Dam-reservoir hydrodynamic fluid-structure interaction simplified efficient calculation method and application

Abstract

The application provides a dam-reservoir hydrodynamic fluid-solid coupling simplified efficient calculation method and application, the reservoir is discretized by SBFEM or FEM, and the hydrodynamic pressure additional mass matrix is calculated; according to the physical meaning and characteristics of the additional mass matrix, the hydrodynamic pressure additional mass matrix is simplified, the calculation time consumption is greatly reduced, and the calculation efficiency is improved under the premise of ensuring good precision, the simplified efficient calculation and analysis of the dam-reservoir hydrodynamic fluid-solid coupling under the condition of earthquake can be realized, the numerical calculation result has higher precision, the coupling calculation time consumption is greatly reduced, an accurate and efficient method is provided for the dam-reservoir hydrodynamic fluid-solid coupling analysis and anti-seismic safety evaluation, and technical support is provided for the application of the dam fluid-solid coupling analysis method in practical engineering or large-scale dam dynamic fine analysis.

Description

Technical Field

[0001] This invention belongs to the field of fluid-structure interaction numerical calculation technology, and in particular relates to a simplified and efficient calculation method and application for dam-reservoir dynamic fluid-structure interaction, which is applicable to the dynamic interaction analysis of dam and reservoir water and the corresponding seismic safety evaluation. Background Technology

[0002] Earthquake forces cause interaction between the dam and the reservoir water, and the resulting hydrodynamic pressure is a crucial factor that cannot be ignored in evaluating the seismic performance of the dam. Currently, there are numerous research results on the numerical calculation and experimentation of hydrodynamic pressure in front of the dam under seismic conditions. The research scope covers three important dam types: arch dams, gravity dams, and panel dams. The numerical calculation methods used include analytical methods, boundary element method (BEM), finite element method (FEM), and the recently emerging proportional boundary finite element method (SBFEM).

[0003] The SBFEM proposed by Wolf and Song has been widely used in the static and dynamic analysis of dams, including the dynamic-fluid-structure interaction analysis of dams and reservoirs under seismic conditions. SBFEM has a unique advantage in the numerical calculation of hydrodynamic pressure upstream of the dam, namely, it can simulate a semi-infinite domain reservoir by discretizing only the fluid-structure interface. Figure 1 As shown. Compared with the finite element method, SBFEM reduces the one-dimensional solution dimension, saves the number of node degrees of freedom, and eliminates the need to introduce artificial boundary conditions at the reservoir tail to simulate far-field effects; compared with the boundary element method, it does not require a fundamental solution. Moreover, this method can directly generate a water body mesh using the (finite element) mesh of the dam's upstream face without re-meshing, improving the preprocessing efficiency of numerical analysis; it can accurately consider the effects of seismic excitation in different directions, the dip angle of the upstream dam face, and complex valley shapes.

[0004] Utilizing accurate hydrodynamic pressure methods to calculate the seismic response of dams is crucial for the accurate evaluation of their seismic safety. However, in the analysis of dam-reservoir hydrodynamic interactions, numerical methods such as SBFEM or FEM, when handling hydrodynamic pressure, result in a full-scale hydrodynamic pressure-added mass matrix. When the number of degrees of freedom in the coupled system reaches a certain scale, solving the coupled equations consumes a significant amount of time, leading to low computational efficiency and high costs, which hinders the engineering application of dam-reservoir hydrodynamic fluid-structure interaction analysis methods. Summary of the Invention

[0005] The first objective of this invention is to provide a simplified and efficient calculation method for hydrodynamic-fluid-structure interaction of dams and reservoirs, addressing the shortcomings of existing technologies.

[0006] Therefore, the above-mentioned objective of the present invention is achieved through the following technical solution:

[0007] A simplified and efficient calculation method for dam-reservoir hydrodynamic-fluid-structure interaction is characterized by the following steps:

[0008] Assuming the reservoir water is an ideal fluid with zero viscosity, incompressibility, and minimal disturbance, under seismic loading, the hydrodynamic pressure in the reservoir upstream of the dam will satisfy the Laplace equation:

[0009] ▽ 2 p = 0 (1)

[0010] Ignoring minor gravity waves, the boundary condition S0 on the free surface of the reservoir water is as follows:

[0011] p = 0 (2)

[0012] Boundary conditions on the upstream face S1 of the dam:

[0013]

[0014] Boundary conditions at interface S2 between the reservoir and its bottom and bank slope:

[0015]

[0016] Of the above formulas: ▽ 2 Here, p is the Laplace operator, n is the hydrodynamic pressure, and ρ is the fluid density. These are the normal accelerations at the dam-reservoir interface S1 and the valley-slope interface S2, respectively.

[0017] The hydrodynamic pressure upstream of the dam can be discretized using SBFEM or FEM based on the above governing equations and boundary conditions, and then the hydrodynamic pressure-added mass matrix [M] can be calculated. p Simultaneously, using FEM to simulate the dam, the dynamic fluid-structure interaction equation of the dam-reservoir system can be expressed as:

[0018]

[0019] Among them, [M s [C] s ] and [K s [These represent the finite element mass, damping, and stiffness matrices of the dam body, respectively.] and{u r (t)} represent the relative acceleration, relative velocity, and relative displacement of the dam body, respectively; The input system is the seismic acceleration;

[0020] As can be seen from equation (5), as long as the hydrodynamic pressure is added to the mass matrix [M], pBy superimposing the mass matrix of the finite element dynamic equation of the dam body, the hydrodynamic pressure effect during seismic input can be considered, and dynamic-fluid-structure interaction analysis of dam-reservoir can be carried out.

[0021] The hydrodynamic pressure additional mass matrix [M] obtained by solving using FEM or SBFEM p ], represented as:

[0022] [M p ] = [L1] T [m u [L1]+[L1] T [m v [L2] (6)

[0023] In the formula, [m u To excite the dam's upstream face S1 with acceleration The associated additional mass matrix, [m v [To excite the S2 acceleration of the bedrock facing the water in the valley] The relevant additional mass matrix, [L1] is the transformation matrix between the global coordinate direction and the dam surface normal, and [L2] is the transformation matrix between the global coordinate direction and the reservoir bottom slope (i.e., the valley) normal;

[0024] The calculated additional mass matrix [m] u [This is a full array where all elements are non-zero. That is, when calculating the hydrodynamic pressure caused by vibration on the upstream side of the dam, the hydrodynamic pressure at a certain node on the dam face is related to the acceleration excitation of all nodes on the dam face.] All are related; however, when calculating the hydrodynamic pressure caused by vibration in the bedrock valley, the hydrodynamic pressure at a certain node on the dam face is only related to the acceleration excitation of the node at the boundary between the dam face and the valley. Correlation, therefore, the additional mass matrix [m] v ] is a very sparse matrix containing a large number of zero elements; obviously, due to the mass matrix [m u The existence of the additional mass matrix [M] makes the additional mass matrix [M]... p The addition of the mass matrix [m] results in a full matrix, which significantly increases the time required to solve for the equivalent stiffness matrix in dynamic analysis. v The impact on the computational efficiency of coupled dynamics is relatively small;

[0025] From the above analysis, it can be seen that we only need to simplify [m] u This can reduce the added mass matrix [M] p The correlation of the nodal degrees of freedom of ]; when the additional mass matrix [m u When the order is n, that is, there are n nodes below the water level on the upstream side of the dam, and its element mu ij The physical meaning is the hydrodynamic pressure acting on node i caused by the unit normal acceleration excitation of the reservoir water by node j on the water-facing side;

[0026] The simplification method is based on [m] u Taking the element in the i-th row of the array as an example, it can be represented as mu. i1 mu i2 …mu ii …mu in Among them, element mu ii In matrix [m u The value at the diagonal position of [] is the largest among the elements in the i-th row; we can first move each element in the i-th row towards the diagonal element mu. ii Superimpose the elements, then remove zeros from the off-diagonal elements; this achieves the additional mass matrix [m]. u Decoupling means that the hydrodynamic pressure on node i on the water-facing surface is only related to the normal acceleration excitation of node i; since directly superimposing off-diagonal elements onto diagonal elements will amplify the hydrodynamic pressure, the off-diagonal elements need to be multiplied by a reduction factor α = 0.65 during the superposition process; thus, processing from the first row to the nth row completes the matrix [m u By simplifying the overall structure, the additional mass matrix of hydrodynamic pressure [M] can be calculated. p ], and [M p The mass matrix of the dam body finite element dynamic equation is superimposed on the dam body mass matrix to perform simplified and efficient calculations of dam-reservoir hydrodynamic coupling.

[0027] The second objective of this invention is to address the shortcomings of existing technologies by providing an application of the aforementioned simplified and efficient calculation method for hydrodynamic-fluid-structure interaction of dams and reservoirs.

[0028] Therefore, the above-mentioned objective of the present invention is achieved through the following technical solution:

[0029] This relates to the application of the simplified and efficient calculation method for dam-reservoir hydrodynamic fluid-structure interaction described above in the detailed dynamic analysis of large-scale dams.

[0030] The third objective of this invention is to provide an electronic device that addresses the shortcomings of existing technologies.

[0031] Therefore, the above-mentioned objective of the present invention is achieved through the following technical solution:

[0032] An electronic device includes a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other via the communication bus, characterized in that:

[0033] The memory, which is used to store computer programs,

[0034] A processor is used to execute a computer program stored in a memory to implement the steps of the simplified and efficient calculation method for hydrodynamic-structure interaction of dam and reservoir described above.

[0035] Another objective of this invention is to provide a computer-readable storage medium to address the shortcomings of existing technologies.

[0036] Therefore, the above-mentioned objective of the present invention is achieved through the following technical solution:

[0037] A computer-readable storage medium, characterized in that: the computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the simplified and efficient calculation method for hydrodynamic fluid-structure interaction of dam-reservoir described above.

[0038] This invention provides a simplified and efficient calculation method and application for dam-reservoir hydrodynamic fluid-structure interaction. The method discretizes the reservoir water using SBFEM or FEM and calculates the dynamic water pressure attachment mass matrix. Based on the physical meaning and characteristics of the attachment mass matrix, the dynamic water pressure attachment mass matrix is ​​simplified. While maintaining good accuracy, this significantly reduces calculation time and improves computational efficiency. It enables simplified and efficient calculation and analysis of dam-reservoir hydrodynamic fluid-structure interaction under seismic conditions. This method ensures high accuracy of numerical calculation results while significantly reducing the time required for coupling calculations. It provides an accurate and efficient method for dam-reservoir hydrodynamic fluid-structure interaction analysis and seismic safety evaluation, and provides technical support for the application of dam fluid-structure interaction analysis methods in practical engineering or large-scale dam dynamic fine analysis. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the reservoir's water grid.

[0040] Figure 2 This is a finite element model illustration of an arch dam.

[0041] Figure 3 This is a time history diagram of seismic acceleration in three directions input during dynamic calculation. Detailed Implementation

[0042] The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.

[0043] 1) Solving for the additional mass matrix of hydrodynamic pressure: SBFEM or FEM can be used to discretize the reservoir water in front of the dam, and the additional mass matrix [m] can be calculated respectively. u ] and [m v ], additional mass matrix [m v ] is a sparse matrix and does not require processing.

[0044] 2) Regarding the additional mass array [m] u Simplification process: Extract the nth-order hydrodynamic pressure-added mass matrix [m] u Let the elements in row i of the matrix be the diagonal elements. The reduction factor α = 0.65; then, the values ​​of the off-diagonal elements are set to zero; following this method, the additional mass matrix [m] is... u Process from line 1 to line 3, simplifying and then appending the mass matrix [m]. u Transform it into a diagonal matrix.

[0045] 3) Simplified calculation method for dam-reservoir hydrodynamic coupling: using a sparse additional mass matrix [m v ] and the simplified attachment mass diagonal matrix [m u According to equation (6), the mass matrix of the hydrodynamic pressure accessory [M] is calculated. p As shown in equation (5), [M] p By superimposing this onto the mass matrix of the dam's finite element dynamic equations, efficient hydrodynamic-fluid-structure interaction analysis of the dam and reservoir can be performed.

[0046] Using the Morrow Point arch dam from the paper "WATER COMPRESSIBILITY INEARTHQUAKE RESPONSE OF ARCH DAMS" published by Professor Anil K. Chopra's research team in the United States as a numerical example, a finite element model of the arch dam was established. The scaled boundary finite element method was then used to automatically generate a semi-infinite domain reservoir model upstream of the dam using the finite element mesh on the dam's upstream side. Both the unmodified dam-reservoir dynamic-fluid-structure interaction calculation method (referred to as the original coupling method) and the improved simplified dam-reservoir dynamic-fluid-structure interaction calculation method (referred to as the method of this invention) were used to perform dynamic-fluid-structure interaction calculations of the dam and reservoir under seismic conditions. Comparative analysis was conducted to verify the accuracy and efficiency of the improved dynamic-fluid-structure interaction calculation method.

[0047] The Morrow Point arch dam is 141.73m high, and the reservoir depth in front of the dam is 133.23m. The finite element model of the arch dam is shown below. Figure 2 It consists of 15,000 units and 18,207 nodes. The dam body parameters are: elastic modulus 25 GPa, Poisson's ratio 0.167, and density 2450 kg / m³. 3 The reservoir water parameters are: density 1000 kg / m³ 3 The time histories of seismic acceleration in the three directions input during dynamic calculations are shown in [reference needed]. Figure 3 A consistent input method is used.

[0048] There are 2397 nodes below the water level on the upstream side of the dam, meaning the semi-infinite domain reservoir has 2397 degrees of freedom. Therefore, the unsimplified additional mass matrix [m]... u The matrix [m] is a full matrix of order 2397, containing 2397 × 2397 = 5,745,609 elements; while the simplified additional mass matrix [m] u] is a diagonal matrix containing only 2397 elements.

[0049] Verification of calculation accuracy:

[0050] The dynamic response of the dam was analyzed using both the original dynamic-fluid-structure interaction calculation method and the improved method of this invention. Table 1 compares the maximum values ​​of the major principal stress σ1 and minor principal stress σ3 of the dam body using the two calculation methods. Tensile stress was taken as positive for dam body stress, and the error in the numerical results of this invention was based on the results of the original dynamic-fluid-structure interaction calculation method. Table 1 shows that the improved simplified dynamic-fluid-structure interaction calculation method produces very small errors, with the errors in both the major and minor principal stresses of the dam body not exceeding 5%, fully demonstrating the effectiveness of this invention and the accuracy of the numerical calculation results.

[0051] Table 1 Error of the maximum dynamic stress in the dam body

[0052]

[0053] Computational efficiency verification:

[0054] The desktop computer used for numerical calculations had an Intel(R) Xeon(R) Gold 6248R CPU with a clock speed of 3.00 Hz. Table 2 lists the computation time and corresponding time ratio required for the original dynamic-fluid-structure interaction (FLSE) calculation method and the method of this invention to complete the dynamic analysis under seismic conditions. When calculating the time ratio of the two dynamic-fluid-structure interaction analysis methods, the original dynamic-fluid-structure interaction calculation method was used as the baseline (i.e., the time ratio was 100%). As can be seen from Table 2, the improved simplified dynamic-fluid-structure interaction calculation method significantly reduces the computation time, to only 5% of the original method, demonstrating high computational efficiency. Moreover, when performing more detailed dam dynamic analysis, the computational scale will continue to expand, and the computation time will continue to increase. Using the method of this invention can save even more computation time, thereby achieving even higher computational efficiency.

[0055] Table 2. Calculation time for dynamic-fluid-structure interaction.

[0056]

[0057] The simplified and efficient calculation method for dam-reservoir hydrodynamic fluid-structure interaction provided by this invention discretizes the reservoir water using SBFEM or FEM and calculates the dynamic water pressure attachment mass matrix. Based on the physical meaning and characteristics of the attachment mass matrix, the dynamic water pressure attachment mass matrix is ​​simplified. While maintaining good accuracy, the calculation time is significantly reduced and the calculation efficiency is improved. This method enables simplified and efficient calculation and analysis of dam-reservoir hydrodynamic fluid-structure interaction under seismic conditions. It ensures high accuracy of numerical calculation results while significantly reducing the time consumed in coupling calculations. This provides an accurate and efficient method for dam-reservoir hydrodynamic fluid-structure interaction analysis and seismic safety evaluation, and provides technical support for the application of dam fluid-structure interaction analysis methods in practical engineering or large-scale dam dynamic fine analysis.

[0058] The present invention also provides an electronic device, which includes a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other via the communication bus.

[0059] The memory, which is used to store computer programs,

[0060] A processor is used to execute a computer program stored in a memory to implement the steps of the simplified and efficient calculation method for hydrodynamic-structure interaction of dam and reservoir described above.

[0061] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the simplified and efficient calculation method for hydrodynamic-structure interaction of dam and reservoir described above.

[0062] The aforementioned computer-readable storage medium can be any available medium or data storage device that can be accessed by the processor in an electronic device, including but not limited to magnetic storage such as floppy disks, hard disks, magnetic tapes, magneto-optical disks (MO), optical storage such as CDs, DVDs, BDs, HVDs, etc., and semiconductor storage such as ROMs, EPROMs, EEPROMs, non-volatile memory (NAND flash), solid-state drives (SSDs), etc.

[0063] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0064] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A simplified and efficient calculation method for hydrodynamic-fluid-structure interaction of dam and reservoir, characterized in that: The simplified and efficient calculation method for dam-reservoir hydrodynamic-fluid-structure interaction includes the following steps: Assuming the reservoir water is an ideal fluid with zero viscosity, incompressibility, and minimal disturbance, under seismic loading, the hydrodynamic pressure in the reservoir upstream of the dam will satisfy the Laplace equation: ▽ 2 p＝0 (1) Ignoring minor gravity waves, the boundary condition S0 on the free surface of the reservoir water is as follows: p＝0 (2) Boundary conditions on the upstream face S1 of the dam: Boundary conditions at interface S2 between the reservoir and its bottom and bank slope: Of the above formulas: ▽ 2 Here, p is the Laplace operator, n is the hydrodynamic pressure, and ρ is the fluid density. These are the normal accelerations at the dam-reservoir interface S1 and the valley-slope interface S2, respectively. The hydrodynamic pressure upstream of the dam can be discretized using SBFEM or FEM based on the above governing equations and boundary conditions, and then the hydrodynamic pressure-added mass matrix [M] can be calculated. p Simultaneously, using FEM to simulate the dam, the dynamic fluid-structure interaction equation of the dam-reservoir system can be expressed as: Among them, [M s [C] s ] and [K s [These represent the finite element mass, damping, and stiffness matrices of the dam body, respectively.] and{u r (t)} represent the relative acceleration, relative velocity, and relative displacement of the dam body, respectively; The input system is the seismic acceleration; As can be seen from equation (5), as long as the hydrodynamic pressure is added to the mass matrix [M], p By superimposing the mass matrix of the finite element dynamic equation of the dam body, the hydrodynamic pressure effect during seismic input can be considered, and dynamic-fluid-structure interaction analysis of dam-reservoir can be carried out. The hydrodynamic pressure additional mass matrix [M] obtained by solving using FEM or SBFEM p ], represented as: [M p ]=[L1] T [m u ][L1]+[L1] T [m v ][L2] (6) In the formula, [m u To excite the dam's upstream face S1 with acceleration The associated additional mass matrix, [m v [To excite the S2 acceleration of the bedrock facing the water in the valley] The relevant additional mass matrix, [L1] is the transformation matrix between the global coordinate direction and the dam surface normal, and [L2] is the transformation matrix between the global coordinate direction and the reservoir bottom slope (i.e., the valley) normal; The calculated additional mass matrix [m] u [This is a full array where all elements are non-zero. That is, when calculating the hydrodynamic pressure caused by vibration on the upstream side of the dam, the hydrodynamic pressure at a certain node on the dam face is related to the acceleration excitation of all nodes on the dam face.] All are related; however, when calculating the hydrodynamic pressure caused by vibration in the bedrock valley, the hydrodynamic pressure at a certain node on the dam face is only related to the acceleration excitation of the node at the boundary between the dam face and the valley. Correlation, therefore, the additional mass matrix [m] v ] is a very sparse matrix containing a large number of zero elements; obviously, due to the mass matrix [m u The existence of the additional mass matrix [M] makes the additional mass matrix [M]... p The addition of the mass matrix [m] results in a full matrix, which significantly increases the time required to solve for the equivalent stiffness matrix in dynamic analysis. v The impact on the computational efficiency of coupled dynamics is relatively small; From the above analysis, it can be seen that we only need to simplify [m] u This can reduce the added mass matrix [M] p The correlation of the nodal degrees of freedom of ]; when the additional mass matrix [m u When the order is n, that is, there are n nodes below the water level on the upstream side of the dam, and its element mu ij The physical meaning is the hydrodynamic pressure acting on node i caused by the unit normal acceleration excitation of the reservoir water by node j on the water-facing side; The simplification method is based on [m] u Taking the element in the i-th row of the array as an example, it can be represented as mu. i1 mu i2 …mu ii …mu in Among them, element mu ii In matrix [m u The value at the diagonal position of [] is the largest among the elements in the i-th row; we can first move each element in the i-th row towards the diagonal element mu. ii Superimpose the elements, then remove zeros from the off-diagonal elements; this achieves the additional mass matrix [m]. u Decoupling means that the hydrodynamic pressure on node i on the water-facing surface is only related to the normal acceleration excitation of node i; since directly superimposing off-diagonal elements onto diagonal elements will amplify the hydrodynamic pressure, the off-diagonal elements need to be multiplied by a reduction factor α = 0.65 during the superposition process; thus, processing from the first row to the nth row completes the matrix [m u By simplifying the overall structure, the additional mass matrix of hydrodynamic pressure [M] can be calculated. p ], and [M p The mass matrix of the dam body's finite element dynamic equation is superimposed on the dam body to perform simplified and efficient calculations of the dam-reservoir hydrodynamic coupling.

2. The application of the simplified and efficient calculation method for hydrodynamic fluid-structure interaction of dams and reservoirs as described in claim 1 in the detailed dynamic analysis of large-scale dams.

3. An electronic device, comprising a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other via the communication bus, characterized in that: The memory, which is used to store computer programs, A processor, wherein the processor is configured to execute a computer program stored in a memory to implement the steps of the simplified and efficient calculation method for hydrodynamic-fluid-structure interaction of a dam-reservoir as described in claim 1.

4. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the simplified and efficient calculation method for hydrodynamic-fluid-structure interaction of dam and reservoir as described in claim 1.

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