Modular floating platform multi-body hydrodynamic coupling analysis method and system based on frequency domain boundary element

Abstract

The application discloses a kind of modularization floating platform multi-body hydrodynamic coupling analysis method and system based on frequency domain boundary element, it is related to marine engineering hydrodynamics analysis technical field, the method includes: constructing wet surface model with cover plate grid;Establish unified boundary integral equation satisfying floating body impermeable, air chamber compressible and net cage water permeable condition, closed joint integral equation group is obtained by solving;Discrete this equation group, through Green function pre-interpolation and adaptive solution, full-coupling hydrodynamic influence matrix is obtained;Constraint matrix is constructed based on hinged point displacement continuous condition, and extended matrix equation including motion response and hinged force is established by introducing Lagrange multiplier;Motion response, hinged force and air chamber velocity potential are solved, and according to this, calculate energy capture efficiency and hinged force amplitude.This will be multi-body hydrodynamic interference, hinged constraint, air chamber aeroelastic response and net cage water permeation effect unified in same linear system jointly solve, improve numerical stability and calculation efficiency.

Description

Technical Field

[0001] This invention relates to the field of marine engineering hydrodynamic analysis technology, and in particular to a modular floating platform multibody hydrodynamic coupling analysis method and system based on frequency domain boundary element method. Background Technology

[0002] Modular floating platforms, due to their advantages of flexible construction and expandable functionality, have significant application prospects in deep-sea aquaculture and marine energy development. These platforms typically consist of multiple rigid floating modules connected by flexible connectors, ball joints, and other structures, and are equipped with oscillating water column (OWC) wave energy devices and flexible net cages. Their hydrodynamic characteristics are influenced by multi-body radiation diffraction interference, mechanical connection constraints between modules, the compressibility of air in the air chambers, and the flow permeability effect of the net cages, making it a multi-physics coupling problem.

[0003] In practical analysis, existing technologies have the following shortcomings: 1) The boundary integral equation of the free-floating penetrating body has a non-unique solution problem at specific frequencies (i.e., irregular frequencies). The traditional cover plate method can eliminate this phenomenon, but it can only be applied in isolation to a single floating body and cannot be combined with multi-body connection constraints; 2) The motion equation of articulated multi-floating body systems usually adopts a step-by-step strategy of first decoupling to obtain the hydrodynamic coefficients of each module and then iteratively introducing the connection conditions. This is not only computationally inefficient, but also difficult to converge or even diverge when the connection stiffness is large; 3) The aerodynamic boundary conditions of the OWC air chamber and the permeable boundary conditions of the net cage are often simplified to equivalent damping or solved separately in existing methods. They are not unified with the overall platform motion and multi-body hydrodynamic interference in the same linear system, making it difficult to accurately assess the coupling effect of the energy device and the net cage on the platform motion and wave field. The above problems make it difficult for existing methods to meet the integrated analysis requirements of large floating platforms that integrate wave and fishery in terms of accuracy, efficiency and versatility in linear frequency domain analysis. Summary of the Invention

[0004] This invention aims to overcome the shortcomings of existing multibody boundary element decoupling analysis, such as low efficiency and insufficient accuracy. It provides a method and system for multibody hydrodynamic coupling analysis of modular floating platforms based on frequency domain boundary element analysis. This method unifies multibody hydrodynamic interference, articulation constraints, air chamber aeroelastic response, and cage permeability effect into a single linear system for joint solution. It obtains the motion response, articulation force load, and OWC energy capture efficiency of each module of the modular floating platform in one go, thereby improving numerical stability and computational efficiency.

[0005] In a first aspect, embodiments of the present invention provide a modular floating platform multibody hydrodynamic coupling analysis method based on frequency domain boundary elements, including: A geometric model of a modular floating platform consisting of multiple floating modules is constructed, and a downwardly offset cover plate mesh is generated within the waterline plane of each floating module to obtain wet surface mesh data with cover plate boundaries. Using the time-harmonic Green's function for finite water depth, a unified boundary integral equation is established that simultaneously satisfies the conditions of impenetrability of the floating body, the dynamic boundary conditions of compressibility of air in the air chamber, and the boundary conditions of water permeability of the cage. The wet surface mesh data with the cover plate boundary is substituted into the unified boundary integral equation to solve, resulting in a closed joint integral equation system for the unknown source strength on each boundary. Discretize the closed joint integral equation system, accelerate the calculation of influence coefficients by pre-interpolating the Green's function, and adaptively select the direct method or iterative method to solve the problem, thereby obtaining the fully coupled hydrodynamic influence matrix; Based on the displacement continuity condition of the hinge points between each floating body module, a constraint matrix is ​​constructed. The constraint matrix is ​​then introduced into the frequency domain motion equation containing the fully coupled hydrodynamic influence matrix using Lagrange multipliers. This equation is then combined with the constraint matrix to construct an extended matrix equation that simultaneously uses the motion response and hinge force of each floating body module as unknowns. Solve the extended matrix equation to obtain the motion response, articulation force, and velocity potential distribution within the air chamber for all modules, and calculate the energy capture efficiency and articulation force amplitude based on the velocity potential distribution.

[0006] In a preferred embodiment, a downwardly offset cover plate grid is generated within the waterline plane of each float module, including: The cover plate mesh is set as a planar mesh parallel to the water surface, and the entire mesh is offset downwards by a preset distance. The normal velocity of the cover plate mesh is set to zero.

[0007] As a preferred implementation, a unified boundary integral equation is established using the finite-depth time-harmonic Green's function, simultaneously satisfying the impenetrable condition of the floating body, the dynamic boundary condition of the compressibility of the air in the air chamber, and the permeable boundary condition of the gabion. The wetted surface mesh data with the cover plate boundary is then substituted into the unified boundary integral equation for solving, yielding a closed joint integral equation system concerning the unknown source strengths on each boundary, including: The cover plate boundary corresponding to the cover plate grid, the wet surface of each floating module, the water surface inside the air chamber, and the equivalent boundary of the cage are all included in the flow field solution domain. A linearized dynamic boundary condition considering the compressibility of air is applied to the water surface inside the air chamber, so that the air chamber pressure is related to the volume flux of the inner water surface through the linearized air state equation. A permeable boundary condition based on the Darcy permeability assumption is applied to the equivalent boundary of the cage, so that the potential difference inside and outside the cage is directly coupled with the normal velocity. Substituting all boundary conditions into Green's third formula simultaneously, a closed joint integral equation system is formed that is independent of decoupling iteration and where the source strengths of each floating module are mutually coupled.

[0008] In a preferred embodiment, the closed joint integral equation system is discretized, and the influence coefficient calculation is accelerated by pre-interpolating the Green's function. Then, either a direct method or an iterative method is adaptively selected for solving the equation, resulting in the fully coupled hydrodynamic influence matrix, including: The closed joint integral equation system is discretized using the constant surface element method. A bivariate pre-interpolation table based on radial and vertical variables is constructed for the fluctuation part of the Green's function, and the hydrodynamic influence coefficient is calculated by combining Gauss-Legends numerical integration to form a system of linear equations to be solved. Based on the scale of the unknowns in the linear equation system, the direct method or iterative method is adaptively selected to solve the problem, and the source strength distribution on each boundary is obtained. The fully coupled hydrodynamic influence matrix is ​​then derived from the source strength distribution.

[0009] In a preferred embodiment, a constraint matrix is ​​constructed based on the displacement continuity condition of the hinge points between each floating module. The constraint matrix is ​​then introduced into the frequency domain motion equations containing the fully coupled hydrodynamic influence matrix using Lagrange multipliers, and combined with the constraint matrix to construct an extended matrix equation that simultaneously uses the motion response and hinge force of each floating module as unknowns. This includes: Based on the type of hinge structure between floating body modules, the displacement continuity constraint relationship at the hinge point is determined, and a constraint matrix is ​​constructed according to the displacement continuity constraint relationship; Establish the frequency domain motion equations for each floating module. The frequency domain motion equations take the six-degree-of-freedom motion response of the module as unknowns, and its system matrix includes the additional mass, radiation damping, and wave excitation force derived from the fully coupled hydrodynamic influence matrix. The Lagrange multiplier is introduced to represent the hinge force at the hinge point. The constraint matrix and the Lagrange multiplier are embedded into the frequency domain motion equation to form an extended matrix equation with the motion response of all modules and all hinge forces as unknowns.

[0010] In a preferred embodiment, the displacement continuity constraint relationship at the hinge point is determined based on the type of hinge structure between the floating body modules, and a constraint matrix is ​​constructed according to the displacement continuity constraint relationship, including: Based on the hinge type between adjacent floating modules, determine the translational and / or rotational degrees of freedom that need to maintain continuous displacement at the hinge point; Establish the transformation relationship between the global coordinate system and the local coordinate systems of each floating module, and uniformly transform the displacement of each hinge point to the global coordinate system; For translational degrees of freedom that need to be kept continuous, construct constraint equations for equal linear displacements; for rotational degrees of freedom that need to be kept continuous, construct constraint equations for equal angular displacements. For the released degrees of freedom, depending on the hinge type, choose to either not apply constraints or introduce constraint stiffness coefficients to describe the relationship between relative displacement and constraint force. The linear displacement equality constraint equations and angular displacement equality constraint equations of all hinge points are assembled into a constraint matrix, the elements of which are determined by the coordinate transformation relationship and the constraint stiffness coefficient.

[0011] In a preferred embodiment, the extended matrix equation is solved to obtain the motion response, articulation force, and velocity potential distribution within the air chamber of all modules, including: Solving the extended matrix equation yields a solution vector containing the motion response of each floating module and the hinge force at each hinge point; The six-degree-of-freedom motion response of each floating module and the hinge force of each hinge point are separated from the solution vector; Based on the source strength distribution on each boundary, and combined with the time-harmonic Green's function at finite water depth, the velocity potential distribution of the water surface inside the air chamber is calculated by inversion.

[0012] In a preferred embodiment, calculating the energy-harvesting efficiency and articulation force amplitude based on the velocity potential distribution includes: The volumetric flow rate of the air chamber is obtained by performing an area integral on the velocity potential distribution; Based on the compressed volume flow rate of the air chamber and the preset energy extraction damping coefficient, the energy capture width ratio or total power generation is calculated as the energy capture efficiency. The hinge force components of each hinge point are extracted from the solution vector, and the hinge force amplitude of each hinge point is calculated by the complex modulus.

[0013] As a preferred embodiment, the solution is adaptively selected using either a direct method or an iterative method based on the size of the unknowns in the linear equation system, including: When the total number of unknowns in the linear equation system is less than a preset threshold, the LU decomposition direct method is used to solve it. When the total number of unknowns in the linear equation system is greater than or equal to a preset threshold, the preprocessing GMRES iterative method is used to solve the problem first, and the convergence tolerance and the maximum number of iteration steps are set. If the iteration residual fails to decrease below the convergence tolerance within the maximum number of iteration steps, it will automatically revert to the LU decomposition direct method.

[0014] Secondly, embodiments of the present invention also provide a modular floating platform multibody hydrodynamic coupling analysis system based on frequency domain boundary element method, used to execute the modular floating platform multibody hydrodynamic coupling analysis method based on frequency domain boundary element method described in any of the above embodiments, including: The geometric modeling module is used to construct the geometric model of a modular floating platform composed of multiple floating modules, and to generate a downward offset cover plate mesh in the waterline plane of each floating module to obtain wet surface mesh data with cover plate boundaries. The boundary integral equation construction module is used to establish a unified boundary integral equation that simultaneously satisfies the floating body impenetrability condition, the air chamber air compressibility dynamic boundary condition, and the net cage water permeability boundary condition using the finite water depth time harmonic Green function. The wet surface mesh data with the cover plate boundary is substituted into the unified boundary integral equation to solve, and a closed joint integral equation system with respect to the unknown source strength on each boundary is obtained. The discretization and solution module is used to discretize the closed joint integral equation system, accelerate the calculation of influence coefficients by pre-interpolating the Green's function, and adaptively select the direct method or iterative method to solve the problem, thereby obtaining the fully coupled hydrodynamic influence matrix. The extended matrix equation construction module is used to construct a constraint matrix based on the displacement continuity condition of the hinge points between each floating body module. The constraint matrix is ​​introduced into the frequency domain motion equation containing the fully coupled hydrodynamic influence matrix using Lagrange multipliers, and then combined with the constraint matrix to construct an extended matrix equation with the motion response and hinge force of each floating body module as unknowns. The joint solution and post-processing module is used to solve the extended matrix equation, obtain the motion response, articulation force and velocity potential distribution in the air chamber of all modules, and calculate the energy capture efficiency and articulation force amplitude based on the velocity potential distribution.

[0015] Thirdly, embodiments of the present invention also provide an electronic device, the electronic device comprising: One or more processors; Storage device for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the modular floating platform multibody hydrodynamic coupling analysis method based on frequency domain boundary elements as described in any embodiment of the present invention.

[0016] Fourthly, embodiments of the present invention also provide a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements a modular floating platform multibody hydrodynamic coupling analysis method based on frequency domain boundary elements as described in any embodiment of the present invention.

[0017] Compared to existing technologies, the following beneficial effects have been achieved: (1) This invention extends the cover plate method to multibody boundary integral systems. By extending the integral domain when constructing the influence matrix, it automatically suppresses pseudo-resonance, making the fully coupled additional mass and damping coefficients continuous and smooth over a wide frequency range, thus avoiding the problem of abnormal jumps in hydrodynamic coefficients at specific frequencies in the traditional multibody boundary element method.

[0018] (2) This invention integrates flow field radiation diffraction, multi-body hinge constraint, air chamber air spring effect and net cage water permeability into a single frequency domain linear system, eliminating the convergence difficulty or failure risk caused by the large connection stiffness of the traditional decoupling iteration method. All response quantities can be obtained in a single frequency scan without multiple iterations, thus improving numerical stability and computational efficiency.

[0019] (3) This invention uses high-precision pre-interpolation of Green's function, Gauss-Legendre numerical integration to replace conventional mean integration, and adaptive linear solver switching strategy to ensure computational accuracy while taking into account solution efficiency and robustness, and has the ability to be extended to more modules. Attached Figure Description

[0020] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings. The drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 This is a flowchart of a modular floating platform multibody hydrodynamic coupling analysis method based on frequency domain boundary element method provided in an embodiment of the present invention; Figure 2 This is an overall technical roadmap of a modular floating platform multibody hydrodynamic coupling analysis method based on frequency domain boundary element method provided by an embodiment of the present invention; Figure 3 This is a diagram showing the wave surface distribution effect of the platform under the ball joint connection provided in the embodiment of the present invention. Figure 4 This is a schematic diagram of the structure of a modular floating platform multibody hydrodynamic coupling analysis system based on frequency domain boundary element method provided in an embodiment of the present invention; Figure 5 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0021] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0022] Before discussing the exemplary embodiments in more detail, it should be mentioned that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although the flowcharts describe operations (or steps) as being processed sequentially, many of these operations (or steps) may be performed in parallel, concurrently, or simultaneously. Furthermore, the order of the operations may be rearranged. The process may be terminated when its operation is completed, but may also have additional steps not included in the figures. The process may correspond to a method, function, procedure, subroutine, subroutine, etc.

[0023] Example 1 like Figure 1 As shown, Embodiment 1 of the present invention provides a modular floating platform multibody hydrodynamic coupling analysis method 100 based on frequency domain boundary element method. The method 100 specifically includes the following steps: Step S110: Construct a geometric model of a modular floating platform consisting of multiple floating modules, and generate a downward offset cover plate mesh within the waterline plane of each floating module to obtain wet surface mesh data with cover plate boundaries.

[0024] In a preferred embodiment, this step obtains the geometric and layout parameters of the modular floating platform and constructs a wetted surface quadrilateral mesh for all floating modules, equivalent boundaries of the cages, and air chamber regions. For each floating module with a waterline, a lid mesh parallel to the water surface is generated inside its waterline, and the lid is offset downwards by a predetermined distance. ,in Take the characteristic dimension as the draft of the floating module. These covers are used to extend the boundary integration domain to eliminate irregular frequencies, and the normal velocity on the covers is set to zero.

[0025] Step S120: Using the finite water depth time-harmonic Green's function, establish a unified boundary integral equation that simultaneously satisfies the impenetrable condition of the floating body, the dynamic boundary condition of the compressibility of the air in the air chamber, and the water-permeable boundary condition of the cage. Substitute the wet surface mesh data with the cover plate boundary into the unified boundary integral equation to solve, and obtain a closed joint integral equation system for the unknown source strength on each boundary.

[0026] As a preferred embodiment, the present invention employs a finite-depth time-harmonic Green's function that simultaneously satisfies the linear free water surface condition, the impenetrable bottom condition, and the infinite radiation condition. Assuming inviscid, incompressible, and irrotational linear potential flow, a total velocity potential is established within the flow field. The boundary integral equation is derived, and the cover plate described in step S110 is incorporated into the integration domain. Based on different types of boundaries, the following conditions are embedded: The wetted surface of the floating body satisfies the condition that the surface is impermeable at an instant; Water surface inside the air chamber Subject to dynamic boundary conditions that take into account the compressibility of air, expressed as follows: ,in The total velocity potential within the flow field is... This refers to the relative pressure of the air in the air chamber. Atmospheric pressure. For fluid density, The acceleration due to gravity is correlated with the volume flux of the internal water surface through a linearized air state equation; the linearization condition applies when the relative pressure within the air chamber satisfies... Operating conditions (usually corresponding to the gas chamber opening ratio) ); Based on Darcy's permeability assumption, permeable boundary conditions are applied to the cage area. ,in For the permeability coefficient, (Permeability coefficient, dimensionless) )Depend on After calibration of the water tank, For the porosity of the wire mesh cage, The drag coefficient, For the incident wave height, These are the velocity potentials inside and outside the cage, respectively; : Vertical coordinates of the field point; : Incident wave angular frequency; : Relative air pressure in the air chamber; : Normal direction of the cage boundary.

[0027] Finally, by substituting all the above boundary conditions into Green's third formula using the layered source dipole distribution, a closed joint integral equation system is obtained regarding the unknown source strengths at each boundary. In this equation system, the source strengths of each module influence each other, and the gas chamber and the net box directly participate in field coupling.

[0028] Step S130: Discretize the closed joint integral equation system, accelerate the calculation of influence coefficients by pre-interpolating the Green's function, and adaptively select the direct method or iterative method to solve the problem, thereby obtaining the fully coupled hydrodynamic influence matrix.

[0029] In a preferred embodiment, this step uses the constant surface element method to discretize the closed joint integral equation system. A bivariate interpolation table is pre-established for the wave component of the Green's function on the free surface, to... For radial variables, Let be the vertical variable, where The horizontal distance between the source and the field point. The vertical coordinates of the field point and the source point are respectively used. When calculating the influence coefficient, Gauss-Legendre numerical integration and polynomial interpolation are used to quickly form the hydrodynamic influence matrix of each module.

[0030] For large systems, two options are provided: the direct method (LU decomposition) and the preprocessed GMRES iterative solver, with an automatic switching mechanism for the convergence threshold. When the total number of unknowns in the linear equation system is less than a preset threshold, the LU decomposition direct method is used to solve it. When the total number of unknowns in the linear equation system is greater than or equal to a preset threshold, the preprocessing GMRES iterative method is used to solve the problem first, and the convergence tolerance and the maximum number of iteration steps are set. If the iteration residual fails to decrease below the convergence tolerance within the maximum number of iteration steps, it will automatically revert to the LU decomposition direct method.

[0031] S140: Construct a constraint matrix based on the displacement continuity condition of the hinge points between each floating module, use Lagrange multipliers to introduce the constraint matrix into the frequency domain motion equation containing the fully coupled hydrodynamic influence matrix, and combine it with the constraint matrix to construct an extended matrix equation with the motion response and hinge force of each floating module as unknowns.

[0032] As a preferred embodiment, this step includes For a system of floating modules, based on the rigid body motion assumption and d'Alembert's principle, the frequency domain motion equations for the unconnected state are constructed as follows: ; Where M is the mass matrix, Here, C represents the fully coupled additional mass matrix and the fully coupled radiation damping matrix calculated by the boundary element method in step S130, and C is the hydrostatic restoring force matrix. Here is the mooring stiffness matrix. To extract the damping matrix for energy, This is the first-order wave excitation force vector. The complex amplitude values ​​of the six degrees of freedom motion for all floating body modules.

[0033] Next, based on the actual connection method between the floating body modules, such as elastic connectors, ball joints, or releasing specific rotational degrees of freedom, the displacement continuity condition of the hinge points is established, and a constraint matrix is ​​used. Formal expression: .

[0034] For translational degrees of freedom that need to be maintained continuously, linear displacement equal constraint equations are constructed; for rotational degrees of freedom that need to be maintained continuously, angular displacement equal constraint equations are constructed. For example, for each pair of adjacent modules, the elastic connector constrains 3 translational degrees of freedom (releasing 3 rotational degrees), forming 3 displacement continuity equations. For the released degrees of freedom, depending on the hinge type, either no constraint is applied or a constraint stiffness coefficient is introduced to describe the relationship between relative displacement and constraint force.

[0035] Assemble the linear displacement equality constraint equations and angular displacement equality constraint equations of all hinge points into a system with dimension [missing information]. Total constraint matrix The total number of hinge constraint equations across the entire platform, the total constraint matrix. The elements are determined by the coordinate transformation relationship and the constraint stiffness coefficient.

[0036] Preferably, a Lagrange multiplier vector is introduced. Representing the connecting forces, the constraint matrix and Lagrange multipliers are embedded into the frequency domain motion equations to construct an extended matrix equation with the motion responses of all modules and all articulation forces as unknowns: ; Wherein the system stiffness matrix The air chamber damping term enters in the form of additional damping. This is combined with the complex velocity potential of the air chamber to achieve synchronous coupling between the equation of motion and the resonance of the air chamber.

[0037] S150: Solve the extended matrix equation to obtain the motion response, articulation force, and velocity potential distribution in the air chamber of all modules, and calculate the energy capture efficiency and articulation force amplitude based on the velocity potential distribution.

[0038] In a preferred embodiment, the above-mentioned extended matrix equation is solved directly in the frequency domain to obtain the complex amplitude values ​​of the six degrees of freedom motion of all floating body modules in one step. The solution involves the following steps: the hinge forces at all hinge points and the velocity potential distribution of the water surface in each air chamber. Solving the extended matrix equation yields a solution vector containing the motion response of each floating module and the hinge force at each hinge point; From the solution vector, separate the complex amplitude values ​​of the six degrees of freedom motion of each floating module (for all floating modules). and the hinge force at each hinge point; Based on the source strength distribution at each boundary, and combined with the time-harmonic Green's function at finite water depth, the velocity potential distribution of the water surface inside each chamber is calculated by inversion. The calculation of energy harvesting efficiency and articulation force amplitude based on the velocity potential distribution includes: performing an area integral on the velocity potential distribution on the water surface inside the air chamber to obtain the air chamber compression volume flow rate; calculating the energy harvesting width ratio or total power generation as the energy harvesting efficiency based on the air chamber compression volume flow rate and a preset energy extraction damping coefficient; extracting the articulation force components of each articulation point from the solution vector; calculating the articulation force amplitude of each articulation point through complex modulus; and evaluating the stress safety of the connector through the articulation force amplitude.

[0039] Based on the above embodiments, the core beneficial effects of the present invention are as follows: (1) This invention extends the cover plate method to multibody boundary integral systems. By extending the integral domain when constructing the influence matrix, it automatically suppresses pseudo-resonance, making the fully coupled additional mass and damping coefficients continuous and smooth over a wide frequency range, thus avoiding the problem of abnormal jumps in hydrodynamic coefficients at specific frequencies in the traditional multibody boundary element method.

[0040] (2) This invention integrates flow field radiation diffraction, multi-body hinge constraint, air chamber air spring effect and net cage water permeability into a single frequency domain linear system, eliminating the convergence difficulty or failure risk caused by the large connection stiffness of the traditional decoupling iteration method. All response quantities can be obtained in a single frequency scan without multiple iterations, thus improving numerical stability and computational efficiency.

[0041] (3) This invention uses high-precision pre-interpolation of Green's function, Gauss-Legendre numerical integration to replace conventional mean integration, and adaptive linear solver switching strategy to ensure computational accuracy while taking into account solution efficiency and robustness, and has the ability to be expanded to more modules.

[0042] Example 2 To illustrate the technical solution of this invention in detail, the invention will be further described below with reference to specific examples. In this second embodiment, a semi-submersible floating platform composed of six cuboid modules is used as an example. The outer side length of each module is 40 m, the inner side length is 30 m, and the draft is... Module spacing 5 m, water depth The modules are interconnected via upper and lower elastic connectors or ball joints, and some modules contain an OWC (Overhead Control) gas chamber. Incident wave number. Satisfy dispersion relation .

[0043] Step 1: Establish the platform's geometric model. Divide the wetted surface of each module into 360 quadrilateral facets, and add a cover plate with 28 facets within the waterline surface. The cover plate is moved downwards by 0.05 m in the vertical direction. The normal direction of the normal surface points towards the fluid domain.

[0044] Step 2: Select a composite Green's function for a finite water depth of 30 m. The damping coefficient at the water surface boundary within the air chamber is calculated based on the opening ratio; in this embodiment, the opening ratio is used. ,satisfy The linearization application conditions. Permeability coefficient of the gabion section. According to the porosity of the wire mesh and incident wave height Based on the water tank calibration, it was determined that in this embodiment... drag coefficient , calibrated In the boundary integral equations, all boundary conditions are discretized simultaneously, and the air chamber and the wire mesh directly participate in the field coupling, so they are no longer treated separately.

[0045] Step 3: Store the fluctuation part of the Green's function using a dimensionless bivariate interpolation table. The interpolation parameters are set such that the maximum interpolation error is less than... Determined by principle: Radial variable exist The interval should be evenly divided into at least 600 points, with vertical variables. The corresponding depth range is divided into at least 100 logarithmic segments; this embodiment uses 5th-order Lagrange polynomial interpolation. When calculating the influence coefficient, each quadrilateral element is... Gauss-Legendre integration points. Solver strategy: When the total number of unknowns in the system is less than 3000, LU decomposition is used by default; when it exceeds 3000, GMRES iteration is preferred, with a tolerance set to [value missing]. If the iteration fails to meet the target, it automatically reverts to LU decomposition. The additional mass matrix of the 6 fully coupled modules obtained from the above steps is... The curve is smooth within the frequency range; compared with the results of the same mesh calculation in WAMIT software, the root mean square error of the diagonally added mass element is less than [value missing]. Irregular frequency prone areas (approximately) The peak anomaly (typical deviation up to) did not occur at the location where the cover plate was not applied. ).

[0046] Step 4: Under the condition of flexible connection, the stiffness of the flexible connector is taken as... The connector is located 1 m above the top surface of the modular floating platform, and the spacing between connectors between adjacent modules is... The constraint matrix for each pair of adjacent modules. To ensure biaxial linear displacement continuity (3 translational constraint equations), three rotational degrees of freedom are released, and the connector stiffness is equivalently included in the overall system stiffness matrix. Below, the stiffness of the ball joint connector is taken as... The constraint matrix also ensures the continuity of biaxial linear displacement. In this embodiment, the entire platform has a total of 5 pairs of adjacent modules, which are elastically connected. The order of the extended matrix is Step. The relative angle of the ball hinge. After converting the (complex amplitude of rotational displacement) to the local coordinate system, it is then calculated according to the formula. Calculate the first The power generation capacity of a single ball joint, This is the energy output damping coefficient corresponding to the relative rotational degree of freedom.

[0047] Step 5: Directly solve the extended linear system at different frequencies to obtain the amplitude operators (RAO) of the heave and pitch motion responses of each module and the articulation force. Calculations show that at the incident wave frequency... At that time, the wavefront on the back wave side of the moonpool significantly increased under the elastic connection, consistent with the trend calculated by commercial software using the same mesh and parameters. The ball joint connection effectively reduced the mid-frequency range ( The peak pitch response is good, while the articulation force response is reasonable. The OWC dual-chamber design achieves optimal performance at the resonant frequency (…). The energy capture efficiency near the single-chamber area is approximately [percentage missing]. ,exist The maximum increase reached approximately This is consistent with the data from the water tank test.

[0048] The above embodiments demonstrate that the present invention can provide complete indicators of all motions, loads, and air chamber energy conversion of a multi-body platform in a single frequency scan, without the need for substructure iteration or third-party fluid-structure interaction software intervention throughout the analysis process, and has significant engineering practical value.

[0049] Figure 3 This study demonstrates the wavefront distribution of a modular floating platform system with a ball-joint connection at a frequency of ω = 0.7 rad / s. The introduction of the ball-joint connection further alters the wavefront morphology, exhibiting distribution characteristics different from those of the elastic connection, and showing a clear wave direction dependence. Under the wave direction angle β = 0° (facing the wave), the free surface wavefront is characterized by a prominent wave crest on the facing side. Compared to the elastic connection, the ball-joint connection somewhat suppresses the wave height in the facing moon pool, while amplifying the wave height in the leeward moon pool. This change indicates that the ball-joint connection alters the relative motion pattern between modules, weakens the accumulation of wave energy on the facing side, and simultaneously promotes energy transfer to the leeward moon pool.

[0050] Under the condition of wave angle β=45° (oblique wave), the free surface wave also exhibits wave crests on the wave-facing side. However, unlike the elastic connection, the wave height in the moonpool on the leeward side is significantly higher than that on the wave-facing side under the ball joint connection. This reversal phenomenon indicates that the ball joint connection can effectively suppress the local wave height on the wave-facing side under oblique wave action, guiding wave energy around to the leeward side region, forming a new wave height extreme region. Overall, at a frequency of ω=0.7 rad / s, the ball joint connection and the elastic connection have an impact on the wave surface distribution.

[0051] Significant differences: The ball joint connection tends to suppress the wave height on the wave-facing side of the moon pool and amplify the response on the wave-receding side, especially under oblique wave conditions, showing a shift in the extreme wave height region from the wave-facing side to the wave-receding side. This result provides an important reference for the hydrodynamic performance evaluation and optimization design of modular floating platforms under different connection methods.

[0052] Example 3 Figure 4 This is a schematic diagram of a modular floating platform multibody hydrodynamic coupling analysis system based on frequency domain boundary element method provided in Embodiment 3 of the present invention, as shown below. Figure 4 As shown, the system includes: The geometric modeling module 410 is used to construct the geometric model of a modular floating platform composed of multiple floating body modules, and to generate a downward offset cover plate mesh in the waterline plane of each floating body module to obtain wet surface mesh data with cover plate boundaries. The boundary integral equation construction module 420 is used to establish a unified boundary integral equation that simultaneously satisfies the floating body impenetrability condition, the air chamber air compressibility dynamic boundary condition, and the net cage water permeability boundary condition using the finite water depth time harmonic Green function. The wet surface mesh data with the cover plate boundary is substituted into the unified boundary integral equation to solve, and a closed joint integral equation system with respect to the unknown source strength on each boundary is obtained. Discretization and solution module 430 is used to discretize the closed joint integral equation system, accelerate the calculation of influence coefficients by pre-interpolating the Green's function, and adaptively select the direct method or iterative method to solve the problem, thereby obtaining the fully coupled hydrodynamic influence matrix. The extended matrix equation construction module 440 is used to construct a constraint matrix based on the displacement continuity condition of the hinge points between each floating body module. The constraint matrix is ​​introduced into the frequency domain motion equation containing the fully coupled hydrodynamic influence matrix using Lagrange multipliers, and is combined with the constraint matrix to construct an extended matrix equation with the motion response and hinge force of each floating body module as unknowns. The joint solution and post-processing module 450 is used to solve the extended matrix equation, obtain the motion response, articulation force and velocity potential distribution in the air chamber of all modules, and calculate the energy capture efficiency and articulation force amplitude based on the velocity potential distribution.

[0053] The modular floating platform multibody hydrodynamic coupling analysis system based on frequency domain boundary element method provided in this embodiment of the invention can execute the modular floating platform multibody hydrodynamic coupling analysis method based on frequency domain boundary element method provided in any of the embodiments of the invention above. It has the corresponding functions and beneficial effects of executing the modular floating platform multibody hydrodynamic coupling analysis method based on frequency domain boundary element method. For detailed process, please refer to the relevant operation of the modular floating platform multibody hydrodynamic coupling analysis method based on frequency domain boundary element method in the foregoing embodiments.

[0054] Example 4 Figure 5 This is a schematic diagram of the structure of an electronic device provided in Embodiment 4 of the present invention. The electronic device 10 is intended to represent various forms of digital computers, and may also represent various forms of mobile devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the invention described and / or claimed herein.

[0055] like Figure 5 As shown, the electronic device 10 includes at least one processor 11 and a memory, such as a read-only memory (ROM) 12 or a random access memory (RAM) 13, communicatively connected to the at least one processor 11. The memory stores computer programs executable by the at least one processor. The processor 11 can perform various appropriate actions and processes based on the computer program stored in the ROM 12 or loaded into the RAM 13 from storage unit 18. The RAM 13 can also store various programs and data required for the operation of the electronic device 10. The processor 11, ROM 12, and RAM 13 are interconnected via a bus 14. An input / output (I / O) interface 15 is also connected to the bus 14.

[0056] Multiple components in electronic device 10 are connected to I / O interface 15, including: input unit 16, such as keyboard, mouse, etc.; output unit 17, such as various types of displays, speakers, etc.; storage unit 18, such as disk, optical disk, etc.; and communication unit 19, such as network card, modem, wireless transceiver, etc. Communication unit 19 allows electronic device 10 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0057] Processor 11 can be a variety of general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of processor 11 include, but are not limited to, central processing unit (CPU), graphics processing unit (GPU), various special-purpose artificial intelligence (AI) computing chips, various processors running machine learning model algorithms, digital signal processors (DSPs), and any suitable processor, controller, microcontroller, etc. Processor 11 executes the modular floating platform multibody hydrodynamic coupling analysis method based on frequency domain boundary element method described above.

[0058] It should be understood that the various forms of processes shown above can be used, with steps reordered, added, or deleted. For example, the steps described in this invention can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution of this invention can be achieved, and this is not limited herein.

[0059] The above embodiments are merely illustrative examples and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A modular floating platform multibody hydrodynamic coupling analysis method based on frequency domain boundary element method, characterized in that, include: A geometric model of a modular floating platform consisting of multiple floating modules is constructed, and a downwardly offset cover plate mesh is generated within the waterline plane of each floating module to obtain wet surface mesh data with cover plate boundaries. Using the time-harmonic Green's function at finite water depth, a unified boundary integral equation is established that simultaneously satisfies the impenetrability condition of the floating body, the dynamic boundary condition of the compressibility of air in the air chamber, and the permeable boundary condition of the net cage. The wetted surface mesh data with the cover plate boundary is substituted into the unified boundary integral equation for solving, resulting in a closed joint integral equation system for the unknown source strength at each boundary. This includes: unifying the cover plate boundary corresponding to the cover plate mesh, the wetted surface of each floating body module, the water surface inside the air chamber, and the equivalent boundary of the net cage into the flow field solution domain; applying a linearized dynamic boundary condition considering air compressibility to the water surface inside the air chamber, so that the air chamber pressure is related to the internal water surface volume flux through the linearized air state equation; applying a permeable boundary condition based on the Darcy permeability assumption to the equivalent boundary of the net cage, so that the potential difference inside and outside the net cage is directly coupled with the normal velocity; and simultaneously substituting all boundary conditions into Green's third formula to form the closed joint integral equation system that is independent of decoupling iteration and where the source strength of each floating body module is mutually coupled. Discretize the closed joint integral equation system, accelerate the calculation of influence coefficients by pre-interpolating the Green's function, and adaptively select the direct method or iterative method to solve the problem, thereby obtaining the fully coupled hydrodynamic influence matrix; Based on the displacement continuity condition of the hinge points between each floating body module, a constraint matrix is ​​constructed. The constraint matrix is ​​then introduced into the frequency domain motion equation containing the fully coupled hydrodynamic influence matrix using Lagrange multipliers. This equation is then combined with the constraint matrix to construct an extended matrix equation that simultaneously uses the motion response and hinge force of each floating body module as unknowns. Solve the extended matrix equation to obtain the motion response, articulation force, and velocity potential distribution within the air chamber for all modules, and calculate the energy capture efficiency and articulation force amplitude based on the velocity potential distribution.

2. The modular floating platform multibody hydrodynamic coupling analysis method based on frequency domain boundary element method according to claim 1, characterized in that, A downwardly offset cover plate grid is generated within the waterline plane of each floating module, including: The cover plate mesh is set as a planar mesh parallel to the water surface, and the entire mesh is offset downwards by a preset distance. The normal velocity of the cover plate mesh is set to zero.

3. The modular floating platform multibody hydrodynamic coupling analysis method based on frequency domain boundary element method according to claim 1, characterized in that, Discretize the closed joint integral equation system, accelerate the calculation of influence coefficients by pre-interpolating the Green's function, and adaptively select either the direct method or the iterative method to solve, obtaining the fully coupled hydrodynamic influence matrix, including: The closed joint integral equation system is discretized using the constant surface element method. A bivariate pre-interpolation table based on radial and vertical variables is constructed for the fluctuation part of the Green's function, and combined with Gaussian... Legendre numerical integration was used to calculate the hydrodynamic influence coefficients, forming a system of linear equations to be solved. Based on the unknown quantity scale of the linear equation system, the direct method or iterative method is adaptively selected to solve the problem, and the source strength distribution on each boundary is obtained. The fully coupled hydrodynamic influence matrix is ​​then derived from the source strength distribution.

4. The modular floating platform multibody hydrodynamic coupling analysis method based on frequency domain boundary element method according to claim 1, characterized in that, Based on the displacement continuity condition of the hinge points between each floating module, a constraint matrix is ​​constructed. Using Lagrange multipliers, this constraint matrix is ​​introduced into the frequency domain motion equations containing the fully coupled hydrodynamic influence matrix, and then combined with the constraint matrix to construct an extended matrix equation that simultaneously uses the motion response and hinge force of each floating module as unknowns. This includes: Based on the type of hinge structure between floating body modules, the displacement continuity constraint relationship at the hinge point is determined, and a constraint matrix is ​​constructed according to the displacement continuity constraint relationship; Establish the frequency domain motion equations for each floating module. The frequency domain motion equations take the six-degree-of-freedom motion response of the module as unknowns, and its system matrix includes the additional mass, radiation damping, and wave excitation force derived from the fully coupled hydrodynamic influence matrix. The Lagrange multiplier is introduced to represent the hinge force at the hinge point. The constraint matrix and the Lagrange multiplier are embedded into the frequency domain motion equation to form an extended matrix equation with the motion response of all modules and all hinge forces as unknowns.

5. The modular floating platform multibody hydrodynamic coupling analysis method based on frequency domain boundary element method according to claim 4, characterized in that, Based on the type of hinge structure between floating body modules, the displacement continuity constraint relationship at the hinge point is determined, and a constraint matrix is ​​constructed according to the displacement continuity constraint relationship, including: Based on the hinge type between adjacent floating modules, determine the translational and / or rotational degrees of freedom that need to maintain continuous displacement at the hinge point; Establish the transformation relationship between the global coordinate system and the local coordinate systems of each floating module, and uniformly transform the displacement of each hinge point to the global coordinate system; For translational degrees of freedom that need to be kept continuous, construct constraint equations for equal linear displacements; for rotational degrees of freedom that need to be kept continuous, construct constraint equations for equal angular displacements. For the released degrees of freedom, depending on the hinge type, choose to either not apply constraints or introduce constraint stiffness coefficients to describe the relationship between relative displacement and constraint force. The linear displacement equality constraint equations and angular displacement equality constraint equations of all hinge points are assembled into a constraint matrix, the elements of which are determined by the coordinate transformation relationship and the constraint stiffness coefficient.

6. The modular floating platform multibody hydrodynamic coupling analysis method based on frequency domain boundary element method according to claim 3, characterized in that, Solving the extended matrix equation yields the motion response, articulation force, and velocity potential distribution within the air chambers of all modules, including: Solving the extended matrix equation yields a solution vector containing the motion response of each floating module and the hinge force at each hinge point; The six-degree-of-freedom motion response of each floating module and the hinge force of each hinge point are separated from the solution vector; Based on the source strength distribution on each boundary, and combined with the time-harmonic Green's function at finite water depth, the velocity potential distribution of the water surface inside the air chamber is calculated by inversion.

7. The modular floating platform multibody hydrodynamic coupling analysis method based on frequency domain boundary element method according to claim 6, characterized in that, The energy-harvesting efficiency and articulation force amplitude are calculated based on the velocity potential distribution, including: The volumetric flow rate of the air chamber is obtained by performing an area integral on the velocity potential distribution; Based on the compressed volume flow rate of the air chamber and the preset energy extraction damping coefficient, the energy capture width ratio or total power generation is calculated as the energy capture efficiency. The hinge force components of each hinge point are extracted from the solution vector, and the hinge force amplitude of each hinge point is calculated by the complex modulus.

8. The modular floating platform multibody hydrodynamic coupling analysis method based on frequency domain boundary element method according to claim 3, characterized in that, The solution to the linear equation system is adaptively selected using either a direct method or an iterative method based on the size of the unknowns, including: When the total number of unknowns in the linear equation system is less than a preset threshold, the LU decomposition direct method is used to solve it. When the total number of unknowns in the linear equation system is greater than or equal to a preset threshold, the preprocessing GMRES iterative method is used to solve the problem first, and the convergence tolerance and the maximum number of iteration steps are set. If the iteration residual fails to decrease below the convergence tolerance within the maximum number of iteration steps, it will automatically revert to the LU decomposition direct method.

9. A modular floating platform multibody hydrodynamic coupling analysis system based on frequency domain boundary element method, characterized in that, The system is used to perform the modular floating platform multibody hydrodynamic coupling analysis method based on frequency domain boundary element method as described in any one of claims 1 to 8, the system comprising: The geometric modeling module is used to construct the geometric model of a modular floating platform composed of multiple floating modules, and to generate a downward offset cover plate mesh in the waterline plane of each floating module to obtain wet surface mesh data with cover plate boundaries. The boundary integral equation construction module is used to establish a unified boundary integral equation that simultaneously satisfies the floating body impenetrability condition, the air chamber air compressibility dynamic boundary condition, and the net cage water permeability boundary condition using the finite water depth time harmonic Green function. The wet surface mesh data with the cover plate boundary is substituted into the unified boundary integral equation to solve, and a closed joint integral equation system with respect to the unknown source strength on each boundary is obtained. The discretization and solution module is used to discretize the closed joint integral equation system, accelerate the calculation of influence coefficients by pre-interpolating the Green's function, and adaptively select the direct method or iterative method to solve the problem, thereby obtaining the fully coupled hydrodynamic influence matrix. The extended matrix equation construction module is used to construct a constraint matrix based on the displacement continuity condition of the hinge points between each floating body module. The constraint matrix is ​​introduced into the frequency domain motion equation containing the fully coupled hydrodynamic influence matrix using Lagrange multipliers, and then combined with the constraint matrix to construct an extended matrix equation with the motion response and hinge force of each floating body module as unknowns. The joint solution and post-processing module is used to solve the extended matrix equation, obtain the motion response, articulation force and velocity potential distribution in the air chamber of all modules, and calculate the energy capture efficiency and articulation force amplitude based on the velocity potential distribution.

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