integration, so that CFD technology has a larger extension and a deeper connotation. Make green buildings have a basis to rely on, achieve mutual benefit and win-win, and promote each other.
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Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching Research on evaluation system of cross-border E-commerce platform based on the combined model A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G) on the set of maximal subgroups of p-groups The internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network