Multi-directional irregular wave numerical simulation method based on single superposition wave model

Abstract

The invention discloses a multidirectional irregular wave numerical simulation method based on a single superposition wave model, and relates to the field of wave numerical simulation, and the method comprises the steps: carrying out the non-uniform discretization of a direction spectrum into a plurality of grid units according to the global wave energy distribution condition of the direction spectrum; for any grid unit, determining wave parameters of composition waves corresponding to the grid unit according to the local wave energy distribution condition of the direction spectrum in the grid unit, and obtaining a wave surface equation of the composition waves; and superposing the wave surface equations of the composition waves based on a single superposition wave model to obtain the multidirectional irregular wave. According to the method disclosed by the invention, the multidirectional irregular waves can be accurately simulated with a small number of composition waves, and compared with a traditional equal-interval uniform discrete method, the simulation precision is higher.

Description

Technical Field

[0001] The present application relates to the field of wave numerical simulation, and in particular to a numerical simulation method for multi-directional irregular waves based on a single superposition wave model. Background Art

[0002] In the process of humans continuously developing marine energy and utilizing marine space, as the working and living environment of marine engineering equipment becomes more and more complex, people's understanding and research on ocean waves have gradually deepened from simple one-way regular waves to multi-directional irregular waves, and multi-directional irregular waves are more in line with the multi-directional waves in the actual ocean.

[0003] In order to study the influence of multi-directional waves on marine structures, it is necessary to numerically simulate multi-directional irregular waves. Considering that multi-directional irregular waves can be composed of several component waves with different frequencies and wave directions superimposed, the numerical simulation of multi-directional irregular waves is mainly achieved by discretizing the directional spectrum to obtain several component waves and then performing wave superposition. Specifically: the directional spectrum is evenly discretized at equal intervals in the frequency distribution range and the wave direction distribution range to obtain a plurality of grid cells, and frequency values and wave direction values are randomly selected within each grid cell as the representative frequency and wave direction of the component wave respectively, and then the component waves within each grid cell are superimposed to obtain multi-directional irregular waves.

[0004] However, since the representative frequency and wave direction of the component wave within each grid cell are randomly selected, it is difficult to control the characteristics of the selected samples. Therefore, in order to ensure the accuracy of the numerical simulation, it is often required that the division density of the grid cells is relatively high, which means that the number of component waves participating in the calculation during the numerical simulation needs to be sufficient, resulting in a proportional increase in the calculation amount, a long calculation time, and low calculation efficiency. Therefore, it is difficult for the existing numerical simulation method of multi-directional irregular waves to achieve good performance in both accuracy and speed. Summary of the Invention

[0005] In view of the above problems and technical requirements, the present application proposes a numerical simulation method for multi-directional irregular waves based on a single superposition wave model. The technical solution of the present application is as follows:

[0006] A numerical simulation method for multi-directional irregular waves based on a single superposition wave model includes the following steps:

[0007] The directional spectrum is non-uniformly discretized into a plurality of grid cells according to the global wave energy distribution of the directional spectrum, and the higher the wave energy in the directional spectrum, the higher the density of the grid cells in the area.

[0008] For any grid cell i, the wave parameters of the component wave corresponding to the grid cell i are determined according to the local wave energy distribution of the directional spectrum in the grid cell i, and the wave surface equation of the component wave is obtained.

[0009] Based on the single superposition wave model, the wave surface equations of each component wave are superimposed to obtain a multi-directional irregular wave.

[0010] Its further technical solution is that the wave parameters include the representative frequency and wave direction. The representative frequency ω of the component wave corresponding to the grid cell is determined according to the local wave energy distribution in the grid cell i in the direction spectrum. i and the wave direction θ i including:

[0011] Calculate the wave energy S(ω,θ) at different frequencies ω and wave directions θ in the grid cell i to obtain the local wave energy distribution in the grid cell i;

[0012] Determine the wave energy center of gravity in the grid cell i according to the local wave energy distribution in the grid cell i. The wave energy center of gravity is the comprehensive action point of the wave energy at different positions in the grid cell i;

[0013] Take the frequency corresponding to the wave energy center of gravity in the grid cell i as the representative frequency ω of the component wave corresponding to the grid cell i i and the wave direction corresponding to the wave energy center of gravity as the wave direction θ of the component wave corresponding to the grid cell i i .

[0014] Its further technical solution is that determining the wave energy center of gravity in the grid cell i includes:

[0015] Determine the value of the frequency corresponding to the wave energy center of gravity in the grid cell i the value of the wave direction corresponding to the wave energy center of gravity

[0016] where ΔS i is the area of the grid cell i, and S(ω,θ) is the wave energy at any frequency ω and wave direction θ in the grid cell i.

[0017] Its further technical solution is that calculating the values of the frequency and wave direction ω i and θ i corresponding to the wave energy center of gravity in the grid cell i includes solving according to the following formula using Gaussian integration:

[0018]

[0019] where N is the total number of nodes of the isoparametric element corresponding to the grid cell i in the isoparametric coordinate system K is the number of Gaussian integration points, is the Jacobian determinant of the isoparametric element and w α and w β are the weights of the Gaussian integration points, is the shape function of the isoparametric element node n is the wave energy at node n in the isoparametric element of grid cell i, is the frequency of node n in the isoparametric element of grid cell i, is the wave direction of node n in the isoparametric element of grid cell i.

[0020] A further technical solution is that when the directional spectrum is non-uniformly discretized into multiple grid cells, the density relationship of the grid cells in different regions of the directional spectrum is proportional to the wave energy relationship in different regions and is at the same order of magnitude level.

[0021] A further technical solution is that non-uniformly discretizing the directional spectrum into multiple grid cells according to the global wave energy distribution of the directional spectrum includes:

[0022] Setting a number of frequency division lines along the frequency axis of the directional spectrum within the frequency range of the directional spectrum, where the number of frequency division lines is more in the vicinity of the spectral peak frequency;

[0023] Setting a number of wave direction division lines along the wave direction axis of the directional spectrum within the wave direction range of the directional spectrum, where the number of wave direction division lines is more in the vicinity of the main wave direction;

[0024] Combining all the frequency division lines and wave direction division lines to obtain a number of quadrilateral eight-node elements; any one frequency division line is perpendicular to the frequency axis of the directional spectrum, any one wave direction division line is perpendicular to the wave direction axis of the directional spectrum, and any grid cell obtained by combining the frequency division line and the wave direction division line is a quadrilateral grid cell.

[0025] A further technical solution is that any grid cell i is a quadrilateral eight-node element, the total number of nodes N of the isoparametric element corresponding to grid cell i is 8, then the number of Gauss integration points K = 4, and

[0026] w α and w β take values of [0.347854845137, 0.652145154863, 0.652145154863, 0.347854845137].

[0027] A further technical solution is that the wave parameters include wave amplitude, wave number and initial phase. Determining the wave amplitude, wave number and initial phase of the component wave corresponding to grid cell i according to the local wave energy distribution of the directional spectrum in grid cell i includes:

[0028] Calculating the surface integral of the directional spectrum in grid cell i to obtain the wave amplitude of the corresponding component wave where ΔS iis the area of grid cell i, and S(ω,θ) is the wave energy at any frequency ω and wave direction θ within grid cell i;

[0029] According to the dispersion relationship, combined with the representative frequency ω of the component wave corresponding to grid cell i i Determine the wave number k of the component wave corresponding to grid cell i i ;

[0030] Randomly select the initial phase ε from the random numbers uniformly distributed within [0, 2π] i .

[0031] Its further technical solution is that the wave amplitude a of the component wave corresponding to grid cell i i Includes solving using Gaussian integration according to the following formula:

[0032]

[0033] where N is the total number of nodes of the isoparametric element corresponding to grid cell i in the isoparametric coordinate system K is the number of Gaussian integration points, is the Jacobian determinant of the isoparametric element and w α and w β are the weights of the Gaussian integration points, is the shape function of the isoparametric element node n, is the wave energy at node n in the isoparametric element of grid cell i, is the frequency of node n in the isoparametric element of grid cell i, is the wave direction of node n in the isoparametric element of grid cell i.

[0034] Its further technical solution is that based on the single superposition wave model, the wave surface equations of each component wave are superimposed to obtain the wave surface equation expression of the multi-directional irregular wave as:

[0035]

[0036] where MI is the total number of grid cells, t is the time, and x, y represent the coordinate axes directions of the geodetic coordinate system.

[0037] The beneficial technical effects of this application are:

[0038] A numerical simulation method of multi-directional irregular waves based on a single superposition wave model discretizes the directional spectrum non-uniformly into multiple grid cells according to the global wave energy distribution of the directional spectrum, thereby obtaining multiple component waves. Compared with the traditional method of equally spaced discretization of the directional spectrum to obtain component waves, the method of the present application can accurately extract the energy distribution characteristics of the directional spectrum with a smaller number of component waves, so that the obtained component waves can more truly and effectively reflect the wave energy distribution of multi-directional irregular waves, thereby effectively improving the simulation accuracy of multi-directional irregular waves.

[0039] By analyzing the local wave energy distribution in the grid cell, the frequency and wave direction corresponding to the wave energy centroid are used as the representative frequency and wave direction of the component wave. Compared with the traditional method of equally spaced selection of representative frequencies and wave directions, it can effectively solve the problem of phase locking and ensure that the simulated multi-directional irregular waves are more reasonable and real. Compared with the method of randomly selecting frequencies and wave directions in the grid cell as the representative frequencies and wave directions of the component wave, the method of the present application can further improve the accuracy of the component wave, thereby ensuring that the simulated multi-directional irregular waves are accurate and reliable.

[0040] Since the energy distribution of the directional spectrum is not uniform and is often concentrated at the spectral peak, in the case of the same number of grid cells, the traditional method of equally spaced discretization of the directional spectrum will result in only a few grid cells near the spectral peak where the energy is concentrated, thus causing a large error. To ensure accuracy, the number of grid cells must be required to be large enough, which will increase the computational amount proportionally, especially for the computational amount of multi-directional irregular waves with non-linear characteristics, which increases more seriously. By non-uniformly discretizing the directional spectrum and selecting the frequency and wave direction corresponding to the wave energy centroid as the representative frequency and wave direction, the present application takes into account both the numerical simulation accuracy and the computational efficiency. Compared with the traditional method, it can effectively improve the accuracy and computational efficiency, which is of great significance for practical applications. Description of the Drawings

[0041] Figure 1 is the flowchart of the numerical simulation method of multi-directional irregular waves.

[0042] Figure 2 is a schematic diagram of equally spaced and uniform discretization of the directional spectrum by the traditional method.

[0043] Figure 3 is a schematic diagram of non-uniform discretization of the directional spectrum by the method of the present application.

[0044] Figure 4 is a comparison chart of the simulation results of the method of the present application and the traditional method. Detailed Embodiments

[0045] The following further describes the detailed embodiments of the present application with reference to the drawings.

[0046] A numerical simulation method of multi-directional irregular waves based on a single superposition wave model proposed in this application, please refer to Figure 1 the flow chart shown below. The specific steps are as follows:

[0047] Step 1: Discretize the directional spectrum non-uniformly into multiple grid cells according to the global wave energy distribution of the directional spectrum. The higher the wave energy in the directional spectrum, the higher the density of the grid cells in that area.

[0048] The directional spectrum S(ω,θ) can characterize the energy distribution of multi-directional irregular waves within a two-dimensional plane range composed of a quite wide frequency and wave direction. It is usually described by the product of the frequency spectrum and the direction distribution function. The specific expression is:

[0049] S(ω,θ) = S(ω)G(ω,θ)

[0050] Among them, S(ω) is the frequency spectrum, and models such as the PM spectrum or the JONSWAP spectrum can be used. The commonly used improved JONSWAP spectrum is:

[0051]

[0052] Among them, T p is the spectral peak period, f p is the spectral peak frequency, T s is the significant wave period, H s is the significant wave height. The intermediate variable σ is the peak shape parameter and ω p is the spectral peak frequency, γ is the spectral peak elevation factor, and its observed value ranges from 1.5 to 6, with an average value of 3.3. The angular frequency expression of the improved JONSWAP spectrum is S(ω) = S(f) / 2π.

[0053] G(ω,θ) is the direction distribution function, and direction distribution functions such as the Gauss type distribution or the semi-cosine distribution can be used. The commonly used direction distribution function G(θ) is the Gauss type distribution. The specific expression is:

[0054]

[0055] Among them, s is the concentration degree of the direction distribution function, θ p is the main wave direction.

[0056] The numerical simulation of multi-directional irregular waves is mainly carried out by discretizing the directional spectrum to obtain several component waves and then performing wave superposition on them. In an example, using the traditional method for parameters: significant wave height H s = 4.0m, spectral peak frequency ω p = 1.0 rad / s, main wave direction θ pThe result of equally spaced discretization of the directional spectrum of multi-directional irregular waves with ω = 0.0 rad / s and concentration s = 8 of the directional distribution function is as follows Figure 2 shown. The warmer the color, the higher the wave energy. It can be seen that the wave energy of multi-directional irregular waves is mainly concentrated at the spectral peak.

[0057] Each discretized grid cell corresponds to a component wave. As Figure 2 can be seen, only a few grid cells of the component waves obtained by the traditional method are arranged near the spectral peak where the wave energy is concentrated. For example Figure 2 among the 300 uniformly arranged grid cells, only 2% of the component waves are arranged near the spectral peak. The multi-directional irregular waves obtained by superposing such component waves cannot accurately represent the global wave energy distribution of multi-directional irregular waves, and the error of the numerical simulation results is relatively large.

[0058] In order to improve the accuracy of numerical simulation and accurately express the wave energy distribution characteristics of multi-directional irregular waves, the component waves obtained by non-uniformly discretizing the directional spectrum into multiple grid cells according to the global wave energy distribution of the directional spectrum are more representative. The result of non-uniform discretization is as follows Figure 3 shown. Compared with Figure 2 the uniformly arranged grid cells, Figure 3 the number of grid cells near the spectral peak in

[0059] significantly increases.

[0060] Step 2, for any grid cell i, determine the wave parameters of the component wave corresponding to grid cell i according to the local wave energy distribution in grid cell i of the directional spectrum, and obtain the wave surface equation of the component wave.

[0061] Each grid cell corresponds to a component wave. Therefore, the wave parameters of the component wave can be determined using the grid cell. The wave parameters of the component wave include the representative frequency and wave direction. In the traditional method, the direction spectrum is evenly discretized at equal intervals to obtain multiple grid cells, and the frequency and wave direction corresponding to the center point of the grid cell are selected as the representative frequency and wave direction of the component wave. The frequency interval of the component wave obtained by this method is Δω. The multi-directional irregular wave obtained by superposing the component waves will repeat with a period which leads to a phase-locking problem, and this does not occur in the actual ocean environment. In the prior art, the phase-locking problem of the simulated multi-directional irregular wave is avoided by randomly selecting a frequency within the grid cell as the representative frequency of the component wave. However, due to the random selection of the frequency in this method, in order to ensure the accuracy of the numerical simulation, it is necessary to require the grid cell to be small enough to select a relatively accurate representative frequency. This means that the number of component waves participating in the calculation during the numerical simulation is very large, which will inevitably lead to a significant increase in the computational amount.

[0062] This application aims to solve the problems of low numerical simulation accuracy and low computational efficiency in the prior art. By analyzing the local wave energy distribution in the grid cell, a representative frequency and wave direction are selected. In one embodiment, the representative frequency ω i and wave direction θ i of the component wave corresponding to the grid cell are determined according to the local wave energy distribution in the grid cell i, including:

[0063] Calculating the wave energy S(ω,θ) at different frequencies ω and wave directions θ in the grid cell i to obtain the local wave energy distribution in the grid cell i.

[0064] According to the local wave energy distribution in the grid cell i, the wave energy centroid of the grid cell i is determined. The wave energy centroid is the comprehensive action point of the wave energy at different positions in the grid cell i. The wave energy centroid can characterize the concentrated action characteristics of the wave energy in the grid cell i and is the most representative position in the grid cell i.

[0065] Therefore, the frequency corresponding to the wave energy centroid in the grid cell i is used as the representative frequency ω i of the component wave corresponding to the grid cell i, and the wave direction corresponding to the wave energy centroid is used as the wave direction θ i of the component wave corresponding to the grid cell i.

[0066] In one embodiment, the specific method for determining the wave energy centroid in the grid cell i is:

[0067] Determine the value of the frequency corresponding to the wave energy centroid in the grid cell i and the value of the wave direction corresponding to the wave energy centroid where ΔS iis the area of grid cell i, and S(ω,θ) is the wave energy at any frequency ω and wave direction θ within grid cell i.

[0068] The wave parameters of the component waves also include wave amplitude, wave number, and initial phase. In one embodiment, determining the wave amplitude, wave number, and initial phase of the component wave corresponding to grid cell i according to the local wave energy distribution of the directional spectrum within grid cell i includes:

[0069] Calculating the area integral of the directional spectrum within grid cell i to obtain the corresponding wave amplitude of the component wave where ΔS i is the area of grid cell i, and S(ω,θ) is the wave energy at any frequency ω and wave direction θ within grid cell i.

[0070] According to the dispersion relation and combining with the representative frequency ω of the component wave corresponding to grid cell i i determine the wave number k of the component wave corresponding to grid cell i i . The dispersion relation satisfied by the wave number and the representative frequency of the component wave is h is the wave height, and g is the acceleration due to gravity.

[0071] Randomly select the initial phase ε from the random numbers uniformly distributed in [0, 2π] i .

[0072] The above wave amplitude, representative frequency, and wave direction need to be solved through the area integral of the directional spectrum within grid cell i. The specific method is as follows:

[0073] First, use the isoparametric transformation to convert the area integral into isoparametric elements. At any point in the isoparametric coordinate system the frequency wave direction and wave energy can be represented by the corresponding shape functions. The specific expressions are:

[0074]

[0075] Then, calculate the area differential in the isoparametric coordinate system from the Jacobian determinant as:

[0076]

[0077] Finally, arrange K Gaussian integration points on each coordinate axis within the isoparametric element, then the area integral within grid cell i is rewritten as:

[0078]

[0079] Thus, the wave amplitude, representative frequency, and wave direction of the component wave corresponding to grid cell i can be calculated based on the area. In one embodiment, the values of the frequency ω and wave direction θ corresponding to the center of gravity of the wave energy in grid cell i are calculated as follows: i and θ i including solving using Gaussian quadrature according to the following formula:

[0080]

[0081] where N is the total number of nodes of the isoparametric element corresponding to grid cell i in the isoparametric coordinate system K is the number of Gaussian quadrature points, is the Jacobian determinant of the isoparametric element and w α and w β are the weights of the Gaussian quadrature points, is the shape function of node n of the isoparametric element, is the wave energy at node n of the isoparametric element of grid cell i, is the frequency at node n of the isoparametric element of grid cell i, is the wave direction at node n of the isoparametric element of grid cell i.

[0082] The wave amplitude a of the component wave corresponding to grid cell i i including solving using Gaussian quadrature according to the following formula:

[0083]

[0084] Specifically, the shape function of the isoparametric element and the weights of the Gaussian quadrature points can be determined according to the shape of the grid cell, so as to calculate the wave amplitude, representative frequency, and wave direction of the component wave. Commonly used grid cells are triangular or quadrilateral, and the Gaussian quadrature points are set according to the shape of the grid cell for integral calculation.

[0085] Different-shaped grid cells can be obtained according to different discretization methods. In one embodiment, the specific method of non-uniformly discretizing the directional spectrum into multiple quadrilateral grid cells according to the global wave energy distribution of the directional spectrum is as follows:

[0086] Set a number of frequency division lines along the frequency axis of the directional spectrum within the frequency range of the directional spectrum, where the number of frequency division lines is more at frequencies closer to the spectral peak frequency;

[0087] Set a number of wave direction division lines along the wave direction axis of the directional spectrum within the wave direction range of the directional spectrum, where the number of wave direction division lines is more at wave directions closer to the main wave direction;

[0088] Combining all the frequency dividing lines and wave direction dividing lines results in multiple quadrilateral eight-node elements; any one frequency dividing line is perpendicular to the frequency axis of the directional spectrum, and any one wave direction dividing line is perpendicular to the wave direction axis of the directional spectrum. Any grid element obtained by combining the frequency dividing line and the wave direction dividing line is a quadrilateral grid element.

[0089] Considering the feasibility and computational accuracy of the grid element division in this application, any grid element i obtained by non-uniform discretization is a quadrilateral eight-node element. The total number of nodes N of the isoparametric element corresponding to the grid element i is 8, and the number of Gaussian integration points K selected is 4. The shape functions corresponding to the 8 isoparametric element nodes are as follows:

[0090]

[0091] Among them, the weights w α and w β of the Gaussian integration points of the quadrilateral eight-node grid element take values in [0.347854845137, 0.652145154863, 0.652145154863, 0.347854845137]. Each value within the interval corresponds to the weight of a Gaussian integration point.

[0092] Step 3: Based on the single superposition wave model, the wave surface equations of the individual component waves are superposed to obtain a multi-directional irregular wave.

[0093] According to the wave parameters of each component wave obtained in Step 2, the wave surface equation of the component wave can be determined. By superposing the wave surface equations of the individual component waves, the wave surface equation of the multi-directional irregular wave can be obtained.

[0094] In one embodiment, the expression of the wave surface equation of the multi-directional irregular wave obtained by superposing the wave surface equations of the individual component waves based on the single superposition wave model is:

[0095]

[0096] Among them, MI is the total number of grid elements, t is the time, and x and y represent the coordinate axes of the geodetic coordinate system.

[0097] To verify the effectiveness of the method of this application, appropriate observation points are arranged in the simulated multi-directional irregular wave incident field. The frequency spectrum S(ω) of the simulated multi-directional irregular wave is obtained by performing a Fourier transform on the time history of the simulated wave surface. Using the method of this application and the traditional method respectively for the parameters of the significant wave height H s = 4.0 m, the spectral peak frequency ω p = 1.0 rad / s, the spectral peak elevation factor γ = 1.87, and the main wave direction θ p=0.0rad / s, the directional spectrum with the concentration of the directional distribution function s=2, 8, 16, 128, ∞ is discretized into 300 grid units to obtain 300 component waves. The spectrum of the multi-directional irregular wave at different concentrations is obtained by superposition of the 300 component waves obtained by the discretization. Please refer to Figure 4 The comparison results are shown in Figure 2. Among them, the concentration of the directional distribution function s = ∞ represents a unidirectional wave, and its wave energy is all concentrated in the main wave direction.

[0098] Figure 4 The black solid line in the figure is the target spectrum (Target), the blue dotted line (Uniform) is the spectrum of the multi-directional irregular wave simulated by the traditional method, and the scattered points of different colors correspond to the spectrum of the multi-directional irregular wave with different concentrations simulated by the method of the present application. Figure 4 From the comparison results, it can be seen that the method of the present application is basically consistent with the target spectrum, and the numerical simulation results have high accuracy. However, the traditional method has a large error at the spectrum peak, and the accuracy of the numerical simulation results is far less than that of the method of the present application. It can be seen that the method of the present application realizes the simulation of multi-directional irregular waves with a relatively small number of component waves, and can especially accurately simulate the distribution of wave energy, and has high practical application value.

[0099] The above is only a preferred embodiment of the present application, and the present application is not limited to the above embodiments. It is understood that other improvements and changes directly derived or associated by those skilled in the art without departing from the spirit and concept of the present application should be considered to be included in the protection scope of the present application.

Claims

1. A numerical simulation method for multi-directional irregular waves based on a single superimposed wave model, characterized in that: The multi-directional irregular wave numerical simulation method comprises: According to the global wave energy distribution of the directional spectrum, the directional spectrum is discretized into multiple grid cells in an inhomogeneous manner. The higher the wave energy in the directional spectrum, the higher the density of the grid cells. For any grid unit i, the wave parameters of the component waves corresponding to the grid unit i are determined according to the local wave energy distribution of the directional spectrum in the grid unit i, and the wave surface equation of the component waves is obtained; Based on the single superposition wave model, the wave surface equations of each component wave are superimposed to obtain multi-directional irregular waves.

2. The multi-directional irregular wave numerical simulation method according to claim 1, characterized in that: The wave parameters include representative frequency and wave direction. The representative frequency ω of the component wave corresponding to the grid unit is determined according to the local wave energy distribution in the grid unit i by the directional spectrum. i and wave direction θ i include: Calculate the wave energy S(ω,θ) at different frequencies ω and wave directions θ in the grid unit i by directional spectrum to obtain the local wave energy distribution in the grid unit i; The wave energy center of gravity in grid unit i is determined according to the local wave energy distribution in grid unit i. The wave energy center of gravity is the comprehensive action point of wave energy at different positions in grid unit i. The frequency corresponding to the center of gravity of wave energy in grid unit i is taken as the representative frequency ω of the component wave corresponding to grid unit i i , the wave direction corresponding to the wave energy center of gravity is used as the wave direction θ of the component wave corresponding to grid unit i i .

3. The multi-directional irregular wave numerical simulation method according to claim 2, characterized in that: Determining the center of gravity of wave energy within grid cell i includes: Determine the value of the frequency corresponding to the center of gravity of wave energy in grid cell i The value of the wave direction corresponding to the wave energy center of gravity Among them, ΔS i is the area of ​​grid cell i, and S(ω,θ) is the wave energy at any frequency ω and wave direction θ in grid cell i.

4. The multi-directional irregular wave numerical simulation method according to claim 3, characterized in that: Calculate the frequency and wave direction corresponding to the wave energy center of gravity in grid cell i i and θ i Including using Gaussian integral to solve according to the following formula: Where N is the grid cell i in the isoparametric coordinate system The total number of nodes of the corresponding isoparametric unit, K is the number of Gaussian integration points, is the Jacobian of the isoparametric unit and w α and w β is the weight of the Gaussian integration point, is the shape function of the isoparametric element node n, is the wave energy at node n in the isoparametric cell of grid cell i, is the frequency of node n in the isoparametric cell of grid cell i, is the wave direction at node n in the isoparametric cell of grid cell i.

5. The multi-directional irregular wave numerical simulation method according to claim 1, characterized in that: When the directional spectrum is discretized non-uniformly into multiple grid cells, the density relationship of the grid cells in different regions of the directional spectrum is proportional to the wave energy relationship in different regions and is at the same order of magnitude.

6. The multi-directional irregular wave numerical simulation method according to claim 4, characterized in that: According to the global wave energy distribution of the directional spectrum, the directional spectrum is discretized non-uniformly into multiple grid units including: A plurality of frequency dividing lines are set along the frequency axis of the directional spectrum within the frequency interval of the directional spectrum, wherein the closer to the peak frequency of the spectrum, the greater the number of frequency dividing lines; A plurality of wave direction dividing lines are arranged along the wave direction axis of the direction spectrum within the wave direction interval of the direction spectrum, wherein the closer to the main wave direction, the more wave direction dividing lines there are; All frequency dividing lines and wave direction dividing lines are combined to obtain multiple quadrilateral eight-node units; any frequency dividing line is perpendicular to the frequency axis of the directional spectrum, any wave direction dividing line is perpendicular to the wave direction axis of the directional spectrum, and any grid unit obtained by combining the frequency dividing line and the wave direction dividing line is a quadrilateral grid unit.

7. The multi-directional irregular wave numerical simulation method according to claim 6, characterized in that: Any mesh element i is a quadrilateral eight-node element, and the total number of nodes of the isoparametric element corresponding to the mesh element i is N = 8, then the number of Gaussian integration points K = 4, and w α and w β The value of is [0.347854845137,0.652145154863,0.652145154863,0.347854845137].

8. The multi-directional irregular wave numerical simulation method according to claim 2, characterized in that: The wave parameters include amplitude, wave number and initial phase. The amplitude, wave number and initial phase of the component wave corresponding to the grid unit i are determined according to the local wave energy distribution of the directional spectrum in the grid unit i. The amplitude, wave number and initial phase include: Calculate the surface integral of the directional spectrum in grid cell i to obtain the amplitude of the corresponding component wave Among them, ΔS i is the area of ​​grid cell i, S(ω,θ) is the wave energy at any frequency ω and wave direction θ in grid cell i; According to the dispersion relation, the representative frequency ω of the component wave corresponding to the grid unit i is i Determine the wave number k of the component wave corresponding to grid cell i i ; Randomly select the initial phase ε from the random numbers uniformly distributed in [0,2π] i .

9. The multi-directional irregular wave numerical simulation method according to claim 8, characterized in that: The amplitude a of the component wave corresponding to grid cell i i Including using Gaussian integral to solve according to the following formula: Where N is the grid cell i in the isoparametric coordinate system The total number of nodes of the corresponding isoparametric unit, K is the number of Gaussian integration points, is the Jacobian of the isoparametric unit and w α and w β is the weight of the Gaussian integration point, is the shape function of the isoparametric element node n, is the wave energy at node n in the isoparametric cell of grid cell i, is the frequency of node n in the isoparametric cell of grid cell i, is the wave direction at node n in the isoparametric cell of grid cell i.

10. The multi-directional irregular wave numerical simulation method according to claim 8, characterized in that: The wave surface equation expression of the multi-directional irregular wave obtained by superimposing the wave surface equations of each component wave based on the single superposition wave model is: Among them, MI is the total number of grid cells, t is the time, and x and y represent the coordinate axis directions of the geodetic coordinate system.

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