Homotopy-bem analysis method and device for hydrodynamic characteristics of marine structures

Abstract

The application relates to the technical field of ocean engineering, and discloses a homotopy-boundary element analysis method and device for hydrodynamic characteristics of a marine structure, which converts a nonlinear equation set into a series of linear sub-problems for solving by adopting a homotopy analysis method, and obtains a high-precision numerical solution of the original nonlinear problem by superposition of linear solutions of various orders; by setting a proper energy dissipation coefficient, energy loss caused by fluid viscosity, flow separation and the like can be effectively evaluated, and the influence of wave height on energy loss is directly considered. Compared with a traditional boundary element method of direct iteration, the homotopy-boundary element analysis method is more convenient and has higher calculation precision. In addition, by introducing a hyper-singular boundary integral equation, degenerate boundaries caused by a dissipation surface are effectively processed, and the problem that a general calculation program cannot be programmed due to fluid partition in a traditional boundary element model is avoided. The homotopy-boundary element analysis method can solve the problem that a classical non-dissipation potential flow numerical model cannot consider wave energy dissipation and the calculation result is distorted.

Description

Technical Field

[0001] This application relates to the field of marine engineering technology, and for example to a homotopy-boundary element analysis method and apparatus for the hydrodynamic properties of marine structures. Background Technology

[0002] Large marine structures are expensive to construct and subjected to complex and severe wave loads over long periods. Failure or damage can result in enormous losses. The interaction mechanism between waves and marine structures is highly complex, and scientifically determining the wave load and dynamic response of structures is a fundamental core issue in the safe design of marine engineering projects. Classical potential flow theory is highly efficient and is the primary method for analyzing wave interactions with marine structures. However, for wave interactions with marine structures involving significant wave energy loss, such as large-amplitude wave resonance between adjacent multi-buoy structures or violent wave motion within a platform moon pool, classical potential flow theory, while efficient, suffers from inaccurate results due to its inability to account for energy loss. Numerical simulations based on viscous fluid dynamics can provide reasonable calculation results, but their computational efficiency is low and insufficient for design analysis needs. Therefore, there is an urgent need to develop a potential flow theory-based hydrodynamic analysis method that can effectively assess wave energy dissipation and provide reasonable calculation results, while maintaining the computational efficiency advantage of classical potential flow theory.

[0003] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0004] To provide a basic understanding of some aspects of the disclosed embodiments, a brief summary is given below. This summary is not intended as a general commentary, nor is it intended to identify key / important components or describe the scope of protection of these embodiments, but rather as a prelude to the detailed description that follows.

[0005] This disclosure provides a homotopy-boundary element analysis method and apparatus for the hydrodynamic characteristics of marine structures, thereby improving the solution accuracy of hydrodynamic problems of marine structures.

[0006] In some embodiments, the homotopy-boundary element analysis method for the hydrodynamic characteristics of the marine structure includes: representing fluid motion using total velocity potential; setting boundary conditions and energy dissipation surfaces on the structure surface; applying nonlinear pressure loss conditions to the energy dissipation surfaces; representing the normal derivative of the scattering potential and the boundary conditions of the energy dissipation surfaces using scattering potential; merging the boundary conditions of the energy dissipation surfaces into conventional boundary integral equations and hypersingular boundary integral equations; dividing the structure into multiple grids; discretizing the merged conventional boundary integral equations and hypersingular boundary integral equations; and obtaining a set of equations using the normal derivative of the scattering potential; defining linear and nonlinear operators using the frequency domain motion response equation of the structure and the total wave force equation, and using the set of equations; establishing a homotopy relation for the hydrodynamic characteristics of the structure using the linear and nonlinear operators; solving for the velocity potential of the structure surface and the normal derivative of the velocity potential of the dissipation surfaces using the homotopy relation; and calculating the total wave force and motion response of the structure based on the velocity potential of the structure surface and the normal derivative of the velocity potential of the dissipation surfaces, combined with the frequency domain motion response equation of the structure and the total wave force equation.

[0007] In some embodiments, the homotopy-boundary element analysis device for the hydrodynamic characteristics of the marine structure includes: a velocity potential and energy dissipation setting module, configured to represent fluid motion using a total velocity potential, set boundary conditions and an energy dissipation surface on the structure surface, and apply a nonlinear pressure loss condition to the energy dissipation surface; representing the normal derivative of the scattering potential and the boundary conditions of the energy dissipation surface using a scattering potential; a boundary integration module, configured to merge the boundary conditions of the energy dissipation surface into a conventional boundary integration equation and a hypersingular boundary integration equation; and an equation derivation module, configured to divide the structure into multiple meshes, discretize the merged conventional boundary integration equation and the hypersingular boundary integration equation, and... Using the normal derivative of the scattering potential, a set of equations is obtained. The homotopy relation establishment module is configured to define linear and nonlinear operators using the frequency domain motion response equation and the total wave force equation of the structure, as well as the set of equations. The linear and nonlinear operators are used to establish the homotopy relation of the hydrodynamic characteristics of the structure, and the normal derivative of the velocity potential of the structure surface and the velocity potential of the dissipation surface is solved through the homotopy relation. The total wave force and motion response calculation module is configured to calculate the total wave force and motion response of the structure based on the velocity potential of the structure surface and the normal derivative of the velocity potential of the dissipation surface, combined with the frequency domain motion response equation and the total wave force equation of the structure.

[0008] The homotopy-boundary element analysis method and apparatus for the hydrodynamic properties of marine structures provided in this disclosure can achieve the following technical effects: Homotopy analysis is employed to transform the nonlinear equations into a series of linear subproblems for solution. A high-precision numerical solution to the original nonlinear problem is obtained by superimposing the linear solutions of each order. By setting an appropriate energy dissipation coefficient, energy losses caused by fluid viscosity and flow separation can be effectively assessed, and the influence of wave height on energy loss is directly considered. Compared with the traditional boundary element method using direct iteration, the homotopy-boundary element analysis method is simpler and has higher computational accuracy. Furthermore, by introducing a hypersingular boundary integral equation, this method effectively handles the degenerate boundary caused by dissipative surfaces, avoiding the problem of traditional boundary element models being unable to write general-purpose computational programs due to fluid partitioning. This invention solves the problem that classical dissipationless potential flow numerical models cannot consider wave energy dissipation and result in distorted calculations, providing an analytical tool for the reasonable and efficient prediction of the hydrodynamic characteristics of marine structures.

[0009] The above general description and the description below are exemplary and illustrative only and are not intended to limit this application. Attached Figure Description

[0010] One or more embodiments are illustrated by way of example with reference to the accompanying drawings. These illustrations and drawings do not constitute a limitation on the embodiments. Elements having the same reference numerals in the drawings are shown as similar elements. The drawings are not to be scaled. And wherein: Figure 1 This is a schematic diagram of the homotopy-boundary element analysis method for the hydrodynamic properties of marine structures provided in this embodiment of the disclosure; Figure 2 This is a schematic diagram of the motion response problem of two floating square boxes on the water surface under wave action provided in the embodiments of this disclosure; Figure 3 This is a schematic diagram comparing the homotopy-boundary element calculation results (line) and experimental results (point) of dimensionless wave height within a narrow slit of a double rectangular box when the wave incident angle is 0°, provided by an embodiment of this disclosure. Figure 4 This is a schematic diagram comparing the homotopy-boundary element calculation results (line) and experimental results (point) of dimensionless wave height within a narrow slit of a double rectangular box when the wave incident angle is 60°, provided by an embodiment of this disclosure. Figure 5 This is a schematic diagram comparing the homotopy-boundary element calculation results (line) and experimental results (point) of dimensionless wave height in a circular moon pool with object constraints provided in this embodiment of the disclosure; Figure 6 This is a schematic diagram comparing the homotopy-boundary element calculation results (line) and experimental results (point) of dimensionless wave height in a lunar pool with inlet constraints provided in this embodiment of the disclosure; Figure 7 This is a schematic diagram of a homotopy-boundary element analysis device for hydrodynamic properties of marine structures provided in an embodiment of this disclosure.

[0011] Figure label: 70. Homotopy-boundary element analysis device for hydrodynamic characteristics of marine structures; 71. Velocity potential and energy dissipation setting module; 72. Boundary integration module; 73. Equation derivation module; 74. Homotopy relation establishment module; 75. Total wave force and motion response calculation module. Detailed Implementation

[0012] To provide a more detailed understanding of the features and technical content of the embodiments of this disclosure, the implementation of the embodiments of this disclosure will be described in detail below with reference to the accompanying drawings. The accompanying drawings are for illustrative purposes only and are not intended to limit the embodiments of this disclosure. In the following technical description, for ease of explanation, several details are used to provide a full understanding of the disclosed embodiments. However, one or more embodiments may still be implemented without these details. In other cases, well-known structures and devices may be simplified in their depiction to simplify the drawings.

[0013] The terms "first," "second," etc., used in the specification, claims, and accompanying drawings of this disclosure are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for the embodiments of this disclosure described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion.

[0014] Unless otherwise stated, the term "multiple" means two or more.

[0015] In this embodiment of the disclosure, the character " / " indicates that the objects before and after it are in an "or" relationship. For example, A / B means: A or B.

[0016] The term "and / or" describes an association between objects, indicating that three relationships can exist. For example, A and / or B means: A or B, or A and B.

[0017] The term "correspondence" can refer to an association or binding relationship. The correspondence between A and B means that there is an association or binding relationship between A and B.

[0018] Combination Figure 1 As shown, this disclosure provides a homotopy-boundary element analysis method for the hydrodynamic properties of marine structures, including: S10 uses the total velocity potential to represent fluid motion, sets boundary conditions on the structure surface and an energy dissipation surface, and applies a nonlinear pressure loss condition to the energy dissipation surface; the boundary conditions of the energy dissipation surface are represented using the scattering potential, the normal derivative of the scattering potential, and the normal derivative of the total velocity potential. Specifically, it includes: S11, taking the motion response problem of two floating square boxes on the water surface under wave action as an example, such as Figure 2 As shown, a three-dimensional Cartesian coordinate system is used to describe this physical problem. oxy The plane coincides with the still water surface. z The axis is considered positive when it is vertically upward.

[0019] Assuming the fluid is inviscid and incompressible, and its motion is irrotational, then a total velocity potential can be used. This describes the motion of the fluid. For the problem of structural motion response, the total velocity potential can be further expressed as the superposition of the incident potential, diffracted potential, and radiated potential: (1) In the formula, This represents the velocity potential of the incident wave; This represents the velocity potential of the diffracted wave; ; ω It is the angular frequency of wave motion; ( j = 1 ~ 6) indicates that the structure is in the 6th... j The radiation wave velocity potential that oscillates with unit amplitude in one degree of freedom; ξ j It is the displacement of the structure.

[0020] The velocity potential of the fluid motion satisfies the Laplace equation, the linearized free surface boundary condition, the impermeable seabed boundary condition, and the far-field radiation boundary condition.

[0021] S12, the velocity potential satisfies the following boundary conditions on the surface of the structure: (2) (3) In the formula, S B Represents the surface of a structure; n 1, n 2, n 3) Represents the unit normal vector of the structure's surface, pointing into the fluid region; ;( x c , y c , z c () are the coordinates of the rotation center of the structure; Represents the normal derivative.

[0022] S13, to account for energy dissipation, an artificial energy dissipation surface (such as...) is set at the narrow slit entrance between the two floating square boxes. Figure 1 As shown), and apply a nonlinear pressure loss condition to the dissipation surface, including: The velocity potential difference across the dissipative surface is linearly related to the square of the normal fluid velocity through the dissipative surface. (4) The normal fluid velocity potential through the dissipative surface is continuous: (5) In the formula, and Represents the velocity potential on both sides of the dissipation surface; ζ It is the artificial energy dissipation coefficient; S D Indicates the energy dissipation surface; subscript n This indicates the calculation of the normal derivative.

[0023] S14, let the scattering potential The normal derivative of the scattering potential can be obtained from equations (2) and (3). : (6) In the formula, ξ is the displacement vector of the structure; n is the generalized normal vector of the structure's surface. Using the scattering potential and its normal derivative, equations (4) and (5) can be further expressed as: (7) (8) This leads to the boundary conditions at the dissipative surface.

[0024] In this way, by representing the normal derivative of the total velocity potential, the scattering potential and its normal derivative, setting the energy dissipation surface, applying nonlinear pressure condition loss to the energy dissipation surface, and setting the surface boundary conditions of the structure and the boundary conditions of the energy dissipation surface, the necessary parameter conditions are preset for homotopy-boundary element analysis.

[0025] S20 integrates the boundary conditions of the energy dissipation surface into the boundary integral equations, including: conventional boundary integral equations and hypersingular boundary integral equations. Specifically, it includes: S21, the boundary element method is used to solve the motion response problem of two floating square boxes on the water surface under wave action. The boundary conditions (7) and (8) at the dissipative surface are combined into the boundary integral equation, which includes: the conventional boundary integral equation and the hypersingular boundary integral equation. We can obtain: The merged conventional boundary integral equations: (9) The merged hypersingular boundary integral equations: (10) In the formula, P Indicates the source point; Q Indicates the field point;G ( P , Q ) is a complex Green's function that satisfies the governing equations, linearized free surface boundary conditions, impermeable bottom boundary conditions, and far-field radiation boundary conditions.

[0026] In this way, by introducing the supersingular boundary integral equation, S20 effectively handles the degenerate boundary caused by the dissipative surface, avoiding the problem that the boundary element model based on the conventional boundary integral equation cannot be programmed with a general-purpose calculation program due to fluid partitioning.

[0027] S30, the structure is divided into multiple grids, the combined conventional boundary integral equations and hypersingular boundary integral equations are discretized, and the normal derivative of the scattering potential in equation (6) is used to obtain the system of equations. Specifically, it includes: S31, dividing the surface of the structure into M One grid divides the dissipation surface into M 2 grids, let M = M 1+ M 2.

[0028] S32, using the constant element method to discretize the boundary integral equations (9) and (10), and using the expression for the normal derivative of the scattering potential (6), the following set of equations can be obtained: (11) In the formula, H and T are matrices about the integral of the Green's function; w and ψ are vectors about the normal derivative of the incident potential; Y is a matrix about the normal vector of the structure surface; U, W and The elements are: (12) (13) (14) In the formula, δ ij = 0 ( i ≠ j ); δ ij = 1 ( i = j ); S,i Indicates the first i The scattering potential at the center of each unit (unknown); Indicates the first i The normal derivative of the total velocity potential at the center of each unit is unknown. The normal derivative of the velocity potential of the structure's surface and the velocity potential of the dissipative surface is represented.

[0029] S40 utilizes the frequency domain motion response equation of the structure and the total wave force equation, as well as the equation set, to define linear and nonlinear operators. Using the linear and nonlinear operators, the homotopy relation of the hydrodynamic characteristics of the structure is established, and the velocity potential of the structure surface and the normal derivative of the velocity potential of the dissipative surface are solved through the homotopy relation.

[0030] Equation (11) contains M +6 unknowns, but only M There are several equations, so it is necessary to solve them together with the kinematic response equations of the structure.

[0031] The frequency domain motion response equation of a structure under wave action is: (15) In the formula, M is the mass matrix of the structure; B is the external damping coefficient matrix; C is the restoring force coefficient matrix; ξ is the displacement vector of the structure (unknown); and F is the total wave force (the sum of excitation force and radiation force).

[0032] Integrating the dynamic water pressure along the surface of the structure yields the total wave force acting on the structure. The equation for the total wave force is: (16) In the formula, ρ is the fluid density; n is the generalized normal vector of the structure's surface; is the generalized normal vector of the computational boundary; S is the area vector of the computational boundary element; the superscript T indicates transpose; F0 is the wave force vector caused by the incident wave.

[0033] If the nonlinear equation system formed by combining equations (11) and (15) can be solved by a two-step iterative numerical method, the calculation process is cumbersome, the number of iterations is large, and the calculation convergence is very slow.

[0034] Therefore, homotopy analysis is used to solve this nonlinear equation system, establishing a homotopy-boundary element numerical analysis method for the hydrodynamic characteristics of marine structures. Specifically, this includes: S41, Substituting the frequency domain motion response equation (15) and the total wave force equation (16) into equation (11), we can obtain: (17) In the formula, ; ; .

[0035] S42, Define linear operators L and nonlinear operators N : (18) (19) In the formula, It is an unknown vector; H, W, X, T, w, Z and ψ are defined in the same way as in equation (17); V and The elements are (20) (twenty one) S43, based on equations (18) and (19), the following homotopy relation is established. (twenty two) In the formula, It is an embedded variable; [0] This is the initial guess value, set to L ( The solution is 0.

[0036] For different embedding variables q The solutions to equation (22) are not the same, that is, the unknown vector sum matrix All with embedded variables q Therefore, equation (22) can be further expressed as follows: (twenty three) when q When = 0, equation (23) degenerates into Then there is (0) = [0] ;when q When = 1, equation (23) degenerates into N [ If (1)] = 0, then we have (1) = In other words, with the embedding variable q As the value gradually increases from 0 to 1, the solution of equation (22) ( q From the initial guess value [0] Transformation to the exact solution of equation (17) .

[0037] S43, ( q Regarding embedded variables q Performing a Taylor series expansion, we obtain (twenty four) S44, Definition Equation (24) can be further expressed as: (25) S45, in formula (25) q = 1, so we can get the solution to equation (17): (26) As can be seen from equation (26), the solution of the nonlinear equation system (17) It was transformed into an initial guess solution. [0] and solutions of each order [m] Linear superposition.

[0038] S46, for calculation [m] Regarding equation (23) with respect to embedded variables q beg m The first derivative is calculated and divided by the first derivative on both sides of the equation. m !, then let q = 0, we can get: (27) In the formula, s 1 = 0; s m = 1 ( m ≥ 2); (28) (29) (30) In the deformation equation (27), the left side of the equation is about [m] A linear expression, where the right side of the equals sign is about ( [0] , [1] , … , [m-1] The expression for (27) is given. Obviously, equation (27) is a system of linear equations, which can be solved by Gaussian elimination. Therefore, based on the above homotopy analysis process, the original nonlinear system of equations (17) is transformed into a linear superposition of solutions to a series of linear equations, which effectively simplifies the numerical solution process.

[0039] S47, by solving equation (27) using Gaussian elimination, we obtain solutions of each order. [m] .Will [m] and the initial guess solution [0] Substituting into equation (26), we can then solve for... .

[0040] S50, based on the velocity potential of the structure's surface and the normal derivative of the velocity potential of the dissipative surface, and combined with the frequency domain motion response equation of the structure and the total wave force equation, the total wave force and motion response of the structure are calculated.

[0041] S51, when the solution of equation (17) is obtained through homotopy analysis. Then, Substituting into equation (16), the total wave force F acting on the structure is calculated.

[0042] S52, substitute F into equation (15) to calculate the motion response of the structure, and thus obtain the numerical solution of the motion response problem of marine structures under nonlinear dissipative boundary conditions.

[0043] Thus, obtained using homotopy analysis The total wave force and motion response of the structure can be obtained.

[0044] In summary, the homotopy-boundary element analysis method for the hydrodynamic characteristics of marine structures provided in this disclosure transforms the nonlinear equations into a series of linear subproblems for solution using homotopy analysis. A high-precision numerical solution to the original nonlinear problem is obtained by superimposing the linear solutions of each order. By setting an appropriate energy dissipation coefficient, energy losses caused by fluid viscosity and flow separation can be effectively assessed, and the influence of wave height on energy loss is directly considered. Compared with the traditional boundary element method using direct iteration, the homotopy-boundary element analysis method is simpler and has higher computational accuracy. Furthermore, by introducing a hypersingular boundary integral equation, this method effectively handles the degenerate boundary caused by the dissipative surface, avoiding the problem that traditional boundary element models cannot be programmed with general-purpose calculations due to fluid partitioning. This invention solves the problem that classical non-dissipative potential flow numerical models cannot consider wave energy dissipation and result in distorted calculations, providing an analytical tool for the reasonable and efficient prediction of the hydrodynamic characteristics of marine structures.

[0045] High-precision verification analysis: To fully verify the performance of the analytical method proposed in this application, the homotopy-boundary element analysis method proposed in this invention was used to solve various hydrodynamic problems, such as narrow-slit fluid resonance between multi-body structures and wave resonance in a platform moonpool. Figures 3 to 6 The homotopy-boundary element method (HEM) calculation results for dimensionless wave height within the narrow slit of the double rectangular box and the lunar pool of the platform are compared with the model test results. As can be seen from the figures, the numerical calculation results of this method agree well with the model test results, verifying the effectiveness of the proposed method.

[0046] Combination Figure 7As shown, this disclosure provides a homotopy-boundary element analysis device 70 for the hydrodynamic characteristics of marine structures, including: a velocity potential and energy dissipation setting module 71, a boundary integration module 72, an equation derivation module 73, a homotopy relation establishment module 74, and a total wave force and motion response calculation module 75. The velocity potential and energy dissipation setting module 71 is configured to represent fluid motion using the total velocity potential, set boundary conditions on the structure surface and an energy dissipation surface, and apply nonlinear pressure loss conditions to the energy dissipation surface; it uses the scattering potential to represent the normal derivative of the scattering potential and the boundary conditions of the energy dissipation surface. The boundary integration module 72 is configured to merge the boundary conditions of the energy dissipation surface into conventional boundary integration equations and hypersingular boundary integration equations; the equation derivation module 73 is configured to divide the structure into multiple meshes, discretize the merged conventional boundary integration equations and hypersingular boundary integration equations, and use the normal derivative of the scattering potential to obtain the equation set. The homotopy relation establishment module 74 is configured to establish the homotopy relation of the hydrodynamic characteristics of the structure using the frequency domain motion response equation and the total wave force equation of the structure, as well as the equation set, defining linear and nonlinear operators. The homotopy relation is then used to solve for the velocity potential of the structure's surface and the normal derivative of the velocity potential of the dissipative surface. The total wave force and motion response calculation module 75 is configured to calculate the total wave force and motion response of the structure based on the velocity potential of the structure's surface and the normal derivative of the velocity potential of the dissipative surface, combined with the frequency domain motion response equation and the total wave force equation of the structure.

[0047] The specific implementation process of the device can be found in the description of the above method embodiments, and will not be repeated here.

[0048] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0049] While the specific embodiments of the present invention have been described above, they are not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A homotopy-boundary element analysis method for the hydrodynamic properties of marine structures, characterized in that, include: Fluid motion is represented by total velocity potential. Boundary conditions and energy dissipation surfaces are set on the surface of the structure. Nonlinear pressure loss conditions are applied to the energy dissipation surfaces. The boundary conditions of the energy dissipation surface are expressed using the scattering potential, the normal derivative of the scattering potential, and the normal derivative of the total velocity potential. The boundary conditions of the energy dissipation surface are combined into the conventional boundary integral equation and the hypersingular boundary integral equation. The structure is divided into multiple grids, and the combined conventional boundary integral equations and hypersingular boundary integral equations are discretized and merged. The normal derivative of the scattering potential is used to obtain the system of equations. Using the frequency domain motion response equation of the structure and the total wave force equation, as well as the equation set, linear and nonlinear operators are defined. The homotopy relation of the hydrodynamic characteristics of the structure is established using the linear and nonlinear operators. The velocity potential of the structure surface and the normal derivative of the velocity potential of the dissipative surface are solved through the homotopy relation. Based on the velocity potential of the structure's surface and the normal derivative of the velocity potential of the dissipative surface, and combined with the structure's frequency domain motion response equation and the total wave force equation, the total wave force and motion response of the structure are calculated.

2. The homotopy-boundary element analysis method for the hydrodynamic properties of marine structures according to claim 1, characterized in that, The structure is divided into multiple grids, and the combined conventional boundary integral equations and hypersingular boundary integral equations are discretized and merged. Using the normal derivative of the scattering potential, a system of equations is obtained, including: The surface of the structure is divided into M1 grids, the dissipative surface is divided into M2 grids, and M = M1 + M2 is set. Using the normal derivative of the scattering potential, the following system of equations is obtained: ， In the formula, H and T are matrices about the integral of the Green's function; w and ψ are vectors about the normal derivative of the incident potential; Y is a matrix about the normal vector of the structure surface; U, W and The elements are: ， ， ， In the formula, δ ij = 0 (i ≠ j); δ ij = 1 (i = j); The scattering potential at the center of the i-th unit is unknown; The normal derivative of the total velocity potential at the center of the i-th unit is unknown; ω is the angular frequency of the wave motion. ξ represents the velocity potential of the structure's surface and the normal derivative of the velocity potential of the dissipative surface; ξ is the displacement vector of the structure; S B Represents the surface of the structure; P represents the source point; ζ is the artificial energy dissipation coefficient; S D This represents the energy dissipation surface.

3. The homotopy-boundary element analysis method for the hydrodynamic properties of marine structures according to claim 2, characterized in that, The method of utilizing the frequency domain motion response equation of the structure and the total wave force equation, and defining linear and nonlinear operators using the set of equations, includes: Substituting the frequency domain motion response equation and the total wave force equation into the system of equations, we obtain: ， In the formula, ; ; F0 is the wave force vector caused by the incident wave; ρ is the fluid density. is the generalized normal vector of the calculated boundary; S is the area vector of the calculated boundary element; the superscript T indicates transpose; M is the mass matrix of the structure; B is the external damping coefficient matrix; C is the restoring force coefficient matrix; Define the linear operator L and the nonlinear operator N: ， ， In the formula, ϑ is an unknown vector; V and The elements are: ， 。 4. The homotopy-boundary element analysis method for the hydrodynamic properties of marine structures according to claim 2, characterized in that, The process of establishing the homotopy relation of the hydrodynamic properties of the structure using the linear and nonlinear operators includes: The homotopy relation is expressed as: ， In the formula, It is an embedded variable; This is the initial guess value, set to... The solution; L is a linear operator, N is a nonlinear operator; Will Taylor series expansion of the embedded variable q yields: ； definition After Taylor series expansion Represented as: ； Let q = 1, then we get , Let m be the normal derivative of the velocity potential of the surface of the structure and the velocity potential of the dissipative surface; m is the order of the derivative.

5. The homotopy-boundary element analysis method for the hydrodynamic properties of marine structures according to claim 4, characterized in that, The process of solving the velocity potential of the structure surface and the normal derivative of the velocity potential of the dissipative surface through the homotopy relation includes: Taking the m-th derivative of the homotopy relation with respect to the variable q, and dividing both sides of the equation by m!, then setting q = 0, we get: ， Solving the above equation using Gaussian elimination yields the following result. And then solve for ; In the formula, s1 = 0; s m = 1 (m ≥ 2); ； ； 。 6. The homotopy-boundary element analysis method for the hydrodynamic properties of marine structures according to claim 1, characterized in that, The calculation of the total wave force and motion response of the structure, based on the velocity potential of the structure's surface and the normal derivative of the velocity potential of the dissipative surface, combined with the structure's frequency domain motion response equation and the total wave force equation, includes: Substituting the velocity potential of the structure's surface and the normal derivative of the velocity potential of the dissipation surface into the equation for the total wave force, the total wave force F acting on the structure is calculated. Substituting the total wave force F into the frequency domain motion response equation, the motion response of the structure is calculated. The frequency domain motion response equation is as follows: ， In the formula, M is the mass matrix of the structure; B is the external damping coefficient matrix; C is the restoring force coefficient matrix; ξ is the displacement vector of the structure; and F is the total wave force. The equation for the total wave force is: ， In the formula, ρ is the fluid density; ω is the angular frequency of the wave motion; This represents the velocity potential of the incident wave; The scattering potential of the diffracted wave is represented by ; n is the generalized normal vector of the structure's surface; is the generalized normal vector of the calculated boundary; S is the area vector of the calculated boundary element; the superscript T indicates transpose; F0 is the wave force vector caused by the incident wave; The normal derivatives of the velocity potential of the structure's surface and the velocity potential of the dissipative surface are given.

7. The homotopy-boundary element analysis method for the hydrodynamic properties of marine structures according to claim 1, characterized in that, The method of using total velocity potential to represent fluid motion, setting boundary conditions and energy dissipation surfaces on the structure surface, includes: The total velocity is expressed as the superposition of the incident potential, the diffraction potential, and the radiation potential; The velocity potential satisfies the following boundary conditions on the structure surface: ， ， In the formula, S B (n1, n2, n3) represents the surface of the structure; (n1, n2, n3) represents the unit normal vector of the surface of the structure, pointing into the fluid region. ;(x c , y c , z c () are the coordinates of the rotation center of the structure; Represents the normal derivative; This represents the velocity potential of the diffracted wave; (j = 1 ~ 6) represents the radiation wave velocity potential of the structure when it oscillates with unit amplitude in the j-th degree of freedom; This represents the velocity potential of the incident wave; The structure is a double-floating box structure, and the energy dissipation surface is set at the narrow slit entrance between the two floating boxes.

8. The homotopy-boundary element analysis method for the hydrodynamic properties of marine structures according to claim 1, characterized in that, The nonlinear pressure loss condition includes: The velocity potential difference across the energy dissipation surface is linearly related to the square of the normal fluid velocity passing through the energy dissipation surface. ； And the normal fluid velocity potential through the energy dissipation surface is continuous: ， In the formula, and The velocity potential on both sides of the dissipation surface is represented by ζ; ζ is the artificial energy dissipation coefficient; S D The surface represents the energy dissipation surface; the subscript n indicates the normal derivative; ω is the angular frequency of the wave motion.

9. The homotopy-boundary element analysis method for the hydrodynamic properties of marine structures according to claim 1, characterized in that, The boundary conditions for the energy dissipation surface, expressed using the scattering potential, the normal derivative of the scattering potential, and the normal derivative of the total velocity potential, include: Let the scattering potential Based on the aforementioned nonlinear pressure loss condition, the following is obtained: ， In the formula, ξ is the displacement vector of the structure; This represents the velocity potential of the incident wave; ω represents the velocity potential of the diffracted wave; ω is the angular frequency of the wave motion. (j = 1 ~ 6) represents the radiation wave velocity potential of the structure oscillating with unit amplitude in the j-th degree of freedom; n is the generalized normal vector of the structure's surface; S B Represents the surface of a structure; The nonlinear pressure loss condition can be expressed using the scattering potential and the normal derivative of the scattering potential as follows: ， ， In the formula, and The velocity potential on both sides of the dissipation surface is represented by ζ; ζ is the artificial energy dissipation coefficient; S D The subscript n indicates the energy dissipation surface; the subscript n indicates the normal derivative.

10. A homotopy-boundary element analysis device for hydrodynamic properties of marine structures, characterized in that, include: The velocity potential and energy dissipation setting module is configured to represent fluid motion using total velocity potential, set boundary conditions and energy dissipation surfaces on the structure surface, apply nonlinear pressure loss conditions to the energy dissipation surface, and represent the normal derivative of the scattering potential and the boundary conditions of the energy dissipation surface using scattering potential. The boundary integral module is configured to incorporate the boundary conditions of the energy dissipation surface into the conventional boundary integral equation and the hypersingular boundary integral equation. The equation derivation module is configured to divide the structure into multiple grids, discretize the merged conventional boundary integral equations and hypersingular boundary integral equations, and use the normal derivative of the scattering potential to obtain the equation system. The homotopy relation establishment module is configured to use the frequency domain motion response equation of the structure and the total wave force equation, as well as the equation set to define linear and nonlinear operators, to establish the homotopy relation of the hydrodynamic characteristics of the structure using the linear and nonlinear operators, and to solve the velocity potential of the structure surface and the velocity potential normal derivative of the dissipative surface through the homotopy relation. The total wave force and motion response calculation module is configured to calculate the total wave force and motion response of the structure based on the velocity potential of the structure surface and the normal derivative of the velocity potential of the dissipative surface, combined with the frequency domain motion response equation of the structure and the total wave force equation.

Images