A Smooth Finite Element Adjustable Damped Implicit Integral Algorithm for Transient Acoustic Scattering of Underwater Targets

Abstract

This invention discloses a smoothed finite element adjustable damping implicit integral algorithm for underwater transient acoustic scattering, belonging to the field of underwater transient acoustic scattering numerical simulation technology. First, the computational domain of the underwater transient acoustic scattering field is discretized into a standard quadrilateral element mesh to construct an interpolation scheme for the sound pressure field. Then, each quadrilateral element is divided into multiple smooth domains, and the smoothed sound pressure gradient matrix is ​​obtained through acoustic generalized gradient smoothing technology. Combining differential control equations, the virtual displacement principle, and the Galerkin weighted residual method, the system matrix equation is constructed. An adjustable damping implicit time integral algorithm is used to complete the time-domain discretization, and the numerical results of the transient acoustic scattering field in the entire time domain are obtained through recursive solution. This invention can soften the "overly stiff" stiffness matrix to reduce spatial discretization errors, suppress high-frequency errors through adjustable numerical damping matching, and achieve coordinated control of spatiotemporal errors. Under the same mesh, its accuracy is superior to the standard finite element method, providing an efficient and reliable solution for underwater transient acoustic scattering engineering simulation.

Description

Technical Field

[0001] This invention relates to the field of underwater transient acoustic scattering numerical simulation technology, and in particular to a smooth finite element adjustable damped implicit integral algorithm for underwater target transient acoustic scattering. Background Technology

[0002] Underwater transient acoustic scattering is a core scientific problem in underwater acoustics research. It focuses on analyzing the transient scattering sound field mechanism generated by targets such as underwater vehicles, bottom mines, underwater vehicles, and seabed geological bodies under the action of short-pulse acoustic signals. The relevant results are the core theoretical support for underwater target detection, identification, and countermeasure technologies, and are also widely used in marine resource exploration, non-destructive testing of underwater engineering facilities, underwater acoustic communication and navigation, and other fields.

[0003] The finite element method (FEM) is currently the mainstream numerical method for handling transient acoustic scattering problems of underwater targets, and it has good adaptability in problems with complex geometries and non-uniform media. However, the standard FEM has inherent defects in solving acoustic wave problems: First, the acoustic stiffness matrix formed during the discretization process suffers from "numerical overstiffness," with the calculated stiffness being much greater than the actual stiffness of the physical system, leading to significant numerical dispersion errors, which increase rapidly with increasing calculation frequency. Second, to control numerical errors, a mesh criterion of "more than 6 elements per wavelength" must be met. High-frequency calculations require global mesh refinement, resulting in an exponential increase in computational degrees of freedom, leading to the "curse of dimensionality," significantly increasing computational costs, and even making it impossible to complete the solution. Third, the numerical damping of existing time integration algorithms is not adjustable, and it is impossible to match and suppress the spatial discretization error that increases with frequency. The coupling and superposition of spatial and temporal discretization errors further reduce the accuracy and reliability of transient calculation results.

[0004] Although the smooth finite element method can alleviate the problem of "over-stiffness" of the stiffness matrix and reduce spatial discretization error through gradient smoothing techniques, there are still significant numerical errors in the high-frequency band. Furthermore, existing implicit time integration algorithms cannot achieve dynamic control of numerical damping, making it difficult to match and suppress spatial discretization errors, and thus failing to fully leverage the accuracy advantages of the smooth finite element method. Summary of the Invention

[0005] The purpose of this invention is to propose a smooth finite element adjustable damped implicit integral algorithm for transient acoustic scattering of underwater targets. It addresses the shortcomings of existing technologies, such as large numerical dispersion error, low high-frequency calculation accuracy, and strong grid dependence of the standard finite element method, as well as the inability of the time integral algorithm to adjust the numerical damping and suppress spatial discretization error. This invention achieves coordinated control of spatial and temporal discretization errors, and significantly improves the calculation accuracy and reliability of transient acoustic scattering field under the same grid conditions.

[0006] To achieve the above objectives, this invention provides a smooth finite element adjustable damped implicit integral algorithm for transient acoustic scattering of underwater targets, comprising the following steps: Step S1: Discretize the spatial computational domain of the transient acoustic scattering field of the underwater target into a standard quadrilateral cell grid, and construct an acoustic pressure field interpolation scheme based on the quadrilateral cell; Step S2: Divide each quadrilateral unit into several smooth regions, and smooth each smooth region using acoustic generalized gradient smoothing technology to obtain the smoothed sound pressure gradient field. Step S3: Numerically integrate the smoothed sound pressure gradient field using the Gaussian integral formula to obtain the smoothed sound pressure gradient matrix; Step S4: Based on the smooth acoustic pressure gradient matrix and the partial differential control equations of underwater transient acoustic scattering, and combining the virtual displacement principle and the Galerkin weighted residual method, construct the system matrix equations for the underwater transient acoustic scattering problem. Step S5: Use the adjustable damping implicit time integration algorithm to discretize the system matrix equation in the time domain to obtain the recursive solution format after time domain discretization; Step S6: Based on the initial conditions, solve the discretized system matrix equations using a recursive solution scheme to obtain the numerical calculation results of the transient acoustic scattering field of the underwater target in the entire time domain; Step S7: Analyze the numerical calculation results, compare the calculation accuracy of different algorithms, and complete the solution and characteristic analysis of the transient acoustic scattering field of the underwater target.

[0007] Preferably, in step S1, the method for constructing the sound pressure field interpolation format is as follows: The sound pressure interpolation format at any point within each quadrilateral element is as follows: ; in, This represents the sound pressure interpolation result at any point within the quadrilateral element. For the quadrilateral unit number Interpolation shape function for each node, For the first Unknown node sound pressure level of each node; The sound pressure interpolation format at any point within the entire spatial computational domain is expressed as follows: ; in, This represents the total number of nodes in the quadrilateral element within the spatial computational domain. This is the sound pressure interpolation result at any point within the computation domain.

[0008] Preferably, in step S2, each quadrilateral unit is divided into 4 smooth domains. The specific process of the acoustic generalized gradient smoothing technique is as follows: The constitutive relation between sound pressure and sound particle vibration velocity in the sound field is expressed as follows: ; in, The imaginary unit, The density of the underwater acoustic fluid medium. The angular frequency of the sound wave The velocity of the sound particle vibration; The acoustic particle vibration velocity field within each smoothed domain is smoothed, and the expression for the smoothed acoustic particle vibration velocity field is as follows: ; in, The velocity field of the smoothed acoustic particles. The original sound particle vibration velocity field, For the spatial region of a smooth domain, It is a smooth function and satisfies ; The smoothing function used is the constant smoothing function, expressed as follows: ; in, For smooth regions The area; Using Green's formula, the smoothed sound particle vibration velocity field is converted into a sound pressure gradient-related form, as shown in the following expression: ; in, For the boundary of a smooth region, Let be the outward normal unit vector of the boundary of the smooth domain; For a two-dimensional acoustic problem, the outward normal unit vector The expression is as follows: ; in, The outward normal unit vector along directional components, The outward normal unit vector along The directional component.

[0009] Preferably, in step S3, the calculation process of the smooth sound pressure gradient matrix is ​​as follows: Based on the spatial computational domain-based sound pressure field interpolation scheme, the smoothed sound particle vibration velocity field is expressed as: ; in, For the first The smooth acoustic pressure gradient matrix corresponding to each node; The smooth sound pressure gradient matrix is ​​calculated using the Gaussian integral formula, as shown below: ; in, The total number of line segments that define the boundary of the smooth domain. The number of Gaussian integration points set on each boundary segment, when using a one-point Gaussian integral. , Let the spatial location of the Gaussian integration point be... These are the weighting coefficients corresponding to the Gaussian integration points.

[0010] Preferably, in step S4, the process of constructing the system matrix equation is as follows: The partial differential governing equations for underwater transient sound propagation are expressed as follows: ; in, The speed of sound wave propagation underwater. sound pressure Regarding time The second derivative; Based on the principle of virtual displacement, the weak integral form of the governing equations is established, as follows: ; in, This represents the imaginary displacement of the sound pressure. By using integration by parts and Gauss's divergence theorem, the weak integral form is transformed into: ; in, The global boundary of the spatial computational domain. The unit vector of the outward normal to the domain boundary is used for computation. By substituting the sound pressure field interpolation scheme into the above formula using the Galerkin weighted residual method, the system matrix equation is obtained, as shown below: ; in, for The sound pressure vector of each unknown node. Let be the second derivative vector of the nodal sound pressure vector with respect to time; The system quality matrix, A vector composed of nodal interpolation shape functions; Here is the system's smooth stiffness matrix. The smooth sound pressure gradient matrix; For the system load vector, This is used to compute the normal acoustic particle velocity vector at the boundary node of the domain.

[0011] Preferably, in step S5, the time-domain discretization process of the adjustable damped implicit time integration algorithm is as follows: A complete time integration step It is broken down into two sub-steps, the first sub-step taking a duration of The second sub-step duration is ,in For time parameters, ,and , These are numerical damping control parameters. By adjusting The integer value controls the magnitude of the discrete numerical damping in the time domain; First step At time t, the update format for the sound pressure vector and its time derivatives is as follows: ; in, , , They are respectively The nodal sound pressure vector, the first time derivative vector of sound pressure, and the second time derivative vector of sound pressure at time t. , , They are respectively The vector corresponding to each time step; Second sub-step At time t, the update format for the sound pressure vector and its time derivatives is as follows: ; in, , , They are respectively The vector corresponding to each time step; and Let be the time integration parameter, and satisfy: ; based on , , The dynamic equilibrium equations at three moments: ; Constructing the recursive solution format after time-domain discretization: ; Among them, the equivalent stiffness matrix , ; , The equivalent load vector at the corresponding moment is calculated from the field vector and the system matrix at the current moment.

[0012] Preferably, in step S6, the recursive solution process of the system matrix equation is as follows: Step S61: Set the initial time The initial conditions, including the initial nodal sound pressure vector. The first time derivative of the initial sound pressure level Quantity, initial sound pressure level, second-order time derivative vector Set the time integration step size Numerical damping control parameters Total computation time; Step S62: Based on the field vector at the initial time, calculate using a recursive solution scheme. Nodal sound pressure vector at time 1 And solve for the value at that moment using the update format of the first sub-step. and ; Step S63: ... Substituting the field vector at time step into the recursive solution format, calculate... Nodal sound pressure vector at time 1 And solve for the value at that moment using the update format of the second sub-step. and ; Step S64: with Using time as the new initial time, repeat steps S62-S63 to complete the recursive calculation for all time steps in the entire time domain, and obtain the numerical calculation results of the transient acoustic scattering field of the underwater target in the entire time domain.

[0013] Preferably, in step S6, for the transient acoustic scattering problem of the underwater target to be solved, the characteristics of the incident sound source are matched, and the quadrilateral element mesh size, time integration step size, and numerical damping control parameters that match the dominant frequency of the sound source are selected. Among them, numerical damping control parameters The value of is positively correlated with the spatial discretization error; the sparser the spatial grid, the higher the computation frequency. The smaller the value, the greater the time-domain numerical damping, thus achieving matched suppression of spatial discrete errors.

[0014] Preferably, in step S7, the result analysis includes analysis of the spatial distribution characteristics of the acoustic scattering field, analysis of the temporal sound pressure response characteristics, and a comparative analysis of the calculation accuracy with the standard finite element method. The "overly stiff" stiffness matrix of the standard finite element method is softened by acoustic generalized gradient smoothing technology to reduce the numerical dispersion error of spatial discretization. At the same time, numerical damping positively correlated with the calculation frequency is introduced by an adjustable damping implicit time integration algorithm to suppress the spatial discretization error in the high-frequency band, thereby achieving coordinated control of spatial and temporal discretization errors. Under the same grid conditions, the transient acoustic scattering field calculation results with higher accuracy than those of the standard finite element method are obtained.

[0015] Therefore, the present invention employs the above-mentioned smooth finite element adjustable damped implicit integral algorithm for transient acoustic scattering of underwater targets, which has the following advantages: (1) The present invention uses acoustic generalized gradient smoothing technology to specifically "soften" the acoustic stiffness matrix of the standard finite element method which is "overly stiff", so that the stiffness of the discrete system is closer to the stiffness of the real physical system. This reduces the numerical dispersion error caused by spatial discretization from the root, greatly alleviates the dependence of numerical calculation on grid density, and has higher spatial calculation accuracy under the same grid conditions. (2) The present invention uses an adjustable damping implicit time integration algorithm for time domain discretization. The magnitude of time domain numerical damping can be dynamically adjusted by numerical damping control parameters. The numerical damping increases with the increase of calculation frequency, which can accurately match and suppress the spatial discretization error that increases with the increase of frequency, realize the coordinated control of spatial and time discretization errors, and further improve the calculation accuracy of the whole frequency band and the whole time domain. (3) This invention deeply integrates smooth finite element spatial discretization with adjustable damped implicit time integral time domain discretization. The algorithm process is standardized and highly adaptable, and can efficiently handle the transient acoustic scattering problem of complex underwater targets. While ensuring the accuracy of calculation, it reduces the calculation cost and provides an efficient and reliable numerical solution for transient acoustic scattering simulation in engineering fields such as underwater target detection and marine resource exploration.

[0016] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0017] Figure 1 This is a flowchart of a smooth finite element adjustable damped implicit integral algorithm for transient acoustic scattering of an underwater target in an embodiment of the present invention; Figure 2 This is a schematic diagram of the quadrilateral unit and smooth domain division in an embodiment of the present invention; Figure 3 This is a schematic diagram of the shape function values ​​of the nodes and integration points of the standard quadrilateral element in an embodiment of the present invention; Figure 4 This is a schematic diagram of the shape function values ​​of the quadrilateral unit nodes and integration points of the two smooth domains in an embodiment of the present invention; Figure 5 This is a schematic diagram of the shape function values ​​of the quadrilateral unit nodes and integration points divided into three smooth regions in an embodiment of the present invention; Figure 6 This is a schematic diagram of the shape function values ​​of the quadrilateral unit nodes and integration points in the four smooth domain divisions of this invention. Figure 7 This is a schematic diagram of the computational domain for the transient acoustic scattering problem of an underwater submarine model in an embodiment of the present invention; Figure 8 This is a schematic diagram of the quadrilateral cell mesh division of the computational domain in an embodiment of the present invention; Figure 9 Transient sound field distribution cloud maps at different times obtained by the standard finite element-implicit time integration algorithm; Figure 10 The transient sound field distribution cloud maps at different times are calculated by the algorithm of this invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0019] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0020] Example like Figure 1-10 As shown, this embodiment proposes a smooth finite element adjustable damped implicit integral algorithm for transient acoustic scattering of underwater targets. This embodiment takes the transient acoustic scattering problem of an underwater submarine model under point sound source incidence as the solution object, and provides a detailed description of the method of the present invention. Figure 7 As shown, the spatial computational domain in this embodiment is a square domain with a side length of 1500m. The submarine model is located at the geometric center of the computational domain, and the point sound source is located at the lower left vertex of the computational domain, capable of emitting short-duration pulsating sound waves. The entire computational domain is discretized into a standard quadrilateral cell mesh, and the mesh division is as follows: Figure 8 As shown.

[0021] like Figure 1 As shown, the smooth finite element-Newmark calculation method for transient acoustic scattering of underwater targets in this embodiment specifically includes the following steps: Step S1: Discretize the square spatial computational domain of the transient acoustic scattering field of the underwater target into a standard quadrilateral element mesh. Based on the bilinear nodal interpolation shape function of the quadrilateral element, construct the acoustic pressure field interpolation scheme. Within each quadrilateral element, the acoustic pressure interpolation scheme at any point is as follows: ; in, This represents the sound pressure interpolation result at any point within the quadrilateral element. For the quadrilateral unit number Interpolation shape function for each node, For the first Unknown node sound pressure level of each node Spatial location coordinates; The sound pressure interpolation format at any point within the entire spatial computational domain is expressed as follows: ; in, This represents the total number of nodes in the quadrilateral element within the spatial computational domain. This is the sound pressure interpolation result at any point within the computation domain.

[0022] Step S2: Divide each quadrilateral unit into 4 smooth regions, and perform acoustic generalized gradient smoothing for each smooth region. The specific process is as follows: Based on the constitutive relationship between sound pressure and sound particle vibration velocity in the sound field: ; in, The imaginary unit, The density of the underwater acoustic fluid medium. The angular frequency of the sound wave The velocity of the sound particle vibration; The sound particle vibration velocity field within each smooth region is smoothed, and the smoothed sound particle vibration velocity field is as follows: ; in, The velocity field of the smoothed acoustic particles. The original sound particle vibration velocity field, For the spatial region of a smooth domain, It is a smooth function and satisfies ; The smooth function is specifically: ; in, For smooth regions The area; Combining Green's formula, the volume integral is transformed into a boundary integral, and the smoothed acoustic particle vibration velocity field is transformed into: ; In the formula, For the boundary of a smooth region, Let be the outward normal unit vector of the smooth domain boundary. For the two-dimensional acoustic problem in this embodiment, , , They are the outward normal unit vectors along , The directional component.

[0023] Step S3: Based on the sound pressure field interpolation scheme, the smoothed sound particle vibration velocity field is represented as: ; in, For the first The smooth acoustic pressure gradient matrix corresponding to each node; The smooth sound pressure gradient matrix is ​​calculated using the Gaussian integral formula: ; in, The number of line segments that divide the boundary of the smooth region. The number of Gaussian integration points set on each boundary segment is taken in this embodiment. , Let the spatial location of the Gaussian integration point be... These are the weighting coefficients corresponding to the Gaussian integration points.

[0024] Step S4: Based on the smooth acoustic pressure gradient matrix and the partial differential governing equations for underwater transient acoustic scattering, and combining the virtual displacement principle and the Galerkin weighted residual method, construct the system matrix equations for the underwater transient acoustic scattering problem. The expression for the partial differential governing equations for underwater transient sound propagation is as follows: ; in, For the Laplace operator, The speed of sound in water is taken as 1500 m / s. sound pressure Regarding time The second derivative; Based on the principle of virtual displacement, the weak integral form of the governing equations is established, and its expression is: ; in, This represents the imaginary displacement of the sound pressure. By using integration by parts and Gauss's divergence theorem, the weak integral form is transformed into: ; in, The global boundary of the spatial computational domain. The unit vector of the outward normal to the domain boundary is used for computation. Using the Galerkin weighted residual method, substituting the sound pressure field interpolation scheme into the above formula, we obtain the system matrix equation, which is expressed as: ; in, for The sound pressure vector of each unknown node. Let be the second derivative vector of the nodal sound pressure vector with respect to time; The system quality matrix, A vector composed of nodal interpolation shape functions; Here is the system's smooth stiffness matrix. The smooth sound pressure gradient matrix; The system load vector is determined by the boundary conditions of the sound source at the incident point. This is used to compute the normal acoustic particle velocity vector at the boundary node of the domain.

[0025] Step S5: Discretize the system matrix equations in the time domain using an adjustable damped implicit time integral algorithm. The specific process is as follows: A complete time integration step It is broken down into two sub-steps, the first sub-step taking a duration of The second sub-step duration is ,in For time parameters, ,and , These are numerical damping control parameters. By adjusting The value of the damping determines the magnitude of the discrete numerical damping in the time domain; First step At time t, the update format for the sound pressure vector and its time derivatives is as follows: ; in, , , They are respectively The nodal sound pressure vector, the first time derivative vector of sound pressure, and the second time derivative vector of sound pressure at time t. , , They are respectively The vector corresponding to each time step; Second sub-step At time t, the update format for the sound pressure vector and its time derivatives is as follows: ; in, , , They are respectively The vector corresponding to each time step; and Let be the time integration parameter, and satisfy: ; based on , , The dynamic equilibrium equations at three moments: ; Constructing the recursive solution format after time-domain discretization: ; Among them, the equivalent stiffness matrix , ; , The equivalent load vector at the corresponding moment is calculated from the field vector and the system matrix at the current moment: ; .

[0026] Step S6: Based on the above recursive scheme, complete the full-time domain numerical solution. The specific process is as follows: Step S61: Set the initial time The initial conditions, including the initial nodal sound pressure vector. Initial sound pressure first-order time derivative vector Initial sound pressure second-order time derivative vector Set the time integration step size s, numerical damping control parameters Total calculation time: 1.0s; Step S62: Based on The field vector at time t is calculated using a recursive solution scheme. Nodal sound pressure vector at time 1 And solve for the value at that moment using the update format of the first sub-step. and ; Step S63: ... Substituting the field vector at time step into the recursive solution format, calculate... Nodal sound pressure vector at time 1 And solve for the value at that moment using the update format of the second sub-step. and ; Step S64: with Using the time step as the new initial time step, repeat the above recursive steps to complete the calculation of 100 time steps, and obtain the numerical calculation results of the transient acoustic scattering field of the underwater target in the full time domain from 0 to 1.0s.

[0027] Step S7: Analyze the numerical calculation results, compare the differences between the results of different calculation methods, and complete the solution and characteristic analysis of the transient acoustic scattering problem of underwater targets. Based on the full-time domain numerical calculation results, extract the spatial distribution data of the transient acoustic scattering field at four times t=0.7s, 0.8s, 0.9s, and 1.0s, and compare the calculation results of the standard finite element-implicit time integration algorithm and the algorithm of this invention under the same grid and time step.

[0028] Figure 9 The transient sound field distribution cloud maps at different times obtained by the standard finite element method show that the calculation results have obvious non-physical oscillations, discontinuous sound pressure distribution, and serious numerical distortion. Figure 10 The image shows the instantaneous transient sound field distribution cloud map calculated by the algorithm of this invention. It can be seen that the sound field distribution is smooth and continuous, without spurious numerical oscillations, accurately capturing the transient characteristics of sound wave propagation and target scattering. Comparative results show that the algorithm of this invention reduces spatial discretization errors through acoustic generalized gradient smoothing technology, and suppresses high-frequency discretization errors through adjustable numerical damping matching. Under the same mesh conditions, its computational accuracy is far higher than that of the standard finite element method, demonstrating excellent numerical stability and engineering applicability.

[0029] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A smooth finite element adjustable damping implicit integration algorithm for transient acoustic scattering from underwater targets, characterized in that, Includes the following steps: Step S1: Discretize the spatial computational domain of the transient acoustic scattering field of the underwater target into a standard quadrilateral cell grid, and construct an acoustic pressure field interpolation scheme based on the quadrilateral cell; Step S2: Divide each quadrilateral unit into several smooth regions, and smooth each smooth region using acoustic generalized gradient smoothing technology to obtain the smoothed sound pressure gradient field. Step S3; The smoothed sound pressure gradient field was numerically integrated using the Gaussian integral formula to obtain the smoothed sound pressure gradient matrix. Step S4: Based on the smooth acoustic pressure gradient matrix and the partial differential control equations of underwater transient acoustic scattering, and combining the virtual displacement principle and the Galerkin weighted residual method, construct the system matrix equations for the underwater transient acoustic scattering problem. Step S5: Use the adjustable damping implicit time integration algorithm to discretize the system matrix equation in the time domain to obtain the recursive solution format after time domain discretization; Step S6: Based on the initial conditions, solve the discretized system matrix equations using a recursive solution scheme to obtain the numerical calculation results of the transient acoustic scattering field of the underwater target in the entire time domain; Step S7: Analyze the numerical calculation results, compare the calculation accuracy of different algorithms, and complete the solution and characteristic analysis of the transient acoustic scattering field of the underwater target.

2. The smooth finite element adjustable damping implicit integration algorithm for transient acoustic scattering from an underwater target of claim 1, wherein: In step S1, the method for constructing the sound pressure field interpolation format is as follows: The sound pressure interpolation format at any point within each quadrilateral element is as follows: ； in, This represents the sound pressure interpolation result at any point within the quadrilateral element. For the quadrilateral unit number Interpolation shape function for each node, For the first Unknown node sound pressure level of each node; The sound pressure interpolation format at any point within the entire spatial computational domain is expressed as follows: ； in, This represents the total number of nodes in the quadrilateral element within the spatial computational domain. This is the sound pressure interpolation result at any point within the computation domain.

3. The smooth finite element adjustable damped implicit integral algorithm for transient acoustic scattering of underwater targets according to claim 1, characterized in that: In step S2, each quadrilateral unit is divided into 4 smooth domains. The specific process of the acoustic generalized gradient smoothing technique is as follows: The constitutive relation between sound pressure and sound particle vibration velocity in the sound field is expressed as follows: ； in, The imaginary unit, The density of the underwater acoustic fluid medium. The angular frequency of the sound wave The velocity of the sound particle vibration; The acoustic particle vibration velocity field within each smoothed domain is smoothed, and the expression for the smoothed acoustic particle vibration velocity field is as follows: ； in, The velocity field of the smoothed acoustic particles. The original sound particle vibration velocity field, For the spatial region of a smooth domain, It is a smooth function and satisfies ; The smoothing function used is the constant smoothing function, expressed as follows: ； in, For smooth regions The area; Using Green's formula, the smoothed sound particle vibration velocity field is converted into a sound pressure gradient-related form, as shown in the following expression: ； in, For the boundary of a smooth region, Let be the outward normal unit vector of the boundary of the smooth domain; For a two-dimensional acoustic problem, the outward normal unit vector The expression is as follows: ； in, The outward normal unit vector along directional components, The outward normal unit vector along The directional component.

4. The smooth finite element adjustable damped implicit integral algorithm for transient acoustic scattering of underwater targets according to claim 3, characterized in that: In step S3, the calculation process of the smooth sound pressure gradient matrix is ​​as follows: Based on the spatial computational domain-based sound pressure field interpolation scheme, the smoothed sound particle vibration velocity field is expressed as: ； in, For the first The smooth acoustic pressure gradient matrix corresponding to each node; The smooth sound pressure gradient matrix is ​​calculated using the Gaussian integral formula, as shown below: ； in, The total number of line segments that define the boundary of the smooth domain. The number of Gaussian integration points set on each boundary segment, when using a one-point Gaussian integral. , Let the spatial location of the Gaussian integration point be... These are the weighting coefficients corresponding to the Gaussian integration points.

5. The smooth finite element adjustable damped implicit integral algorithm for transient acoustic scattering of underwater targets according to claim 4, characterized in that: In step S4, the specific process of constructing the system matrix equation is as follows: The partial differential governing equations for underwater transient sound propagation are expressed as follows: ； in, The speed of sound wave propagation underwater. sound pressure Regarding time The second derivative; Based on the principle of virtual displacement, the weak integral form of the governing equations is established, as follows: ； in, This represents the imaginary displacement of the sound pressure. By using integration by parts and Gauss's divergence theorem, the weak integral form is transformed into: ； in, The global boundary of the spatial computational domain. The unit vector of the outward normal to the domain boundary is used for computation. By substituting the sound pressure field interpolation scheme into the above formula using the Galerkin weighted residual method, the system matrix equation is obtained, as shown below: ； in, for The sound pressure vector of each unknown node. Let be the second derivative vector of the nodal sound pressure vector with respect to time; The system quality matrix, A vector composed of nodal interpolation shape functions; Here is the system's smooth stiffness matrix. The smooth sound pressure gradient matrix; For the system load vector, This is used to compute the normal acoustic particle velocity vector at the boundary node of the domain.

6. The smooth finite element adjustable damped implicit integral algorithm for transient acoustic scattering of underwater targets according to claim 5, characterized in that: In step S5, the time-domain discretization process of the adjustable damped implicit time integral algorithm is as follows: A complete time integration step It is broken down into two sub-steps, the first sub-step taking a duration of The second sub-step duration is ,in For time parameters, ,and , These are numerical damping control parameters. By adjusting The integer value controls the magnitude of the discrete numerical damping in the time domain; First step At time t, the update format for the sound pressure vector and its time derivatives is as follows: ； in, , , They are respectively The nodal sound pressure vector, the first time derivative vector of sound pressure, and the second time derivative vector of sound pressure at time t. , , They are respectively The vector corresponding to each time step; Second sub-step At time t, the update format for the sound pressure vector and its time derivatives is as follows: ； in, , , They are respectively The vector corresponding to each time step; and Let be the time integration parameter, and satisfy: ； based on , , The dynamic equilibrium equations at three moments: ； Constructing the recursive solution format after time-domain discretization: ； Among them, the equivalent stiffness matrix , ; , The equivalent load vector at the corresponding moment is calculated from the field vector and the system matrix at the current moment.

7. The smooth finite element adjustable damped implicit integral algorithm for transient acoustic scattering of underwater targets according to claim 6, characterized in that: In step S6, the recursive solution process of the system matrix equation is as follows: Step S61: Set the initial time The initial conditions, including the initial nodal sound pressure vector. The first time derivative of the initial sound pressure level Quantity, initial sound pressure level, second-order time derivative vector Set the time integration step size Numerical damping control parameters Total computation time; Step S62: Based on the field vector at the initial time, calculate using a recursive solution scheme. Nodal sound pressure vector at time 1 And solve for the value at that moment using the update format of the first sub-step. and ; Step S63: ... Substituting the field vector at time step into the recursive solution format, calculate... Nodal sound pressure vector at time 1 And solve for the value at that moment using the update format of the second sub-step. and ; Step S64: with Using time as the new initial time, repeat steps S62-S63 to complete the recursive calculation for all time steps in the entire time domain, and obtain the numerical calculation results of the transient acoustic scattering field of the underwater target in the entire time domain.

8. The smooth finite element adjustable damped implicit integral algorithm for transient acoustic scattering of underwater targets according to claim 1, characterized in that: In step S6, for the transient acoustic scattering problem of the underwater target to be solved, the characteristics of the incident sound source are matched, and the quadrilateral element mesh size, time integration step size and numerical damping control parameters that match the dominant frequency of the sound source are selected. Among them, numerical damping control parameters The value of is positively correlated with the spatial discretization error; the sparser the spatial grid, the higher the computation frequency. The smaller the value, the greater the time-domain numerical damping, thus achieving matched suppression of spatial discrete errors.

9. The smooth finite element adjustable damped implicit integral algorithm for transient acoustic scattering of underwater targets according to claim 1, characterized in that: In step S7, the result analysis includes the analysis of the spatial distribution characteristics of the acoustic scattering field, the analysis of the temporal sound pressure response characteristics, and the comparison analysis of the calculation accuracy with the standard finite element method. The "overly stiff" stiffness matrix of the standard finite element method is softened by the acoustic generalized gradient smoothing technique to reduce the numerical dispersion error of spatial discretization. At the same time, the numerical damping positively correlated with the calculation frequency is introduced by the adjustable damping implicit time integration algorithm to suppress the spatial discretization error in the high-frequency band, thereby achieving the coordinated control of spatial and temporal discretization errors. Under the same grid conditions, the transient acoustic scattering field calculation results with higher accuracy than those of the standard finite element method are obtained.

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