Finite element integral method for wave height attenuation of wave propagation onshore by wave-cut platform

Abstract

The present invention discloses a finite element integral calculation method for wave height attenuation of nearshore wave propagation by a sea erosion platform, which relates to the field of marine disasters and disaster prevention and mitigation. The method comprises: performing geomorphological interpretation on the sea erosion platform and recording the positions of the seaward boundary and the shoreward boundary of the sea erosion platform, obtaining the width W and the inclination angle a of the sea erosion platform; performing finite element meshing on the sea erosion platform to form n grids with a horizontal width d; and calculating the wave height H at the seaward edge of the grid according to the wave height H at the seaward edge of the grid. i , the horizontal width of the grid is d, the attenuation parameter α i and β i Iteratively calculate the wave height H reaching the shore boundary of the grid j , set the iteration stop condition, when the iteration stop condition is reached, move the grid to the wave height H on the shore boundary j The wave height H that finally reaches the coast after attenuation c The present invention can solve the problems of traditional process numerical simulation methods that consume a lot of calculation resources and require many parameters.

Description

Technical Field

[0001] The present invention relates to the calculation technology of nearshore propagation of waves on bedrock coasts and the field of marine disasters and disaster prevention and mitigation, and in particular to a finite element integral calculation method for wave height attenuation of nearshore propagation of waves by a sea erosion platform. Background Art

[0002] In the field of marine disasters and disaster prevention and mitigation technologies on bedrock coasts, how to accurately simulate the nearshore propagation characteristics of waves and precisely predict the final wave height reaching the bedrock coast is an important basis for scientifically protecting coastal erosion disasters and promoting the sustainable development of bedrock coastal resources.

[0003] The persistent erosion of bedrock coasts by waves results in the formation of seaward-sloping platform-like landforms in the intertidal zone—tidal platforms. As waves propagate nearshore, they interact with the surface of the tidal platforms, attenuating the wave energy ultimately reaching the coast. Therefore, accurately characterizing the impact of tidal platforms on nearshore wave propagation has long been a crucial foundation for numerical simulations of bedrock coastal geomorphological evolution. However, currently used methods for calculating nearshore wave propagation primarily utilize numerical models based on wave propagation processes. These models require not only significant computational resources but also a large number of highly accurate boundary conditions, including far-field wave characteristics, seafloor bathymetry, and bottom roughness. However, accurately capturing the seafloor topography and far-field wave conditions over long geological timescales is impossible, rendering these process-based numerical models inapplicable. Furthermore, given my country's vast coastline, obtaining accurate environmental parameters for all coasts requires significant human and material resources. Consequently, these process-based models are unsuitable for large-scale coastal erosion disaster prevention and mitigation. In the field of bedrock coasts, a set of parameterized empirical formulas was only developed in 2014, which simplified the quantitative requirements for the numerical simulation of nearshore wave propagation. However, this model is only applicable to nearly horizontal sea erosion platforms, while actual bedrock coasts are more likely to develop inclined sea erosion platforms. This makes the applicability of its formula to inclined sea erosion platforms a key issue that restricts the promotion and application of this model in the field of coastal erosion disaster prevention and mitigation.

[0004] Therefore, there is a great need for a method that has high computational efficiency, requires few parameters, is applicable to both inclined and horizontal sea erosion platforms, and can accurately evaluate the attenuation of wave height caused by nearshore propagation of waves on sea erosion platforms. Summary of the Invention

[0005] In response to the deficiencies in the prior art, the present invention provides a method for calculating the attenuation of wave height caused by the development of sea erosion platforms on the nearshore propagation of waves based on finite element integration theory, which solves the problem that traditional process-based numerical simulation methods consume a lot of resources and require many parameters for calculation, and solves the restrictive problem that parameterized empirical formulas are only applicable to nearly horizontal sea erosion platforms and cannot be widely used in the field of bedrock coastal erosion disaster prevention and mitigation.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A finite element integral calculation method for wave height attenuation of nearshore wave propagation by a sea erosion platform comprises the following steps:

[0008] Performing geomorphic interpretation on the sea erosion platform and recording the positions of the seaward boundary and the shoreward boundary of the sea erosion platform to obtain the width W and the inclination angle a of the sea erosion platform;

[0009] Performing finite element mesh division on the sea erosion platform to form n grids with a horizontal width of d;

[0010] According to the wave height H at the seaward edge of the grid i , the horizontal width of the grid is d, the attenuation parameter α i and β i Iteratively calculate the wave height H reaching the shore boundary of the grid j , set the iteration stop condition, when the iteration stop condition is reached, move the grid to the wave height H on the shore boundary j The wave height H that finally reaches the coast after attenuation c .

[0011] The finite element integral calculation method for the wave height attenuation of nearshore wave propagation by the sea erosion platform as described above, further, the sea erosion platform width W refers to the horizontal distance between the sea side boundary and the shore side boundary of the sea erosion platform, the input value of W is a natural number greater than 0, and the unit is meter; the sea erosion platform inclination angle a refers to the average angle of inclination of the sea erosion platform to the sea, the input value of a is a natural number between 0 and 90, and the unit is degree.

[0012] The finite element integral calculation method for the attenuation of wave height propagation nearshore by the sea erosion platform as described above, further, the grid is divided into stepped units, wherein the horizontal width d is a natural number greater than 0, in meters, and the total number of cells n is calculated as follows:

[0013] n=W / d.

[0014] The finite element integral calculation method for the attenuation of wave height propagation near the shore by the sea erosion platform as described above, further, the wave height H at the seaward edge of the grid iIt refers to the wave height at the seaward boundary of the i-th cell. The grid number i is a natural integer between 1 and n. When i=1, H i =H1, H1 is the initial wave height of the seaward boundary of the sea erosion platform, in meters, and the input value should be a natural number greater than 0.

[0015] The finite element integral calculation method for the attenuation of wave height propagation near the shore by the sea erosion platform as described above, further, the wave height H reaching the shore boundary of the grid j It means that in the ith cell, the seaward wave height H i After propagating the grid width d, the wave height reaching the shoreward boundary is calculated as:

[0016]

[0017] Where, the attenuation parameter α i and β i The calculation formulas are:

[0018] a i =exp[-0.016(h i / H i ) 4 ]

[0019] β i =0.03exp[-0.7(h i / H i )]

[0020] Where h i is the water depth of the i-th cell, and its calculation formula is:

[0021] h i =[(w-(i-1)d]tan a.

[0022] The finite element integral calculation method for the attenuation of wave height of nearshore propagation by the sea erosion platform as described above, further, the iterative calculation process includes the following steps: j is used as the wave height input value at the seaward edge of the i+1th cell, that is, H i+1 =H j .

[0023] The finite element integral calculation method for the attenuation of wave height propagation near the shore by the sea erosion platform as described above, further, the iteration stopping condition is that the wave height H at the seaward edge of the grid of the nth grid is calculated. i , that is, H i =H n Stop when

[0024] The finite element integral calculation method for the attenuation of wave height propagation near the shore by the sea erosion platform is as follows: c It refers to the wave height H calculated towards the shore boundary when i=n. j At the end of the cycle, H j =H c .

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] (1) Compared with the traditional process-based numerical calculation technology, which requires accurate seabed topography and wave field characteristics, the present invention only requires three environmental parameters as input parameters: the initial wave height at the outermost end of the sea erosion platform, the width of the sea erosion platform, and the inclination angle, which greatly reduces the requirement for the number of environmental parameters in the simulation process.

[0027] (2) The present invention designs an adjustable number of computing units and determines the size of the segmented grid according to actual application requirements. Compared with traditional technologies that consume a large amount of computing resources, the efficiency of the calculation is greatly improved.

[0028] (3) The present invention utilizes the finite element integration algorithm to transform the empirical formula originally applicable only to horizontal sea erosion platforms into a parametric empirical formula that is applicable to both inclined and horizontal sea erosion platforms by integrating the intensity of wave attenuation of each horizontal cell to obtain the wave height that ultimately reaches the coast.

[0029] (4) Because the present invention requires fewer boundary parameters, it can be applied to the simulation of bedrock coastal landform evolution over long geological periods, even when limited information is available on environmental parameters at various stages. Furthermore, because it can balance computational accuracy and speed by adjusting the computational unit grid size, it is highly suitable for high-speed simulations of dynamic coastal erosion assessments of large groups of offshore islands. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0031] Figure 1 This is a flow chart of a finite element integral calculation method for wave height attenuation of nearshore propagation of waves on a sea erosion platform according to the present invention;

[0032] Figure 2 A schematic diagram of a geometric model of a finite element integral calculation method for measuring the attenuation of wave height of nearshore propagation of waves on a sea erosion platform according to the present invention;

[0033] Figure 3 Schematic diagram of interpretation results of sea erosion platform terrain parameters in an embodiment of the present invention;

[0034] Figure 4 . Schematic diagram comparing the wave height simulation calculation results and actual observation data in an embodiment of the present invention. DETAILED DESCRIPTION

[0035] The following will be combined with the accompanying drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0036] Example:

[0037] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof in the embodiments of the present invention are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0038] In the description of the present invention, "plurality" means at least two, such as two or three, unless otherwise specifically defined. Furthermore, unless otherwise specified or defined, the terms "mounted," "connected," and "connected" should be understood broadly, meaning, for example, fixed, removable, or integral; mechanical or electrical; direct or indirect through an intermediary; and internal communication between two components. Those skilled in the art will understand the specific meanings of these terms in the present invention based on the specific circumstances.

[0039] The word “exemplary” is used hereinafter to mean “serving as an example, example, or illustration.” Any embodiment described as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments.

[0040] See also Figure 1 The present invention proposes a finite element integral calculation method for wave height attenuation of nearshore wave propagation by a sea erosion platform, which can specifically include the following steps:

[0041] Step 1: Perform geomorphic interpretation on the sea erosion platform and record the positions of the seaward boundary and the shoreward boundary of the sea erosion platform to obtain the width W and inclination angle a of the sea erosion platform.

[0042] Corresponding to Figure 1 S1: input the width W of the sea erosion platform and S2: input the inclination angle a of the sea erosion platform.

[0043] Specifically, in step S1, the width W of the sea erosion platform refers to the horizontal distance between the seaward boundary and the shoreward boundary of the sea erosion platform. The input value of W should be a natural number greater than 0, in meters (m), and can be rounded to an integer natural number to improve calculation efficiency.

[0044] In step S2, the inclination angle a of the sea erosion platform refers to the average angle of inclination of the sea erosion platform toward the sea, in degrees (°). The input value of a should be a natural number between 0 and 90. In actual coastal landform applications, the maximum value of a generally does not exceed 30.

[0045] Step 2: Perform finite element mesh division on the sea erosion platform to form n grids with a horizontal width of d.

[0046] Corresponding to Figure 1 S3: Divide the marine erosion platform into n horizontal stepped units according to the finite element integration grid size d.

[0047] Specifically, in step S3, the finite element integration grid size d is the horizontal width of the divided step unit, and the input value of d should be a natural number greater than 0, in meters (m). The smaller the value of d, the slower the calculation rate, but the higher the accuracy of the calculation result, and vice versa. In practical applications, it is recommended to use a value between 0 and 2 to balance the relationship between accuracy and computational efficiency. The calculation formula for the total number of cells n is:

[0048] n=W / d(1)

[0049] Step 3: Calculate the wave height H at the seaward edge of the grid i , the horizontal width of the grid is d, the attenuation parameter α i and β i Iteratively calculate the wave height H reaching the shore boundary of the grid j , set the iteration stop condition, when the iteration stop condition is reached, move the grid to the wave height H on the shore boundary j The wave height H that finally reaches the coast after attenuation c .

[0050] Corresponding to Figure 1 S4: Input the wave height H at the seaward edge of the grid i and S5: Calculate the wave height H reaching the shore boundary of the gridj And S6: loop and use the calculation results of S5 as the input value of S4 until the nth grid and S7: obtain the wave height H that finally reaches the coast after attenuation c .

[0051] Specifically, in step S4, the wave height H at the seaward edge of the input grid is i Refers to the wave height at the seaward boundary of the i-th cell. The grid number i is a natural integer between 1 and n. When i=1, H i =H1, H1 is the initial wave height of the seaward boundary of the sea erosion platform, in meters (m). The input value should be a natural number greater than 0. In actual wave height application, the maximum value of H1 generally does not exceed 20.

[0052] In step S5, the wave height H reaching the shore boundary of the grid is j In the ith cell, the seaward wave height H i After propagating the grid width d, the wave height reaching the shoreward boundary is calculated as:

[0053]

[0054] Where, the attenuation parameter α i and β i The calculation formulas are:

[0055] a i =exp[-0.016(h i / H i ) 4 ] (3)

[0056] β i =0.03exp[-0.7(h i / H i )] (4)

[0057] Where h i is the water depth of the i-th cell, and its calculation formula is:

[0058] h i =[(w-(i-1)d]tan a (5)

[0059] In step S6, the calculation result of S5 is used as the input value of S4, which means that the result H obtained by calculating the i-th cell is j is used as the wave height input value at the seaward edge of the i+1th cell, that is, H i+1 =H j The cycle is in H i =H n Stop when

[0060] In step S7, the wave height H that finally reaches the coast after attenuation is c It refers to the wave height H calculated towards the shore boundary when i=n. j , that is, when the S6 calculation cycle ends, H j =H c .

[0061] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings and actual data in the embodiments of the present invention.

[0062] This embodiment selects a typical sea erosion platform developed on a bedrock coast and provides a finite element integration method for measuring the attenuation of wave height due to nearshore wave propagation on the sea erosion platform. The method includes eight steps, S1 to S7:

[0063] In step S1, Figure 3 As shown in the figure, first, it is necessary to use ArcGIS or other coastal topography interpretation software to interpret the sea erosion platform, mark the positions of the seaward and shoreward boundaries of the sea erosion platform, and then measure the horizontal distance between the two boundaries as the input value of the sea erosion platform width W. Figure 3 In the figure, the width of the sea erosion platform is W = 115 meters.

[0064] In step S2, Figure 3 As shown in Figure 1, it is necessary to continue to use coastal topography and geomorphology interpretation software to measure the average angle of the sea erosion platform tilted to the sea as the input value of the sea erosion platform tilt angle a. Figure 3 In the figure, the angle of the sea erosion platform is a = 1.8°.

[0065] In step S3, the finite element integration grid size d is set to 0.5 m, and the total number of cells n = 115 / 0.5 = 230 is calculated based on formula (1).

[0066] In step S4, the initial wave height H1 at the seaward boundary of the erosion platform is first obtained using ocean wave observation equipment or the ERA global ocean reanalysis data model. Figure 4 In the example, the initial wave height H1 at the seaward boundary of the erosion platform is 1 m. The input value of H1 is then used as the wave height Hi at the seaward edge of the first cell to start the subsequent calculations.

[0067] In step S5, the water depth of the i-th cell is first obtained using formula (4). In the initial calculation, i = 1, so the water depth of the first cell h1 = [(115-(1-1)*0.5)*tan(1.5°) = 3.01m; h i Substitute the value of into formula (3) and (4) to obtain the attenuation parameter α of the i-th cell i and β i, i=1 in the initial calculation, so the decay parameter α of the first cell is i =exp[-0.016*(3.01 / 1)^4]=0.27; attenuation parameter β i =0.03exp[-0.7*(3.01 / 1)]=3.65*10^-3; then α i and β i Substitute the calculated value into formula (2) to obtain the wave height H at the shore boundary of the i-th cell j , i=1 in the initial calculation, so the wave height H at the shore boundary of the first cell is j =1*0.27*(e ((-3.65*10^-3)*0.5) -1)+1=0.9995m.

[0068] In step S6, the calculation result H of S5 is looped j As the input value H of S4 i+1 , in the initial calculation, i=1, the wave height input value at the seaward edge of the second cell is equal to the wave height at the shoreward edge of the first cell, that is, H2=0.9995m. Figure 4 As shown, until the 230th cell, the S6 loop ends.

[0069] In step S7, Figure 4 As shown, at the 230th cell, H j = 0.5058m, so the wave height H that finally reaches the coast after attenuation on the 115m sea erosion platform c =0.5058m;

[0070] from Figure 4 It can be seen from the figure that the root mean square error between the numerical simulation results of this embodiment and the actual field observation data at 12 different locations of the sea erosion platform is only 0.05m.

[0071] In the description of this specification, the reference terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0072] The above embodiments are intended only to illustrate the technical concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. They are not intended to limit the scope of protection of the present invention. Any equivalent changes or modifications made based on the essence of the present invention are intended to be covered by the scope of protection of the present invention.

Claims

1. A finite element integral calculation method for wave height attenuation of nearshore wave propagation caused by a sea erosion platform, characterized in that: The steps include: Performing geomorphic interpretation on the sea erosion platform and recording the positions of the seaward boundary and the shoreward boundary of the sea erosion platform to obtain the width W and the inclination angle a of the sea erosion platform; Performing finite element mesh division on the sea erosion platform to form n grids with a horizontal width of d; According to the wave height H at the seaward edge of the grid i , the horizontal width of the grid is d, the attenuation parameter α i and β i Iteratively calculate the wave height H reaching the shore boundary of the grid j , set the iteration stop condition, when the iteration stop condition is reached, move the grid to the wave height H on the shore boundary j The wave height H that finally reaches the coast after attenuation c ; The wave height H reaching the shore boundary of the grid j It means that in the ith cell, the seaward wave height H i After propagating the grid width d, the wave height reaching the shoreward boundary is calculated as: Where, the attenuation parameter α i and β i The calculation formulas are: a i =exp[-0.016(h i / h i ) 4 ] b i =0.03exp[-0.7(h i / H i )] Where h i is the water depth of the i-th cell, and its calculation formula is: h i =[(w-(i-1)d]tana。 2. The finite element integral calculation method for wave height attenuation of nearshore wave propagation by a sea erosion platform according to claim 1 is characterized in that: The width W of the sea erosion platform refers to the horizontal distance between the seaward boundary and the shoreward boundary of the sea erosion platform. The input value of W is a natural number greater than 0, and the unit is meter. The inclination angle a of the sea erosion platform refers to the average angle at which the sea erosion platform is inclined toward the sea. The input value of a is a natural number between 0 and 90, and the unit is degree.

3. The finite element integral calculation method for wave height attenuation of nearshore wave propagation by a sea erosion platform according to claim 1 is characterized in that: The grid is divided into stepped units, where the horizontal width d is a natural number greater than 0 and the unit is meter. The total number of cells n is calculated as follows: n=W / d.

4. The finite element integral calculation method for wave height attenuation of nearshore wave propagation by a sea erosion platform according to claim 1 is characterized in that: The wave height H at the seaward edge of the grid i It refers to the wave height at the seaward boundary of the i-th cell. The grid number i is a natural integer between 1 and n. When i=1, H i =H1, H1 is the initial wave height of the seaward boundary of the sea erosion platform, in meters, and the input value should be a natural number greater than 0.

5. The finite element integral calculation method for wave height attenuation of nearshore wave propagation by a sea erosion platform according to claim 1 is characterized in that: The iterative calculation process includes: calculating the result H obtained by the calculation of the i-th cell j is used as the wave height input value at the seaward edge of the i+1th cell, that is, H i+1 =H j .

6. The finite element integral calculation method for wave height attenuation of nearshore wave propagation by a sea erosion platform according to claim 1 is characterized in that: The iteration stop condition is that the wave height H at the seaward edge of the grid of the nth grid is calculated. i , that is, H i =H n Stop when 7. The finite element integral calculation method for wave height attenuation of nearshore wave propagation by a sea erosion platform according to claim 1 is characterized in that: The wave height H that finally reaches the coast after attenuation c It refers to the wave height H calculated towards the shore boundary when i=n. j , at the end of the cycle H j =H c .

Images