Calculation method for accurately capturing mixed flow energy transfer based on least square method

Abstract

The invention provides a calculation method for accurately capturing mixed flow energy transfer based on a least square method, and the method comprises the following steps: arranging discrete nodes in a calculation domain, and constructing a spatial partial derivative discrete expression based on a moving least square method; discretizing a time derivative item by adopting a Houbolt three-order time integral method, and initializing physical quantity data at the first two moments in combination with an Euler method; coupling the level set function and the volume fraction to track a gas-liquid interface, and simultaneously solving a comprehensive two-dimensional control equation; the pressure field is corrected by solving a Poisson equation containing a surface tension item, and the velocity field meeting the continuity equation is updated; kinetic energy and gravitational potential energy of water and air are calculated in a split-phase mode, and periodic characteristics of energy conversion are analyzed.

Description

Technical Field

[0001] The present invention belongs to the technical fields of pipeline systems, energy transfer, etc., and particularly relates to a calculation method for accurately capturing the energy transfer of mixed flow based on the least squares method. Background Art

[0002] Pipeline systems are widely used in the fields of water conservancy and water supply and drainage engineering. Under sudden and rapid drainage conditions, transient airflows occur in the system, and the drainage capacity of the system decreases. The study of transient air-water mixed flow is very important for the design and operation of pipelines and is of great significance for improving the resilience of these critical infrastructure networks to natural disasters. Energy analysis can support a comprehensive understanding of the transient dynamic propagation in closed pipeline flows and can explain complex transition processes in a simple and effective way. The energy transfer characteristics of pipeline mixed flow directly affect the efficiency of the system, energy consumption, and the safety of equipment. However, due to insufficient data on the fluid velocity and pressure inside the pipe, a detailed analysis of the influence of gas-phase participation on the energy dissipation pattern during transient air-water transition has not been fully studied, and the energy transfer process between air and water in the mixed flow cannot be fully understood. Summary of the Invention

[0003] Aiming at the defects and deficiencies of the existing technology, the present invention proposes a calculation method for accurately capturing the energy transfer of mixed flow based on the least squares method, accurately discretizes the physical quantities in the control equation, and better adapts to complex air-water boundary geometries by adjusting the order of the difference template and the node distribution. It is used to solve the full two-dimensional numerical model, retrieve the detailed pressure and velocity distribution patterns, and obtain the energy transfer between transient air and water by solving the energy expression, including the conversion of potential energy and kinetic energy of air and water, and efficiently and accurately simulate the transient air-water flow in the drainage pipeline system. The aim is to accurately and efficiently determine the energy transfer characteristics of pipeline mixed flow and provide a reliable theoretical basis for engineering design.

[0004] In the solution of the present invention, the two-dimensional pipeline water-air two-phase flow equations are discretized to obtain a full two-dimensional numerical model; initial conditions are set, and the momentum equation is solved to obtain an intermediate velocity field U * , the level set function and volume fraction are updated; the Poisson equation is solved by the least squares method to obtain the pressure field P n+1 ; the obtained pressure field P n+1 is used to correct the intermediate velocity field U * to obtain a velocity field U n+1 that meets the conditions; based on the obtained U n+1 and P n+1 the energy transfer process is calculated based on the energy expression.

[0005] The innovative design adopted by the present invention to solve its technical problems is reflected in:

[0006] A computational method for accurately capturing mixed flow energy transfer based on the least squares method comprises the following steps:

[0007] Arrange discrete nodes in the computational domain, and construct a discrete expression of spatial partial derivatives based on the moving least squares method; (MLS spatial discretization, corresponding to step S1 and formula 2 of the embodiment)

[0008] The Houbolt third-order time integral method is used to discretize the time derivative term, and the Euler method is combined to initialize the physical quantity data of the first two moments; (Houbolt+Euler initialization, corresponding to step S3 of the embodiment, formula 13-16)

[0009] The gas-liquid interface is tracked by coupling the level set function and the volume fraction, and the full two-dimensional governing equations are solved simultaneously; (CLSVOF interface tracking, corresponding to step S2 and formulas 11-12 of the embodiment)

[0010] The pressure field is corrected by solving the Poisson equation including the surface tension term, and the velocity field that satisfies the continuity equation is updated; (Pressure correction (Poisson equation), corresponding to step S5, formula 24 of the embodiment)

[0011] The kinetic energy and gravitational potential energy of water and air are calculated in phases, and the periodic characteristics of energy conversion are analyzed (phase energy analysis, corresponding to step S7 and formulas 25-28 of the embodiment).

[0012] Furthermore, the moving least squares method is implemented as follows:

[0013] Dynamically select several nearest nodes in adjacent sub-regions for each node;

[0014] The residual function is constructed based on Taylor expansion, and the residual is minimized by the least squares method to generate a linear system of spatial partial derivatives.

[0015] Furthermore, the residual function includes a weight function, and the value of the weight function is related to the distance between nodes.

[0016] The above reflects the MLS discrete details (residual function, weight function) implemented in the design of the present invention, corresponding to Formula 2.

[0017] Furthermore, the time derivative term of the Houbolt third-order time integration method discretely uses the physical quantity data of the current moment, the previous moment and the previous two moments;

[0018] The data at the first two moments are estimated by initialization using a single-step explicit Euler method.

[0019] The above reflects the specific design of Houbolt method + Euler initialization implemented in the design of the present invention, including the specific design of time integration and initial conditions, corresponding to formulas 11-12.

[0020] Furthermore, the coupling level set function and the volume fraction calculate the interface curvature through the level set function, and correct the interface position through the volume fraction to ensure mass conservation;

[0021] The full two-dimensional control equations include the continuity equation, the momentum equation, the volume fraction, and the level set function transport equation.

[0022] The above reflects the specific design of the CLSVOF interface tracking implemented in the design of the present invention to achieve gas-liquid interface capture, corresponding to Formulas 13-16.

[0023] Furthermore, the Poisson equation includes a surface tension term and a gravity body force term, corresponding to Formula 24.

[0024] Furthermore, the separated-phase calculation calculates the kinetic energy and gravitational potential energy of water and air, and analyzing the periodic characteristics of energy conversion specifically includes:

[0025] Dynamically divide the occupied regions of the water phase and the gas phase based on the volume fraction;

[0026] Perform integral calculations of the kinetic energy and gravitational potential energy for the water phase and the gas phase respectively;

[0027] Quantify the energy dissipation rate through the energy conversion frequency and amplitude differences.

[0028] Corresponding to Formulas 25-28.

[0029] Furthermore, the range of adjacent sub-regions is dynamically adjusted according to the change of the gas-liquid interface curvature, specifically including:

[0030] When the interface curvature exceeds a preset threshold, expand the sub-region range to include more adjacent nodes;

[0031] When the interface curvature is lower than the preset threshold, shrink the sub-region range to reduce the calculation amount.

[0032] The above reflects the dynamic sub-region adjustment based on the interface curvature change implemented in the design of the present invention to achieve interface tracking and calculation efficiency optimization.

[0033] And, an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein when the processor executes the program, the steps of the above method are implemented.

[0034] A non-transitory computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the above method are implemented.

[0035] Compared with the prior art, the present invention and its preferred embodiments are based on the least squares discrete partial differential equations, which can solve the velocity and pressure data of the mixed fluid in the pipe, so as to accurately and efficiently determine the energy transfer characteristics of the pipe mixed flow and provide a reliable theoretical basis for engineering design.

[0036] Its core design points and beneficial effects at least include:

[0037] 1. High precision and adaptability to complex boundaries

[0038] Based on the unstructured node discretization technology of the moving least squares method (MLS), it breaks through the dependence of traditional grid methods on regular geometries. By dynamically adjusting weights and fitting with local Taylor expansion, it significantly improves the capture accuracy of complex gas-liquid interfaces (such as bubble rupture, transient oscillation), and effectively avoids interface blurring and numerical dissipation problems.

[0039] 2. Balance between time integration stability and efficiency

[0040] Adopting the Houbolt third-order time integration method combined with explicit Euler initialization, taking into account high-order accuracy and compatibility with initial conditions, reducing numerical oscillations in scenarios of intense gas-liquid interaction (such as sudden pressure changes, transient energy transfer), and ensuring the stability of long-term simulations.

[0041] 3. Unity of interface tracking and mass conservation

[0042] The CLSVOF method that couples the level set function (curvature calculation) with the volume fraction (mass conservation), by dynamically correcting the interface position, solves the defects of a single interface tracking model in mass loss or curvature calculation errors, and is especially suitable for refined simulations of gas-liquid mixing regions.

[0043] 4. Interpretability of the phase-separated energy transfer mechanism

[0044] By independently integrating the kinetic energy and potential energy of the separated phases (water phase and gas phase), for the first time, the periodic characteristics of energy conversion (such as the kinetic energy change frequency being twice that of the potential energy) are revealed in the transient flow of a closed pipe, providing a theoretical basis for the optimal design of the pipe system to resist transient pressure fluctuations.

[0045] 5. Computational resource optimization and self-adaptability

[0046] Based on the dynamic sub-region adjustment strategy based on interface curvature, the node coverage is expanded in high-curvature regions to improve accuracy, and the range is shrunk in low-curvature regions to save computing power, realizing an intelligent balance between computing efficiency and accuracy. Description of the Drawings

[0047] The present invention will be further described in detail below with reference to the drawings and specific embodiments:

[0048] Figure 1 It is a schematic diagram of the method flow in the embodiment of the present invention;

[0049] Figure 2 It is a schematic diagram of the experimental system in the embodiment of the present invention;

[0050] Figure 3 It is a comparison diagram of the pressure oscillation at the bottom of the vertical riser for different models and experimental data in the embodiment of the present invention;

[0051] Figure 4 It is a comparison diagram of the numerical solutions and analytical solutions of the evolution of different energy forms over time in the embodiment of the present invention. Specific implementation manner

[0052] To make the features and advantages of this patent more obvious and understandable, specific embodiments are given below for detailed description as follows:

[0053] It should be noted that the following detailed description is illustrative and aims to provide further explanation for the present application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs.

[0054] It should be noted that the terms used herein are only for describing specific implementation manners and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0055] As Figure 1 As shown, the embodiment of the present invention provides a calculation method for the energy transfer between water and gas in a pipeline mixed flow, and proposes to accurately discretize each physical quantity in the control equation based on the least squares method for solving the full two-dimensional numerical model to obtain the pressure and velocity distribution data required for the energy expression.

[0056] The specific steps are as follows:

[0057] S1: Points are distributed in the entire calculation domain and sub-regions are established. Based on the moving least squares method, the spatial partial differential terms at each point in the calculation domain to be solved are converted into a linear accumulation of the product of the physical quantities at each point in the sub-region and the weight coefficients, so as to discretize the spatial partial differential terms in the control equations;

[0058] S2: According to the linear system obtained in step S1, the expression of the spatial partial differential term is extracted, and the expression of the time partial differential term is obtained according to the Houbolt method, and the partial differential equation can be discretized into an algebraic equation;

[0059] S3: Substitute the equation obtained in S2 into the borrowed two-dimensional pipe water-air two-phase flow equations to obtain a full two-dimensional numerical model;

[0060] S4: Set the initial conditions: Initialize and define parameters such as the velocity U n , the pressure P n , the level set function , the volume fraction α n , etc. Solve the momentum equation according to the initialized data to first obtain an intermediate velocity field U * , update the level set function and the volume fraction α n+1 ;

[0061] S5: Solve the Poisson equation by the least squares method to obtain the pressure field P n+1 ;

[0062] S6: Then use the pressure field P n+1 obtained in S5 to correct the intermediate velocity field U * so as to obtain a velocity field U n+1 that satisfies the continuity equation;

[0063] S7: Use the obtained pressure P and velocity U distribution data to solve and calculate the energy expression to capture the energy transfer process of the transient water-air mixed flow

[0064] As a preferred solution of this embodiment, S1 first distributes N points in the entire calculation domain, takes n s points closest to the ath point, and expresses the ath point in the form of a Taylor expansion

[0065]

[0066] Substitute the n s points into the Taylor expansion and sum to obtain the residual function B(Φ)

[0067]

[0068] In the formula, Φ i,0 is the unknown value of the ith th node, Φ i,j is the unknown value of the jth s node in the n th sub-region, h ij = x i，0 - x i,j , kij = yi,0 - yi,j represents the vector distance between the ith node and the jth node, and W(h ij ) is the weight function of the jth node.

[0069] According to the least squares method, find the minimum value of the partial derivative term of the residual function, and let Each order partial derivative term D Φ can be obtained from the linear system A·D Φ = b as follows:

[0070]

[0071] As a preferred solution of this embodiment, S2 extracts the expressions containing each order spatial differential term in the equation set according to the linear system obtained in step S1 as follows:

[0072]

[0073] Adopt the Houbolt method: Set the time step Δt, discretize the time axis to obtain a series of discrete time points, and solve the physical quantity Φ at the unknown time layer through the backward difference format n+1 , for the physical quantity at the unknown time t = n + 1, approximate it as:

[0074]

[0075] When solving the physical quantity at the n + 1 moment, the physical quantities at the n - 1 and n - 2 moments are involved, but the initial conditions do not give their values, so the Euler method is used to solve the first two initial values of the Houbolt method, and its expressions are as follows

[0076]

[0077] As a preferred solution of this embodiment, S3 first introduces the control equations for simulating hydraulic characteristics and the coupled gas-liquid interface tracking scheme (coupled level set and volume of fluid model):

[0078] Continuity equation:

[0079] ▽·U = 0 (13)

[0080] Momentum conservation equation:

[0081]

[0082] Volume fraction transport equation:

[0083] α t + U·▽α = 0 (15)

[0084] Level set function transport equation:

[0085]

[0086] where U = (u, v) is the velocity field (u is the horizontal velocity, v is the vertical velocity), P is the pressure, σ is the surface tension coefficient, is the local average curvature, and F is the body force generated by gravity, F = (0, g). is the level set function defined as the signed distance to the interface (i.e., the zero level set), and α is the volume fraction. In this case, the level set function is positive in water and negative in air; the density viscosity and curvature depend on the level set function is the Heaviside function defined as follows:

[0087]

[0088] Substituting equations (4) to (12) into the two-dimensional pipe water-air two-phase flow control equations with applications, the full two-dimensional numerical model is obtained as follows:

[0089] Continuity equation:

[0090]

[0091] Momentum conservation equation:

[0092] In the x direction:

[0093]

[0094] In the y direction:

[0095]

[0096] Volume fraction transport equation:

[0097]

[0098] Level set function transport equation:

[0099]

[0100] As a preferred solution of this embodiment, S4 sets the initial conditions and boundary conditions: set the velocity value U at the initial moment according to the actual situation n , set the initial pressure value P n ; according to the initial gas-water two-phase distribution, initialize the level set function and the volume fraction; define the time step Δt and the boundary conditions.

[0101] Solve the momentum equation of formula (14) according to the initialized data to first obtain an intermediate velocity field U * , update the level set function and the volume fraction α n+1 , volume fraction transport equation:

[0102]

[0103] Level set function transport equation:

[0104]

[0105] Capture the position change and deformation of the gas-liquid interface and viscosity during the transient air-water flow process and curvature for use in the calculation of the next time step.

[0106] As a preferred solution of this embodiment, S5 further derives the Poisson equation containing the pressure term by combining the momentum equation of formula (14) with the continuity equation of formula (13):

[0107]

[0108] Solve the Poisson equation discretized by formulas (4)-(12) in step S2 to obtain the pressure field P n+1 .

[0109] As a preferred solution of this embodiment, S6 uses the pressure field P obtained in step S5 n+1 to correct the intermediate velocity field U * to obtain the velocity field U that satisfies the continuity equation n+1 , and during the entire simulation process, continuously update the values of physical quantities to gradually simulate the dynamic evolution process of the gas-water two-phase flow.

[0110] As a preferred solution of this embodiment, S7 uses the obtained pressure P and velocity U distribution data to solve and calculate the energy expression.

[0111] Kinetic energy expression of the water phase:

[0112]

[0113] Gravitational potential energy expression of the water phase:

[0114]

[0115] Kinetic energy expression of the air:

[0116]

[0117] Gravitational potential energy expression of the air:

[0118]

[0119] Where E pw is the kinetic energy of water, E kw is the gravitational potential energy of water, E pa is the kinetic energy of air, E kais the gravitational potential energy of air.

[0120] By calculation, the kinetic energy and gravitational potential energy changes between the air and water phases can be retrieved to capture the complex dynamics and energy transfer processes of transient water-air mixed flows.

[0121] Based on the above method, points are distributed within the entire computational domain and sub-regions are established. Using the moving least squares method, a linear system of partial derivative terms of each order is obtained; the expressions of spatial partial differential terms are extracted, and combined with the Houbolt method to obtain the expressions of temporal partial differential terms. Furthermore, the partial differential equations are discretized into algebraic equations to construct a full two-dimensional numerical model; the momentum equation is solved according to the set initial data to obtain the intermediate velocity field; subsequently, the Poisson equation is solved by the least squares method to obtain the pressure field, and the intermediate velocity field is corrected using this pressure field to obtain a velocity field that satisfies the continuity equation; the energy expression is solved based on the obtained pressure and velocity distribution data to achieve the capture of the energy transfer process of transient water-air mixed flows. By comparing the results of solving different models and analytical solutions and other numerical methods, the accuracy of the model and method proposed in this embodiment can be verified.

[0122] The following further demonstrates and introduces the solution of this embodiment in more detail with a specific design example:

[0123] The following example verifies and evaluates the proposed numerical model and solution through a laboratory system. The overall schematic diagram of the experimental system used is as Figure 2 shown. The system consists of an upstream supply tank, horizontal and vertical pipes, a downstream drainage tank, and valves. The initial air length is 1.00 m, and the water length is 1.00 m. During the test, the air and water parts are initially separated by a butterfly valve, and an air-water interface may form after the valve is quickly opened.

[0124] Through calculation, Figure 3 provides the pressure changes at the bottom of the vertical riser under different models and experimental results during the transient gas-water evolution process. The data calculated using the numerical algorithm of the present invention (black solid line) is in good agreement with the experimentally measured data in the maximum amplitude and oscillation phase of the pressure trajectory. After the initial setting and formation of the bubbles, the full two-dimensional model adopted in this study performs better than the two-dimensional compressible model in terms of oscillation amplitude and phase. Based on the above results and analysis, this numerical model can capture the detailed gas-water interaction and evolution, which is of great significance for in-depth understanding of the physical mechanisms and processes of such complex phenomena in actual engineering systems.

[0125] The entire gas-water flow evolution process of the experimental case can be divided into four key stages as Figure 4 shown, and their different formation and evolution mechanisms are as follows. In the initial stage (t = 0 - 7 s), the bubbles gradually propagate upstream under pressurized conditions. During this period, the potential energy E of the waterpw (See Figure 4 (a)), it is gradually converted into other forms of energy: the kinetic energy E of water kw , the potential energy E of air pa and the kinetic energy E of air ka , as shown in Figure 4 (b, c, and d) respectively. The energy E pw continuously decreases, and the energy E pa continuously increases. When the pressurized gas reaches the vertical riser (t = 7 s), bubbles will rapidly form in the vertical riser for replacement. This is because the pressure of the arriving airbag is relatively large. Thereafter, due to the pressure and density differences between the gas phase and the water phase, it begins to rise. This transition of the air-water interaction stage may cause the potential energy E pw to instantaneously decrease and the kinetic energy E kw to instantaneously soar until t = 8.7 seconds. After that, the bubbles rising with deceleration approach the peak height position of the vertical riser, and the kinetic energy E kw drops sharply from t = 8.7 seconds to t = 9.6 seconds. During this period, since part of the water column in the vertical riser is lifted by the rising bubbles, the potential energy E pw slightly rises as the position of the water in the vertical riser increases. Finally, entering the fourth stage (t = 9.7 - 13.6 s), due to the pressure and velocity oscillations in the system, the bubbles burst at the peak position of the vertical riser. In this stage, if the formed velocity and pressure are large enough, and at the same time the riser opens to allow the release of the mixed fluid (air and water), a spring-like geyser phenomenon of air-water mixed eruption may form at the top of the riser. After the air-water mixture erupts, the split air-water mixture will drop as E pw decreases. In addition, it can be clearly seen that the potential energy changes of the gas phase and the water phase always show opposite trends, as shown in Figure 4 (a, c). However, for the kinetic energy, although the change amplitudes of the gas phase and the water phase are different, in each evolution process, they maintain a consistent change trend. Compared with the potential energy conversion, the kinetic energy changes of the two phases are more frequent. It is estimated that the change period of the kinetic energy is about half of the potential energy change period. This indicates that there is a local intense interaction between the gas phase and the water phase during the process of the bubbles moving along the pipeline and rising upward in the riser.

[0126] Based on the same inventive concept, the present invention further provides a computer device, which includes: one or more processors, and a memory for storing one or more computer programs; the program includes program instructions, and the processor is configured to execute the program instructions stored in the memory. The processor may be a Central Processing Unit (CPU), or may also be other general-purpose processors, Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, and is used to implement one or more instructions, specifically for loading and executing one or more instructions in the computer storage medium to implement the above method.

[0127] It should be further noted that, based on the same inventive concept, the present invention further provides a computer storage medium, on which a computer program is stored, and the computer program, when run by a processor, executes the above method. The storage medium may adopt any combination of one or more computer-readable media. The computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium. The computer-readable storage medium may, for example, but not be limited to, be an electrical, magnetic, optical, electrical, magnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples (non-exhaustive list) of the computer-readable storage medium include: an electrical connection having one or more wires, a portable computer disk, a hard disk, a Random Access Memory (RAM), a Read-Only Memory (ROM), an Erasable Programmable Read-Only Memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present invention, the computer-readable storage medium may be any tangible medium that contains or stores a program, and the program may be used by or combined with an instruction execution system, apparatus, or device.

[0128] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the ordinary meanings understood by those with ordinary skills in the field to which the present invention pertains. The "first", "second" and similar terms used in the present invention do not denote any order, quantity or importance, but are only used to distinguish different components. The terms such as "comprising" or "including" mean that the elements or objects appearing before this word cover the elements or objects listed after this word and their equivalents, without excluding other elements or objects. The terms such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The terms such as "upper", "lower", "left" and "right" are only used to represent relative positional relationships, and when the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0129] As described above, it is only the preferred embodiment of the present invention, and it is not a limitation to the present invention in other forms. Any person skilled in the art may use the technical content disclosed above to make changes or modifications into equivalent embodiments with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the technical solution content of the present invention still fall within the protection scope of the technical solution of the present invention.

[0130] This patent is not limited to the above best mode. Anyone inspired by this patent can obtain various other forms of a calculation method for accurately capturing the energy transfer of a mixed flow based on the least squares method. All equal changes and modifications made according to the scope of the patent application of the present invention shall fall within the scope covered by this patent.

Claims

1. A calculation method for accurately capturing the energy transfer of a mixed flow based on the least squares method, characterized in that It includes the following steps: Discrete nodes are arranged within the computational domain, and a discrete expression of the spatial partial derivative is constructed based on the moving least squares method; The Houbolt third-order time integration method is used to discretize the time derivative term, and the physical quantity data of the first two time instants are initialized by combining with the Euler method; The level set function and the volume fraction are coupled to track the gas-liquid interface, and the full two-dimensional control equations are solved simultaneously; The pressure field is corrected by solving the Poisson equation containing the surface tension term, and the velocity field satisfying the continuity equation is updated; The kinetic energy and gravitational potential energy of water and air are calculated separately, and the periodic characteristics of energy conversion are analyzed.

2. A calculation method for accurately capturing the energy transfer of a mixed flow based on the least squares method according to claim 1, characterized in that: The implementation method of the moving least squares method is as follows: A number of nearest nodes within the adjacent sub-region are dynamically selected for each node; Based on the Taylor expansion, a residual function is constructed, and the residual is minimized by the least squares method to generate a linear system of spatial partial derivatives.

3. A calculation method for accurately capturing the energy transfer of a mixed flow based on the least squares method according to claim 2, characterized in that: The residual function contains a weight function, and the value of the weight function is related to the distance between nodes.

4. A calculation method for accurately capturing the energy transfer of a mixed flow based on the least squares method according to claim 1, characterized in that: The time derivative term of the Houbolt third-order time integration method is discretized using the physical quantity data of the current time instant, the previous time instant, and the first two previous time instants; The data of the first two time instants are initialized and estimated by the single-step explicit Euler method.

5. A calculation method for accurately capturing the energy transfer of a mixed flow based on the least squares method according to claim 1, characterized in that: The coupling of the level set function and the volume fraction calculates the interface curvature through the level set function, and corrects the interface position through the volume fraction to ensure mass conservation; The full two-dimensional control equations include the continuity equation, the momentum equation, the volume fraction, and the level set function transport equation.

6. A calculation method for accurately capturing the energy transfer of a mixed flow based on the least squares method according to claim 1, characterized in that: The Poisson equation contains the surface tension term and the gravitational body force term.

7. A calculation method for accurately capturing the energy transfer of a mixed flow based on the least squares method according to claim 1, characterized in that: The specific steps of calculating the kinetic energy and gravitational potential energy of water and air separately and analyzing the periodic characteristics of energy conversion include: Based on the volume fraction, the occupied regions of the water phase and the gas phase are dynamically divided; The kinetic energy and gravitational potential energy of the water phase and the gas phase are calculated by integral respectively; The energy dissipation rate is quantified by the difference in energy conversion frequency and amplitude.

8. A calculation method for accurately capturing the energy transfer of a mixed flow based on the least squares method according to claim 2, characterized in that: The range of the adjacent sub-region is dynamically adjusted according to the change of the gas-liquid interface curvature, specifically including: When the interface curvature exceeds the preset threshold, the sub-region range is expanded to include more adjacent nodes; When the interface curvature is lower than the preset threshold, the sub-region range is shrunk to reduce the calculation amount.

9. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method according to any one of claims 1-8.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method according to any one of claims 1-8.

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