Unidirectional fluid-solid coupling method based on additional mass boundary

Abstract

The invention relates to the technical field of ship design, and discloses a one-way fluid-solid coupling method based on an additional mass boundary, which enables one-way iteration between a flow field and a solid field to meet calculation convergence requirements based on an additional mass boundary method, and does not need repeated iteration between solution of the flow field and solution of a structure field, thereby effectively improving calculation efficiency. Therefore, the fluid-solid coupling calculation of the ship body structure based on the complex grillage finite element model becomes possible, and the fluid-solid coupling simulation capability of full-scale coverage of the whole ship is realized.

Description

[0001] The application belongs to the technical field of ship structure design, and particularly relates to a one-way fluid-structure coupling method based on an added mass boundary. BACKGROUND

[0002] In ship structure design, it is necessary to predict the structural load and response of a ship body under waves. The structural load usually includes static water bending moment, vertical wave bending moment, horizontal wave bending moment, torque, slamming vibration bending moment, etc. Under these loads, not only the vertical, horizontal or torsional deformation of the ship body as a whole needs to be concerned, but also the structural deformation and stress level of the local position of the ship body, such as the slamming position of the ship body, the local key plate structure inside the ship body, the propeller shaft arrangement position of the stern, or the local position of the piece body of a multi-hull ship.

[0003] The action of waves on the ship body is not only a simple static or periodic load, but also a complex dynamic load. In order to predict the deformation response of the ship body in waves, it is necessary to first simulate the real wave environment, and the nonlinear load under large waves or extreme conditions can be simulated and modeled to predict the hydrodynamic load exerted by the waves on the ship body structure. After obtaining the load, the load needs to be loaded on the ship body structure.

[0004] Therefore, the prediction of the structural load and response of the ship body under waves needs to calculate and simulate the wave (flow field) and the ship body structure (elastic body) respectively. The flow field calculation can simulate the real wave environment and can simulate and predict the nonlinear load under large waves or extreme conditions. The structure calculation can predict the deformation and stress response of the ship body structure under different fluid loads. After the hydrodynamic load generated by the flow field calculation is loaded on the structure, the motion and deformation of the structure are caused, and at the same time, the flow field is disturbed by the displacement and deformation of the structure. The two parts of calculation influence each other and are causally related.

[0005] The flow field and structure calculation have mature algorithms and software that can be used in their respective fields, such as the commercial software Starccm or the open source software OpenFOAM based on the finite volume method to solve the Reynolds average equation and the two-phase flow model to realize the simulation of waves for fluid calculation, and the plate-beam structure element based on the finite element method to carry out simulation of structural deformation and stress for structure calculation. Since the flow field and structure solving adopt different methods, their data are not communicated, which requires designing an algorithm to control the solving sequence of the two solvers and realizing the coupling of data exchange.

[0006] However, in the coupling process, in order to calculate convergence, the fluid calculation and the structure calculation often need to be calculated multiple times within one time step. This is due to the existence of added mass effect, which makes the coupling calculation easy to diverge.

[0007] The additional mass can be explained as when an external force acts on a rigid body, the acceleration generated is determined by the mass of the rigid body and the additional mass of the surrounding fluid. The surrounding fluid will generate acceleration due to the motion of the rigid body, and at the same time, it will also exert a reaction force on the rigid body, making the rigid body seem to increase in mass, which is called additional mass. The lighter the density of the rigid body relative to the fluid, the greater the influence of the additional mass, and the more likely it is to cause the fluid-structure coupling calculation to diverge.

[0008] To avoid the problem of calculation divergence caused by excessive additional mass in the traditional fluid-structure coupling method, the influence of additional mass is considered by using the coupling iteration method of flow field and structure calculation. For the simulation of a deformable body, first, the flow field calculation is responsible for providing the pressure and friction force on the boundary of the deformable body, denoted as , which is transmitted to the structure solver as a boundary condition for calculation, and then a structure displacement and deformation denoted as is obtained. The displacement of the structure will act on the fluid, and the fluid will also exert a reaction force on the structure, i.e. the additional mass effect. Since the structure has changed by , it has an impact on the flow field, so the deformation needs to be transmitted to the flow field to re-solve the boundary force of the flow field acting on the structure , the change of the boundary force leads to the need to re-solve the structure deformation to obtain , and so on until and converge, which is the coupling iteration process considering additional mass.

[0009] Due to multiple data exchanges between each other, the calculation efficiency is greatly reduced, especially for fluid calculation using finite volume and whole ship finite element calculation using complex plate structure, which often takes several days to develop simulation separately, and each additional iteration will double the calculation time, which loses the application significance for industrial design.

[0010] In order to control the calculation time, two schemes of reducing the load of structure calculation or reducing the load of fluid calculation are proposed. To simplify the calculation load of the structure, the ship structure can be simplified as a one-dimensional ship beam. But using this simplified method makes the structure calculation lose details, and only the bending moment and shear force information at some sections of the ship can be obtained. It is powerless for the prediction of local plate deformation of the ship bow caused by wave slamming. To simplify the load of fluid calculation, the potential flow calculation method can be used instead of the CFD method of finite volume method. But this method also sacrifices the calculation accuracy of the flow field. For example, the potential flow method does not consider the influence of the surface and free surface changes on the disturbance force, ignores the nonlinear phenomena such as irregular wet surface changes, strong nonlinear motion, and free surface curling. It is not conducive to the accurate prediction of local plate load.

[0011] The first existing scheme: for the first part of the wave load calculation, the load of the flow field is predicted based on the CFD method. The finite element model of the structure part is a grillage model composed of one-dimensional beams and two-dimensional plates, and the calculation uses the finite element transient analysis method to solve the structure deformation. After the flow field and structure calculation is completed, bidirectional data exchange is needed between them, that is, the pressure field solved by CFD is input as the boundary condition to the structure solver to calculate the deformation and displacement. The calculated deformation and displacement are input as the boundary condition to the CFD solver to calculate the new pressure field. In one calculation time step, the calculation process iterates the flow field and structure calculation multiple times until convergence, and then the calculation of the next time step is performed. The disadvantage of this scheme is that the flow field solution and the structure solution each have a certain demand for the calculation amount. The flow-solid coupling iteration strategy adopted to eliminate the influence of additional mass makes the calculation time increase by several times, so that the actual application requires very high calculation demand, which is not suitable for use in design work.

[0012] The second existing scheme: on the basis of the first scheme, the structure calculation model is modified, and the ship body structure is simplified as one-dimensional beams, so as to reduce the time required for structure calculation.

[0013] This scheme sacrifices the fineness of the structure finite element model, and cannot predict the stress and deformation of the local grillage structure of the ship body.

[0014] The third existing scheme: on the basis of the second scheme, the flow field calculation is simplified, and the finite volume CFD method is replaced by the potential flow method, the boundary element method or the momentum theorem to calculate the flow field load for predicting the load such as slamming and green water. This scheme cannot predict the stress and deformation of the local grillage structure of the ship body, nor can it simulate the nonlinear load such as local slamming and green water of the ship.

[0015] Moreover, in the traditional fluid-solid coupling method, the flow field calculation is responsible for providing the pressure and friction force on the boundary of the deformed body, which is transmitted to the structure solver responsible for calculating the structure deformation. In the process of solving the structure solver, the deformation is not decomposed into two parts of the structure rigid body motion and elastic deformation. SUMMARY

[0016] The purpose of the present application is to provide a one-way fluid-solid coupling method based on the additional mass boundary, to solve the problem that the existing technology does not decompose the deformation and make a fine prediction, by modifying the boundary condition of the flow field solution, proposing the additional mass boundary method, dividing the rigid body motion solution into the flow field solver, eliminating the calculation divergence caused by the additional mass, so that the iteration between the flow field and the structure calculation can be changed to one-time one-way transmission, avoiding repeated iteration. While significantly improving the calculation efficiency, the accuracy can also be guaranteed, and the deformation and stress of the grillage structure at any position inside and outside the ship body can be finely predicted.

[0017] To achieve the above objectives, the technical solution adopted by the present invention is to provide a unidirectional fluid-structure interaction method based on an additional mass boundary.

[0018] The technical solution of this invention is a unidirectional fluid-structure interaction method based on an additional mass boundary, comprising the following steps: Step 1: Predict the velocity and acceleration of the rigid body. Step 2, using the predicted values Update the grid coordinates of the object's position: ; Step 3, update the flow field velocity ; Step 4: Update the pressure and rigid body acceleration , The pressure is in the boundary conditions of the object surface (where the pressure is in the boundary conditions of the object surface). (On the mesh surface) contains the acceleration along the line of the rigid body's center of mass. and angular acceleration , , in and These are the forces and moments acting on a rigid body caused by flow field pressure and friction. D is defined as ,in,

[0019]

[0020]

[0021] , in The additional viscous characteristic length parameter is defined as follows: , ,in The kinematic viscosity of water; For those involving vectors Cross product matrix ; Step 5: Update the rigid body motion state using the predicted rigid body motion state. ,

[0022] , ; Step 6, Update the object surface mesh ; Step 7: Update the flow field velocity to the (n+1)th time step. This step is again in the boundary conditions of the object surface ( The linear velocity of the rigid body's center of mass is contained on the mesh surface. and angular velocity ,

[0023] ; Step 8, Update and rigid body acceleration , At time step n+1, the pressure is again applied to the boundary conditions of the object surface. (On the mesh surface) contains the acceleration along the line of the rigid body's center of mass. and angular acceleration , ; Step 9: Update the rigid body motion state to the (n+1)th time step.

[0024]

[0025]

[0026]

[0027] ; Step 10, Update the object surface mesh And return to step 1 to proceed to the next moment of calculation until the calculation is complete; Step 11: Pressure field mapping interpolation to obtain the time-varying pressure boundary conditions required for structural calculation; Step 12: Establish forced displacement constraints to assign motion boundary conditions to the rigid body's center of mass in the finite element structural solution; Step 13: Begin the finite element structural solution and complete the calculation to obtain the stress and deformation of the hull structure at different times.

[0028] According to the present invention, the rigid body motion in step 1 is further defined by rotation and translation about its center of mass. To describe the rigid body motion, the following physical quantities are defined: : Rigid body mass; : Coordinates of a point on the surface of a rigid body; : Rigid body density; : Matrix of rotational inertia; : Coordinates of the centroid position; : Angle of rotation of the center of mass; : Center of mass position and velocity; : A matrix whose column vectors are the principal axes of inertia; : Center-of-mass acceleration; : angular acceleration of the center of mass; External forces (such as gravity); External torque; Predicting rigid body acceleration using linear extrapolation

[0029]

[0030] Predicting rigid body displacement and velocity in the next time step using the frog-leap algorithm:

[0031]

[0032]

[0033]

[0034] The superscript n represents the nth time step, and p represents the prediction.

[0035] According to the present invention, further, the flow field velocity in step 3... In the boundary conditions of the object surface ( The linear velocity of the rigid body's center of mass is contained on the mesh surface. and angular velocity ,

[0036]

[0037] in and Representing point i within the computational domain and on the object's boundary, defined as follows: These are the convection and pressure terms in the momentum equation, where Let be the fluid velocity in the i-th grid of the flow field. Let be the mesh velocity caused by the deformation of the i-th mesh. For pressure, Gradient operator.

[0038] According to the present invention, step 11 further assigns pressure boundary conditions to the finite element structural solution, maps the pressure field in step 8 to the mesh used for structural solution, and maps the pressure and shear force values ​​at the center of the finite volume mesh of fluid calculation to the structural solver.

[0039] According to the present invention, the target interpolation grid center is at point a, and is indicated in red. The interpolation first finds the grid where the nearest 0 is located at the center point a, and then finds the grids where faces 1 to 11 are adjacent to that grid.

[0040] According to the present invention, the approximate function is further expanded at point a using a first-order Taylor series. f ,but ; Calculate using the least squares method ; By minimizing the residuals in the following equation Solve The expression is used to interpolate the target difference grid a; Among them, the interpolation contribution cell grid of the known solution i Represented in blue, its center value is f i .

[0041] According to the present invention, in the process of solving the flow field, the pressure at each time step is interpolated and recorded to obtain the time-varying pressure boundary conditions required for structural calculation.

[0042] According to the present invention, further, the ship's center of mass in step 12 Translation and rotation Consistent with the calculation in step 9.

[0043] According to the present invention, further, a spring is provided in the step, with one end of the spring connected to the center of gravity of the hull, such that the deformation of the spring is equal to the displacement of the center of gravity of the hull; if the spring is compressed or stretched by a certain distance, the center of gravity of the hull will also translate by the same distance, and the displacement of the center of gravity of the hull is... ,in k Let F be the stiffness of the spring and F be the external force.

[0044] According to the present invention, further, when the external force F is a very large force, and the stiffness... k When it is also very large, then there is In this process, the forced translation constraint of the ship's center of mass is achieved by controlling the changes in external forces.

[0045] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention aims to address the challenge of simultaneously achieving both high precision and high efficiency in the structural deformation and response of ship hulls under wave loads. It employs a unidirectional fluid-structure interaction method with finite volume discretization of the fluid environment computational domain to calculate fluid loads, enabling precise prediction of nonlinear loads. Structural calculations utilize plate and beam elements to discretize the three-dimensional hull using finite element methods, ensuring computational accuracy.

[0046] In this invention, structural deformation is decomposed into two parts: the displacement of the object's center of mass and the elastic deformation of the object's other positions relative to the center of mass. The purpose of this decomposition is to separately handle the additional mass effects caused by the object's motion and elastic deformation. For a relatively rigid structure like a ship, the displacement of its center of mass is one to two orders of magnitude larger than the deformation of the hull relative to the center of mass. Therefore, most of the additional mass is caused by the translation and rotation of the hull as a complete rigid body. The influence of the structural deformation relative to the center of mass on the flow field is small, and the impact of this elastic deformation's additional mass effect on the calculation can be ignored.

[0047] This invention assigns the rigid body motion of the structure to the flow field solver for solution. By introducing additional mass boundary conditions into the flow field solver, the interaction between rigid body motion and the flow field is considered. This method incorporates the rigid body displacement as a parameter into the boundary conditions for solving the flow field momentum and pressure equations, thus taking into account the additional mass effect caused by rigid body motion and eliminating the adverse effects of the additional mass on the calculation. Subsequently, the rigid body displacement and the boundary forces induced by the flow field are directly passed to the structural solver as boundary conditions.

[0048] This method solves the computational divergence problem caused by the added mass, thereby eliminating the bidirectional data exchange and iteration process between the fluid and the structure and improving computational efficiency.

[0049] The improved computational efficiency frees the structure from the limitation of using only one-dimensional hull beam models with lower computational resource requirements, making it possible to calculate the hull finite element method based on a detailed plate structure model. Simultaneously, fluid dynamics calculations can also employ the high-precision CFD finite volume method, achieving high-precision fluid-structure interaction solutions for local plate structure deformations and stresses in ships. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the grid interpolation method of the present invention; Figure 2 This is a schematic diagram of the ship pitching motion time history data according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the ship heave motion time history data according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the ship's roll motion time history data according to an embodiment of the present invention; Figure 5This is a schematic diagram showing the wave free surface calculation results of a ship navigating in oblique waves according to an embodiment of the present invention. Figure 6 This is a schematic diagram of the pressure interpolation results at the stern of a ship according to an embodiment of the present invention; Figure 7 This is a Mises stress cloud diagram of the stern section of a ship according to an embodiment of the present invention; Figure 8 This is a schematic diagram of the lateral deformation time-history curves of different ribs at the propulsion shaft position of the stern section of a ship according to an embodiment of the present invention. Detailed Implementation

[0051] To make the content of this invention more apparent and understandable, the following detailed description is provided in conjunction with preferred embodiments and accompanying drawings.

[0052] This application provides a unidirectional fluid-structure interaction method based on an additional mass boundary, comprising the following steps: Step 1: Predict the velocity and acceleration of the rigid body. Rigid body motion is defined by rotation and translation about its center of mass. To describe rigid body motion, the following physical quantities are defined: : Rigid body mass; : Coordinates of a point on the surface of a rigid body; : Rigid body density; : Matrix of rotational inertia; : Coordinates of the centroid position; : Angle of rotation of the center of mass; : Center of mass position and velocity; : A matrix whose column vectors are the principal axes of inertia; : Center-of-mass acceleration; : angular acceleration of the center of mass; External forces (such as gravity); External torque; Predicting rigid body acceleration using linear extrapolation (1) (2) Predicting rigid body displacement and velocity in the next time step using the frog-leap algorithm: (3) (4) (5) (6) Where the superscript n represents the nth time step, and p represents the prediction; Step 2, using the predicted values Update the grid coordinates of the object's position: (7); Step 3, update the flow field velocity The velocity is in the boundary conditions of the object surface ( The linear velocity of the rigid body's center of mass is contained on the mesh surface. and angular velocity Therefore, the influence of rigid body motion on the velocity field should be considered. (8) (9) in and Representing point i within the computational domain and on the object's boundary, defined as follows: These are the convection and pressure terms in the momentum equation, where Let be the fluid velocity in the i-th grid of the flow field. Let be the mesh velocity caused by the deformation of the i-th mesh. For pressure, Gradient operator; Step 4: Update the pressure and rigid body acceleration , The pressure is in the boundary conditions of the object surface (where the pressure is in the boundary conditions of the object surface). (On the mesh surface) contains the acceleration along the line of the rigid body's center of mass. and angular acceleration Therefore, the influence of rigid body acceleration on the pressure field is considered. (10) in and These are the forces and moments acting on a rigid body caused by flow field pressure and friction. D is defined as ,in (11) (12) (13) (14) in The additional viscous characteristic length parameter is defined as follows: , ,in The kinematic viscosity of water; For those involving vectors Cross product matrix ; Step 5: Update the rigid body motion state using the predicted rigid body motion state. , (15) , (16); Step 6, Update the object surface mesh ; Step 7: Update the flow field velocity to the (n+1)th time step. This step is again in the boundary conditions of the object surface ( The linear velocity of the rigid body's center of mass is contained on the mesh surface. and angular velocity Therefore, the influence of rigid body motion on the velocity field should be considered. (17) (18); Step 8, Update and rigid body acceleration , At time step n+1, the pressure is again applied to the boundary conditions of the object surface. (On the mesh surface) contains the acceleration along the line of the rigid body's center of mass. and angular acceleration Therefore, the influence of rigid body acceleration on the pressure field is considered. (19); Step 9: Update the rigid body motion state to the (n+1)th time step. (20) (twenty one) (twenty two) (twenty three) (twenty four); Step 10, Update the object surface mesh And return to step 1 to proceed to the next moment of calculation until the calculation is complete; Step 11, Pressure Field Mapping Interpolation; This step assigns pressure boundary conditions to the finite element structure solution, maps the pressure field from Step 8 to the mesh used for the structure solution, and maps the pressure and shear force values ​​at the center of the finite volume mesh of the fluid calculation to the structure solver. Figure 1 shows a schematic diagram of the mesh interpolation, where the target interpolation mesh center is at point a and is indicated in red. The interpolation contribution cell mesh of the known solution is also shown. i Represented in blue, its center value is f i Interpolation first finds the grid closest to center point a (the grid containing 0), and then finds the faces adjacent to that grid (the grids containing 1 to 11). To perform interpolation at grid position a, an approximate function is expanded at point a using a first-order Taylor series. f ,but Then, the least squares method is used to calculate. By minimizing the residual in the following formula Solve The expression; in the process of solving the flow field, the pressure at each time step is interpolated and recorded to obtain the time-varying pressure boundary conditions required for structural calculation; Step 12, establish forced displacement constraints. This step assigns motion boundary conditions to the rigid body's center of mass in the finite element structural solution; the purpose of this step is to make the ship's center of mass in the structural calculation... Translation and rotation Consistent with the calculation in step 9; in this step, a spring is set up, with one end connected to the ship's center of mass, so that the spring's deformation is equal to the displacement of the ship's center of mass; if the spring is compressed or stretched by a certain distance, the ship's center of mass will also translate by the same distance. The displacement of the ship's center of mass can be expressed as... ,in k Let F be the stiffness of the spring and F be the external force. When the external force F is a very large force, and the stiffness... k When it is also very large, then there is As can be seen from this formula, when both the spring stiffness and the external force are large, the effect of the ship's mass on the spring can be ignored. Forced translational constraint on the ship's center of mass can be achieved by controlling the change in the external force. The principle of rotational constraint is similar to that of translational constraint. Step 13: Begin the finite element structural solution and complete the calculation to obtain the stress and deformation of the hull structure at different times.

[0053] This invention addresses the problem that the solution of fluid-structure interaction (FSI) for ship hulls requires iterative methods to ensure computational convergence, which leads to huge computation time and excessive computational cost. It proposes a unidirectional FSI method based on an additional mass boundary to calculate the deformation and stress of the ship hull structure in waves.

[0054] This method considers the additional mass caused by structural deformation as consisting of two parts: the displacement of the rigid body at the center of mass and the elastic deformation relative to the center of mass. The solution for the rigid body displacement is incorporated into the flow field solution, where the interaction between the rigid body and the fluid is considered by introducing additional mass boundary conditions. This boundary method introduces the rigid body displacement as an independent variable into the boundary conditions for solving the flow field momentum and pressure equations, fully considering the influence of rigid body motion during the flow field velocity and pressure solutions, thus resolving the computational divergence problem caused by additional mass. For the additional mass caused by deformation relative to the center of mass, since the ship structure has high stiffness and its displacement at the center of mass is much larger than the relative deformation, it is neglected.

[0055] This invention is based on the additional mass boundary method, which enables the unidirectional iteration between the flow field and the solid field to meet the computational convergence requirements. It eliminates the need for repeated iterations between the solutions of the flow field and the structural field, thereby effectively improving computational efficiency. This makes it possible to perform fluid-structure interaction calculations on ship hull structures based on complex plate frame finite element models, and realizes the ability to simulate fluid-structure interaction across the entire ship at all scales.

[0056] The invention will be further described below with reference to the accompanying drawings and examples. The following is the process of predicting the stern deformation of a ship moving on oblique waves using this method.

[0057] First, the motion of the ship is predicted using steps 1 to 10 above, and schematic diagrams of the ship's trim, heave, and roll data are obtained, as shown in Figures 2, 3, and 4; the free surface of the waves during the simulation process is shown in Figure 5.

[0058] According to the method in step 11, the hull pressure obtained from the flow field calculation is mapped, and the stern pressure mapping result is shown in Figure 6.

[0059] After completing the forced motion settings in step 12, step 13 can be performed to conduct finite element calculations on the structure. The Mises stress distribution at the stern of a certain ship is shown in Figure 7. After post-processing, the time-history curves of the lateral displacement of the stern at different rib positions can be obtained as follows: Figure 8 As shown.

[0060] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any form or substance. It should be noted that those skilled in the art can make various improvements and additions without departing from the principles of the present invention, and these improvements and additions should also be considered within the scope of protection of the present invention. Any equivalent changes, modifications, and evolutions made by those skilled in the art to the above embodiments based on the essential technology of the present invention shall still fall within the scope of the technical solution of the present invention.

Claims

1. A unidirectional fluid-structure interaction method based on an additional mass boundary, comprising the following steps: Step 1: Predict the velocity and acceleration of the rigid body. Step 2, using the predicted values Update the grid coordinates of the object's position: ； Step 3, update the flow field velocity ; Step 4: Update the pressure and rigid body acceleration , The pressure is in the boundary conditions of the object surface (where the pressure is in the boundary conditions of the object surface). (On the mesh surface) contains the acceleration along the line of the rigid body's center of mass. and angular acceleration , ， in and These are the forces and moments acting on a rigid body caused by flow field pressure and friction. D is defined as ,in, ， in The additional viscous characteristic length parameter is defined as follows: , ,in The kinematic viscosity of water; For those involving vectors Cross product matrix ; Step 5: Update the rigid body motion state using the predicted rigid body motion state. ， ， ； Step 6, Update the object surface mesh ; Step 7: Update the flow field velocity to the (n+1)th time step. This step is again in the boundary conditions of the object surface ( The linear velocity of the rigid body's center of mass is contained on the mesh surface. and angular velocity , ； Step 8, Update and rigid body acceleration , At time step n+1, the pressure is again applied to the boundary conditions of the object surface. (On the mesh surface) contains the acceleration along the line of the rigid body's center of mass. and angular acceleration , ； Step 9: Update the rigid body motion state to the (n+1)th time step. ； Step 10, Update the object surface mesh And return to step 1 to proceed to the next moment of calculation until the calculation is complete; Step 11: Pressure field mapping interpolation to obtain the time-varying pressure boundary conditions required for structural calculation; Step 12: Establish forced displacement constraints to assign motion boundary conditions to the rigid body's center of mass in the finite element structural solution; Step 13: Begin the finite element structural solution and complete the calculation to obtain the stress and deformation of the hull structure at different times.

2. The unidirectional fluid-structure interaction method based on an additional mass boundary as described in claim 1, characterized in that, The rigid body motion in step 1 is defined by rotation and translation about its center of mass. To describe the rigid body motion, the following physical quantities are defined: : Rigid body mass; : Coordinates of a point on the surface of a rigid body; : Rigid body density; : Matrix of rotational inertia; : Coordinates of the centroid position; : Angle of rotation of the center of mass; : Center of mass position and velocity; : A matrix whose column vectors are the principal axes of inertia; : Center-of-mass acceleration; : angular acceleration of the center of mass; External forces (such as gravity); External torque; Predicting rigid body acceleration using linear extrapolation Predicting rigid body displacement and velocity in the next time step using the frog-leap algorithm: The superscript n represents the nth time step, and p represents the prediction.

3. The unidirectional fluid-structure interaction method based on an additional mass boundary as described in claim 1, characterized in that, The flow field velocity in step 3 In the boundary conditions of the object surface ( The linear velocity of the rigid body's center of mass is contained on the mesh surface. and angular velocity , in and Representing point i within the computational domain and on the object's boundary, defined as follows: These are the convection and pressure terms in the momentum equation, where Let be the fluid velocity in the i-th grid of the flow field. Let be the mesh velocity caused by the deformation of the i-th mesh. For pressure, Gradient operator.

4. The unidirectional fluid-structure interaction method based on an additional mass boundary as described in claim 1, characterized in that, Step 11 assigns pressure boundary conditions to the finite element structure solution, maps the pressure field in step 8 to the mesh used for the structure solution, and maps the pressure and shear force values ​​at the center of the finite volume mesh of the fluid calculation to the structure solver.

5. The unidirectional fluid-structure interaction method based on an additional mass boundary as described in claim 4, characterized in that, The target interpolation grid center is at point a, and is indicated in red. The interpolation first finds the grid where the nearest 0 is located at the center point a, and then finds the grids where faces 1 to 11 are adjacent to that grid.

6. The unidirectional fluid-structure interaction method based on an additional mass boundary as described in claim 5, characterized in that, The approximate function is expanded at point a using a first-order Taylor series. f ,but ; Calculate using the least squares method ; By minimizing the residuals in the following equation Solve The expression is used to interpolate the target difference grid a; Among them, the interpolation contribution cell grid of the known solution i Represented in blue, its center value is f i .

7. The unidirectional fluid-structure interaction method based on an additional mass boundary as described in claim 5 or 6, characterized in that, During the flow field solution process, the pressure at each time step is interpolated and recorded to obtain the time-varying pressure boundary conditions required for structural calculation.

8. The unidirectional fluid-structure interaction method based on an additional mass boundary as described in claim 1, characterized in that, The ship's center of gravity in step 12 Translation and rotation Consistent with the calculation in step 9.

9. The unidirectional fluid-structure interaction method based on an additional mass boundary as described in claim 8, characterized in that, In the aforementioned steps, a spring is used, with one end connected to the ship's center of gravity, such that the spring's deformation equals the displacement of the ship's center of gravity. If the spring is compressed or stretched by a certain distance, the ship's center of gravity will also shift by the same distance, resulting in a displacement of [missing information]. ,in k Let F be the stiffness of the spring and F be the external force.

10. The unidirectional fluid-structure interaction method based on an additional mass boundary as described in claim 9, characterized in that, When the external force F is a very large force, and the stiffness k When it is also very large, then there is In this process, the forced translation constraint of the ship's center of mass is achieved by controlling the changes in external forces.

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