Numerical calculation method for accurately capturing transient pressure of mixed flow in tunnel

Abstract

The invention provides a numerical calculation method for accurately capturing transient pressure of mixed flow in a tunnel, and the method comprises the following steps: non-dimensionalization processing: carrying out the non-dimensionalization processing on a transient mixed flow equation set, so as to reduce the parameter sensitivity; spatio-temporal discrete modeling: discretizing spatio-temporal derivative items by combining a meshless finite difference method with a Houbolt method, and constructing a transient mixed flow numerical model; nonlinear solving: establishing a value function based on the numerical model, iteratively adjusting a Jacobian matrix condition number, a damping factor and a sub-relaxation factor through a damping least square algorithm, realizing strong nonlinear decoupling of a transient flow water pressure coupling term, and solving a nonlinear equation set; and convergence and output: judging iteration convergence according to a residual norm or a parameter increment norm, repeating the steps of nonlinear solution and convergence judgment if the iteration convergence is not carried out, and outputting a transient pressure and flow field distribution result until a convergence condition is met.

Description

Technical Field

[0001] The present invention belongs to the technical fields of hydraulics and tunnel drainage engineering, and particularly relates to a numerical calculation method for accurately capturing transient pressures in a mixed flow in a tunnel. Background Art

[0002] The simulation of transient pressures in a tunnel mixed flow (alternating open-channel and full-flow) is a key topic in the safety assessment of tunnel drainage engineering. The fluid flow in a tunnel often exhibits complex transient characteristics. Especially when encountering changes in flow velocity, sudden opening or closing of valves, equipment failures, or other flow disturbances, the transient pressure fluctuations are often non-negligible. The transient pressure changes in the fluid flow in a tunnel, if not effectively captured and warned, may lead to structural damage, equipment damage, or other safety accidents. Therefore, accurately capturing the transient pressures in a transient mixed flow in a tunnel is of great practical significance for ensuring the safety and stability of tunnel drainage engineering.

[0003] The transient mixed flow in a tunnel is often accompanied by strong coupling effects of water hammer, free surface fluctuations, and pressure wave propagation. Its governing equations are usually strongly nonlinear partial differential equation systems. Traditional numerical methods rely on structured grids and face problems such as grid distortion and poor computational stability when solving strongly nonlinear partial differential equation systems. Although meshless methods avoid grid limitations through node discretization, they still have bottlenecks in the spatial derivative discretization accuracy, nonlinear term processing, and large-scale parallel computing efficiency. Summary of the Invention

[0004] Aiming at the above-mentioned defects and deficiencies existing in the prior art, the present invention aims to develop a numerical calculation method with both meshless flexibility, high spatio-temporal discretization accuracy, and strong nonlinear robust solution ability to meet the urgent need for accurately capturing transient pressures in a transient mixed flow in a tunnel and break through the limitations of traditional algorithms in dealing with strongly nonlinear terms. The equations describing the dynamic behavior of transient mixed fluids involve multiple physical parameters and variables and are highly complex and strongly nonlinear due to the strong coupling effects of water hammer, free surface fluctuations, and pressure wave propagation. Ordinary discretization and iterative methods are difficult to accurately solve. The present invention combines the meshless finite difference method with the damped least squares algorithm. The former shows high-precision advantages in simulating complex boundary flows through local Taylor expansion combined with weighted least squares optimization. The latter achieves high convergence by dynamically adjusting the condition number of the Jacobian matrix (to improve the ill-conditioning of the equation system), the damping factor, and the under-relaxation factor (to enhance the stability of nonlinear iteration), and introduces an identity matrix to avoid interference from ill-conditioned Jacobian matrices. This method effectively solves the problem of solving transient mixed flow equation systems containing nonlinear terms, spatio-temporal derivatives, and multi-physical coupling terms. Through the coupling term separation strategy of reconstructing the Jacobian matrix, it realizes the strong nonlinear decoupling of transient flow pressure coupling terms, can accurately simulate the transient mixed flow in a tunnel, accurately capture transient pressure changes, and solve flow state characteristics.

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

[0006] A numerical calculation method for accurately capturing the transient pressure of the mixed flow in a tunnel, comprising the following steps:

[0007] Dimensionless treatment: Perform dimensionless treatment on the transient mixed flow equations to reduce parameter sensitivity;

[0008] Space-time discrete modeling: Discretize the space-time derivative terms by using the meshless finite difference method combined with the Houbolt method to construct a numerical model of the transient mixed flow;

[0009] Nonlinear solution: Establish a value function based on the numerical model, and iteratively adjust the condition number of the Jacobian matrix, the damping factor, and the under-relaxation factor through the damped least squares algorithm to achieve strong nonlinear decoupling of the transient flow pressure coupling term and solve the nonlinear equations;

[0010] Convergence and output: Judge the iteration convergence according to the residual norm or the parameter increment norm. If not converged, repeat the steps of nonlinear solution and convergence judgment until the transient pressure and the flow field distribution results are output after meeting the convergence conditions.

[0011] Further, the meshless finite difference method realizes the spatial derivative discretization through local Taylor expansion and weighted least squares optimization; (corresponding to formula 7) the Houbolt method uses the physical quantities of three time levels for time discretization (corresponding to formula 9).

[0012] Further, the weighted least squares optimization is realized by minimizing the weighted sum of squares of the residuals of neighboring nodes; (corresponding to formula 7) the truncation error of the time discretization is determined by the three-time-level discretization format of the Houbolt method; (corresponding to formula 9) When constructing the numerical model of the transient mixed flow, the Jacobian matrix is reconstructed to decouple the multi-physical field coupling terms.

[0013] Further, the damping factor is dynamically updated based on the ratio factor of the actual descent amount to the predicted descent amount; (corresponding to formulas 19-23) the under-relaxation factor enhances the nonlinear iteration stability by restricting the parameter increment step size (corresponding to formulas 15-18).

[0014] Further, the damping factor is proportional to the absolute value of the product of the transposed vector of the Jacobian matrix; (corresponding to formula 18) The update rule of the ratio factor is: when the ratio factor is less than 0.25, the step size is enlarged; when it is greater than or equal to 0.75, the step size is reduced to the lower limit of 0.001; in other cases, the step size remains unchanged. (corresponding to formula 23).

[0015] Further, the dimensionless processing includes: using the tunnel length as the reference scale to normalize the flow velocity, head, and hydraulic radius (corresponding to Formula 4-6); introducing the flexural rigidity to balance the inertial force and elastic force to reduce the parameter sensitivity (corresponding to Formula 4).

[0016] Further, the residual norm threshold is set to 1×10 -6 to ensure the transient pressure simulation accuracy; the parameter increment norm threshold is set to 1×10 -10 , and its convergence efficiency is verified through experimental data (corresponding to Formula 25).

[0017] Further, the transient mixed-flow numerical model is implemented as follows: arranging unstructured nodes in the computational domain, defining a weighting function based on the reciprocal square of the distance between nodes, and transforming the partial derivative terms into weighted linear combinations of physical quantities of neighboring nodes (corresponding to Formula 7); constructing a spatio-temporal coupled discretized equation system that combines the continuity equation and the momentum equation (corresponding to Formulas 10-11).

[0018] Further, the discretized equation is solved by simultaneously iterating to solve the spatio-temporal coupling terms of the continuity equation and the momentum equation (corresponding to Formulas 10-11); the non-linear friction term in the momentum equation is made dimensionless through the Manning coefficient to eliminate the dimensional dependence (corresponding to Formula 6).

[0019] Further, the reconstruction of the Jacobian matrix includes: explicitly separating the partial derivative terms of the pressure term and the flow velocity term to suppress the coupling oscillation (corresponding to Formulas 6, 10-11).

[0020] It should be noted that when applying this solution to the tunnel drainage project, it includes:

[0021] establishing a geometric model based on the dimensionless tunnel length, flow velocity, and head parameters;

[0022] verifying the simulation accuracy by comparing the transient pressure distribution map with the experimental measurement data.

[0023] In addition, an electronic device includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the steps of the above method are implemented.

[0024] A non-transitory computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the above method are implemented.

[0025] Compared with the prior art, the present invention and its preferred embodiments introduce the damped least squares algorithm into the meshless finite difference method. By dynamically adjusting the condition number of the Jacobian matrix and introducing the under-relaxation factor, the problem of solving complex equations with nonlinear terms, spatio-temporal derivatives, and multi-physical coupling terms is effectively solved, and it can be applied to the strongly nonlinear calculation of transient pressure in mixed flows.

[0026] Through the deep integration of the meshless finite difference method and the damped least squares algorithm, the following breakthrough improvements are achieved in the transient mixed flow simulation:

[0027] 1. High precision and strong robustness:

[0028] Through local weighted least squares optimization (Equation 7) and high-order time discretization of the Houbolt method (Equation 9), the spatio-temporal discretization error is significantly lower than that of traditional methods;

[0029] Dynamically adjusting the condition number of the Jacobian matrix (Equations 18 - 23) and the under-relaxation factor (Equations 15 - 17) to suppress the interference of ill-conditioned matrices, and the convergence speed is increased by more than 40%.

[0030] 2. Nonlinear decoupling ability:

[0031] Reconstructing the Jacobian matrix to explicitly separate the coupled contributions of the pressure term and the flow velocity term (Equations 6, 10 - 11), and the residual magnitude decreases from 10 -5 to 10 -8 (Equation 25).

[0032] 3. Engineering practical value:

[0033] In the case of a tunnel drainage project (pipe length 14.33 m, Manning coefficient 0.012), the reliability of the method in complex flow states such as open-channel and pressurized flow alternation and water hammer effect is verified. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The present invention will be further described in detail below with reference to the drawings and specific embodiments:

[0035] Figure 1 is a schematic flow chart of the method in an embodiment of the present invention;

[0036] Figure 2 is a flow chart of the iterative loop solution of the damped least squares method in an embodiment of the present invention;

[0037] Figure 3 is an instantaneous pressure diagram of the mixed flow in an embodiment of the present invention;

[0038] Figure 4 is an instantaneous flow velocity diagram of the mixed flow in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0039] To make the features and advantages of this patent more obvious and understandable, specific embodiments are given below for detailed description as follows:

[0040] It should be noted that the following detailed description is illustrative and is intended to provide further explanation of 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 this application belongs.

[0041] It should be noted that the terms used herein are only for describing specific embodiments 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.

[0042] As Figure 1 shown, the embodiments of the present invention provide a complete implementation process of a numerical calculation method for accurately capturing the transient pressure of the mixed flow in a tunnel. The specific steps are as follows:

[0043] S1: Nondimensionalize the transient mixed flow equations based on dimensional analysis theory to effectively reduce parameter sensitivity.

[0044] S2: Use the meshless finite difference method to discretize the spatial partial derivative terms with high precision, and at the same time combine the Houbolt method to achieve the discretization of the time derivative terms, construct a cross-scale coupled spatio-temporal adaptive analytical framework, and establish a mixed flow numerical model containing transient pressure based on the spatio-temporal heterogeneous feature integration paradigm of multi-physical field co-evolution.

[0045] S3: Establish a value function from the equations in S3, solve the non-linear equations by minimizing the value function, and then initialize the parameter vector to calculate the Jacobian matrix of the equations.

[0046] S4: Construct an increment equation through the Jacobian matrix and the identity matrix to improve the robustness of the iteration method in the process of solving non-linear equations.

[0047] S5: Evaluate the effectiveness of the step size and establish a step size update strategy to ensure that the iteration process takes into account both speed and stability, and then update the parameter vector and the Jacobian matrix.

[0048] S6: Repeat steps S5 and S6 in a loop until the iteration converges, and return the final parameter vector as the result.

[0049] As a preferred solution of this embodiment, the mixed flow equations containing transient pressure in step S1:

[0050] Continuity equation:

[0051]

[0052] Momentum equation:

[0053]

[0054]

[0055] wherein, V is the water flow velocity, h c is the distance between the free surface and the centroid of the flow cross-sectional area, h s is the boost head, A p is the area of the original tunnel, g is the acceleration due to gravity, R h is the hydraulic radius, n m is the Manning coefficient, K is the local loss coefficient, and L is the length of the tunnel.

[0056] The following non-dimensionalization is performed on each physical quantity:

[0057]

[0058] wherein, EI is the flexural rigidity.

[0059] The non-dimensional equations for transient flow are obtained as follows:

[0060] Continuity equation:

[0061]

[0062] Momentum equation:

[0063]

[0064] As a preferred solution of this embodiment, in step S2, the meshless finite difference method is used to perform high-precision discretization on the spatial partial derivative terms, and at the same time, the Houbolt method is combined to achieve the discretization of the time derivative terms. Based on the spatio-temporal heterogeneous feature integration paradigm of multi-physical field co-evolution, a spatio-temporal adaptive analytical framework for cross-scale coupling is constructed, and a numerical model for transient mixed flow is established to solve the transient pressure of the mixed flow. The specific implementation is to arrange N points in the entire calculation region, and through the local weighted approximation strategy, the partial differential terms of each node are transformed into a weighted linear combination of the physical quantities of adjacent points. The residual function B(Φ) is defined as follows:

[0065]

[0066] wherein, Φ i,0 is the unknown value of node i th Φ i,j is the unknown value of node j in sub-region n s h th ​ij = x i，0 -x i,j represents i th the vector distance between node and j th nodes, and W(h ij ) is the weight function of node j th and can be in the form of a Gaussian kernel function, etc.

[0067] To make the residual function B(Φ) a minimum value, taking the partial derivatives of each term and setting them to zero can obtain a linear system:

[0068]

[0069] After determining the time step, perform equally spaced division in the time direction, and use the physical quantities of three known time levels to solve the physical quantities of the next unknown time level, approximately expressed as:

[0070]

[0071] where Φ n+1 is the physical quantity at time t = n + 1, and the time step is Δt = t n+1 - t n .

[0072] According to the spatio-temporal heterogeneous feature integration paradigm of the physical field co-evolution in equations (7) and (8), establish a transient mixed-flow numerical model to solve the transient pressure of the mixed flow:

[0073] Continuity equation:

[0074]

[0075] Momentum equation:

[0076]

[0077] As a preferred solution of this embodiment, in step S3, establish a value function from the equations in S2, solve the non-linear equations by minimizing the value function, and perform a first-order Taylor expansion on it. Subsequently, initialize the parameter vector according to the initial conditions, calculate the Jacobian matrix of the equations, and the value function and the Jacobian matrix are approximately expressed as:

[0078] G(Φ k ) = ||F(Φ k )|| 2 (12)

[0079] G(Φ k ) = ||F(Φ k ) + J(Φ k ) T ΔΦ|| 2 (13)

[0080]

[0081] Wherein, Φ k is the parameter vector at the k-th step, F(Φ k ) is the matrix composed of all equations, G(Φ k ) is the value function, f i (Φ k ) is the i-th equation, J(Φ k ) is the Jacobian matrix at the k-th step.

[0082] As a preferred solution of this embodiment, step S4 is to make the value function obtain a minimum value. Taking the derivative of Equation (12) to obtain an extreme value when the derivative is zero. Since the defined value function is the matrix norm which is the sum of the squares of each element and there is no maximum value, a minimum value is obtained when the derivative is zero, and the incremental equation is expressed as:

[0083]

[0084] Wherein, ΔΦ is the parameter increment.

[0085] Due to problems such as strong non-linearity of some terms of the equation and too large parameter vector, there will be an ill-conditioned Jacobian matrix in the iterative process, making it not necessarily invertible. By introducing the identity matrix and constructing the incremental equation through the Jacobian matrix and the identity matrix, the final incremental equation can be obtained:

[0086] ΔΦ = -(J(Φ k )J(Φ k ) T + uI) -1 J(Φ k ) T F(Φ k ) (17)

[0087] u = α k ||J(Φ k ) T F(Φ k )|| (18)

[0088] Wherein, I is the identity matrix, α k is the step size change coefficient in the iterative process. The damping factor u suppresses the interference of the ill-conditioned Jacobian matrix by balancing the gradient descent and the Gauss-Newton method.

[0089] This iterative method approximates the Hesse matrix through the Jacobi matrix, regularizes the approximated Hesse matrix, combines the global search of the gradient descent method and the local fast convergence characteristics of the Gauss-Newton method, can balance the advantages and disadvantages of both during the solution process, avoid falling into local optimal solutions, and maintain the stability of the calculation process. Specifically, when the gradient is large or the condition of the Hessian matrix is poor, this iterative method will tend to use the gradient descent method to avoid divergence caused by an overly large step size in the Gauss-Newton method. Conversely, when the optimization process approaches the optimal solution, this iterative method gradually transitions to the Gauss-Newton method to ensure fast convergence. This adaptive mechanism enables the LM method to maintain good stability and robustness in different optimization problems.

[0090] As a preferred solution of this embodiment, step S5 compares the actual decrease amount and the estimated decrease amount of the value function after the change of the parameter vector to determine whether the step size is effective, and establishes a step size update strategy to ensure that the iterative process takes into account both speed and stability. Subsequently, the parameter vector and the Jacobi matrix are updated. The judgment formula is:

[0091] Ared k =||F(Φ k )|| 2 -||F(Φ k +ΔΦ)|| 2 (19)

[0092] Pred k =||F(Φ k )|| 2 -||F(Φ k )+J(Φ k )·ΔΦ|| 2 (20)

[0093]

[0094] In the formula, Ared k is the actual decrease amount, Pred k is the estimated decrease amount, and r k is the proportional factor coefficient.

[0095] A step size update strategy is established through the proportional factor coefficient r k . A coefficient greater than zero indicates that the value function is decreasing. The larger the coefficient, the more the objective function decreases. The parameter vector can be updated, and it is hoped to make the iteration step size larger by reducing u, and vice versa.

[0096]

[0097]

[0098] As a preferred solution of this embodiment, as Figure 2 shown, step S6 repeats steps S4 and S5 in a loop until iteration converges, and returns the final parameter vector as the result. The loop process and convergence condition are:

[0099]

[0100] ||F(Φ k )|| < 1×10 -6 or ||ΔΦ|| < 1×10 -10 (25)

[0101] The following further demonstrates and introduces the solution of this embodiment more fully in combination with a specific design example:

[0102] Taking an experimental case of a water tank - drain pipe system as an example, the experimental device consists of upper and lower water tanks connected by pipes: the horizontal pipe is 14.33 m long, with a diameter of 0.094 m, the height of the upstream water tank is 0.31 m, the bottom is square with a size of 0.25 m, the bottom of the downstream water tank is designed as circular, with a height sufficient to prevent overflow, the bottom diameter is 0.19 m, the Manning coefficient is 0.012, a sluice gate is installed downstream of the pipe, and in order to eliminate the influence of the trapped air in the system on the experiment, a ventilation pipe is set near the downstream. The initial water depth of the experiment is 0.073 m, a constant water inflow of 3.1 L / s is set at the upstream rainwater well, the water exceeding the height of the upstream water tank will overflow from the top of the pipe, the measured pressure and velocity data are 9.9 m away from the upstream boundary, and the simulation time is 40 seconds.

[0103] Step 1:

[0104] Based on the dimensional analysis theory, non - dimensionalization is performed on the transient mixed - flow equations. The mixed - flow equations containing transient pressure:

[0105] Continuity equation:

[0106]

[0107] Momentum equation:

[0108]

[0109] The following non - dimensionalization is performed on each physical quantity:

[0110]

[0111] The obtained non - dimensional equations of transient flow are:

[0112] Continuity equation:

[0113]

[0114] Momentum equation:

[0115]

[0116] Step 2: Use the meshless finite difference method to discretize the spatial partial derivative terms with high precision, and at the same time combine the Houbolt method to realize the discretization of the time derivative terms, and establish a transient mixed-flow numerical model. The number of distribution points is 102, the number of internal points is 100, the number of boundary points is 2, and the time step is taken as 0.01 s, and the model is obtained as follows:

[0117] Continuity equation:

[0118]

[0119] Momentum equation:

[0120]

[0121] Step 3: Establish a value function, perform a first-order Taylor expansion on it, then initialize the parameter vector according to the initial conditions, and calculate the Jacobian matrix of the system of equations. The value function and the Jacobian matrix are approximately expressed as:

[0122] G(Φ k ) = ||F(Φ k )|| 2

[0123] G(Φ k ) = ||F(Φ k ) + J(Φ k ) T ΔΦ|| 2

[0124]

[0125] Step 4: Take the derivative of equation (9) to make the derivative zero, and introduce the identity matrix to construct an increment equation through the Jacobian matrix and the identity matrix:

[0126] ΔΦ = -(J(Φ k )J(Φ k ) T + uI) -1 J(Φ k ) T F(Φ k )

[0127] u = α k ||J(Φ k ) T F(Φ k )||

[0128] Step 5: Determine whether the step size is valid and establish a step size update strategy. The judgment formula is:

[0129] Ared k = ||F(Φ k )|| 2 - ||F(Φ k + ΔΦ)|| 2

[0130] Pred k = ||F(Φ k )|| 2 - ||F(Φ k ) + J(Φ k )·ΔΦ|| 2

[0131]

[0132] In the formula, Ared k is the actual decrease, Pred k is the estimated decrease, and r k is the proportional factor coefficient.

[0133] Establish a step size update strategy through the proportional factor coefficient r k , and α k starts iteration from 0.1:

[0134]

[0135] Step 6: Repeat steps S4 and S5 in a loop until convergence, and return the final parameter vector as the result. The loop process and convergence conditions are:

[0136]

[0137] ||F(Φ k )|| < 1×10 -8 or ||ΔΦ|| < 1×10 -10

[0138] Calculation result analysis:

[0139] Figure 3 and Figure 4 are the flow velocity and pressure change diagrams at different times of the measurement points respectively. By comparing the results of the method in this embodiment with the experimental results, the overall trends are close and the peak errors are small, verifying that the method can accurately calculate the complex flow pattern of the mixed flow containing transient pressure; by comparing the results of the method in this embodiment with the results of the traditional method, it is verified that the method has higher accuracy when calculating complex equations with strong nonlinearity, containing space-time derivatives and multi-physical coupling terms.

[0140] 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, it is used to load and execute one or more instructions in the computer storage medium to implement the above method.

[0141] 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 is not limited to, 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 or combined with an instruction execution system, apparatus, or device.

[0142] 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 indicate relative positional relationships, and when the absolute position of the object being described changes, the relative positional relationships may also change accordingly.

[0143] The above are only the preferred embodiments of the present invention, and are not intended to limit the present invention in any other form. 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 modifications, equivalent changes and modifications 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.

[0144] This patent is not limited to the above best mode. Anyone inspired by this patent can obtain various other forms of a numerical calculation method for accurately capturing the transient pressure of the mixed flow in a tunnel. 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 numerical calculation method for accurately capturing transient pressures of mixed flows in a tunnel, characterized in that, The following steps are involved: Dimensionless processing: Dimensionless processing is performed on the transient mixed flow equations to reduce parameter sensitivity; Time-space discrete modeling: The time-space derivatives are discretized by using the meshless finite difference method combined with the Houbolt method to construct a transient mixed flow numerical model; Nonlinear solution: Based on the numerical model, a value function is established, and the Jacobian matrix condition number, damping factor and sub-relaxation factor are iteratively adjusted by a damped least squares algorithm to achieve strong nonlinear decoupling of transient flow-water pressure coupling terms and solve the nonlinear equations. Convergence and output: The iterative convergence is judged according to the residual norm or parameter increment norm. If it has not converged, the nonlinear solution and convergence judgment steps are repeated until the convergence conditions are met and the transient pressure and flow field distribution results are output.

2. The numerical calculation method for accurately capturing the transient pressure of the mixed flow in the tunnel according to claim 1, characterized in that: The meshless finite difference method realizes spatial derivative discretization through local Taylor expansion and weighted least squares optimization; the Houbolt method uses three time layer physical quantities for time discretization.

3. A numerical calculation method for accurately capturing transient pressure of mixed flow in a tunnel according to claim 2, characterized in that: The weighted least squares optimization is achieved by minimizing the weighted sum of squares of residuals of adjacent nodes; the truncation error of the time discretization is determined by the three-time layer discretization format of the Houbolt method; when constructing the transient mixed flow numerical model, the Jacobian matrix is reconstructed to decouple the multi-physical field coupling terms.

4. A numerical calculation method for accurately capturing transient pressures of mixed flows in tunnels according to claim 1, characterized in that: The damping factor is dynamically updated based on a ratio factor between the actual drop amount and the estimated drop amount; The under-relaxation factor enhances the stability of nonlinear iteration by limiting the parameter increment step size.

5. A numerical calculation method for accurately capturing the transient pressure of mixed flow in a tunnel according to claim 4, characterized in that: The damping factor is proportional to the absolute value of the transposed vector product of the Jacobian matrix; the updating rule of the proportional factor is: when the proportional factor is less than 0.25, the step size is enlarged; when it is greater than or equal to 0.75, the step size is reduced to the lower limit of 0.001; in other cases, the step size remains unchanged.

6. The numerical calculation method for accurately capturing the transient pressure of the mixed flow in the tunnel according to claim 1, wherein: The dimensionless processing includes: taking the tunnel length as a reference scale, normalizing the flow velocity, pressure head and hydraulic radius; balancing the inertial force and the elastic force by introducing the bending stiffness to reduce the parameter sensitivity.

7. A numerical calculation method for accurately capturing transient pressures of mixed flows in tunnels according to claim 1, characterized in that: The residual norm threshold is set to 1×10 -6 to ensure the simulation accuracy of transient pressure; the parameter increment norm threshold is set to 1×10 -10 , and its convergence efficiency is verified by experimental data.

8. A numerical calculation method for accurately capturing transient pressures of mixed flows in tunnels according to claim 1, characterized in that: The transient mixed flow numerical model is implemented in the following ways: unstructured nodes are arranged in the computational domain, a weighting function is defined based on the inverse square of the distance between nodes, partial differential terms are converted into weighted linear combinations of physical quantities of adjacent nodes; and a time-space coupled discretized equation group of simultaneous continuity equations and momentum equations is constructed.

9. A numerical calculation method for accurately capturing the transient pressure of mixed flow in a tunnel according to claim 8, characterized in that: The discretized equation solves the spatiotemporal coupling terms of the continuity equation and the momentum equation by simultaneous iteration; the nonlinear friction term in the momentum equation is dimensionally processed by the Manning coefficient to eliminate the dimensional dependence.

10. A numerical calculation method for accurately capturing transient pressures of mixed flows in a tunnel according to claim 3, characterized in that: The reconstruction of the Jacobian matrix includes: explicitly separating the partial derivative terms of the pressure term and the velocity term to suppress coupled oscillations.

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