A high-precision enhanced radial point interpolation meshless calculation method with applications in computational acoustics problems

Abstract

The present invention discloses an application of a high-precision enhanced radial point interpolation gridless calculation method in computational acoustic problems, which relates to the application of grid calculation methods in the field of computational acoustic problems. First, the wave propagation problem domain is discretized into a series of scattered points, and the interpolation format of the general scalar field is constructed based on the radial basis function, and each scattered point interpolation basis function is derived; in order to improve the interpolation accuracy of the obtained interpolation format, a new node degree of freedom is constructed at each scattered point, and the node degree of freedom is a local numerical approximation composed of a local enhanced interpolation basis function and a coefficient to be determined. Based on the obtained local numerical approximation, a global interpolation format of the general scalar field is constructed under the premise of satisfying the unit decomposition characteristics. The final discrete system matrix equation is obtained, and the matrix equation is solved to obtain the sound pressure of any point within the entire acoustic problem calculation domain. The present invention realizes high-order interpolation without increasing unit nodes, which can reduce numerical calculation errors.

Description

[0001] Methodology

[0002] The present invention relates to the application of a grid computing method in the field of computational acoustics problems, and in particular to the application of a high-precision enhanced radial point interpolation gridless computing method in computational acoustics problems.

[0003] Background Methods

[0004] In today's society, noise pollution has become a serious environmental and social issue. It not only severely impacts people's daily lives, work, and studies, but also threatens their physical and mental health. Acoustic issues are also ubiquitous in engineering applications. In mechanical engineering, as people's daily lives improve, the quality and performance requirements for mechanical products are also increasing. Therefore, designing low-noise, high-performance products is a major concern for mechanical engineers. In architectural acoustics, ensuring optimal acoustic effects in parts of a building is a key concern for architectural engineers. In the petrochemical industry, the vibration and sound propagation of fluid pipelines are also a focus of attention.

[0005] Acoustic problems can only be solved analytically under extremely simple and special circumstances. However, in most real-world engineering problems, the topology of the problem domain is diverse, and the boundary conditions are even more complex and changeable. Analytical solutions are generally unavailable for these situations; in these cases, numerical methods are the only solution. Among the various numerical methods used to solve acoustic problems, the finite element method (FEM) is the most widely used. However, due to the influence of dispersion error and contamination error, the wavelength of the finite element solution is always larger than the actual wavelength. Furthermore, this error increases dramatically with increasing computational frequency.

[0006] When the finite element method is actually used to solve acoustic problems, it can obtain relatively accurate calculation results in the low-frequency region. However, in the high-frequency region, the error of the finite element solution is relatively large, and the finite element solution is usually extremely unreliable. In order to solve this problem, a commonly used method in engineering is to increase the density of the finite element mesh to improve the quality of the finite element mesh. However, an overly dense calculation mesh will consume a lot of computing resources and computing time, especially for some large and complex three-dimensional problems and external sound field problems. This method is not advisable.

[0007] Therefore, a high-precision enhanced radial point interpolation meshless calculation method is provided for application in computational acoustics problems to solve the above problems. Summary of the Invention

[0008] The purpose of the present invention is to provide a high-precision enhanced radial point interpolation meshless calculation method for application in computational acoustic problems. The original interpolation space is enhanced by using appropriate basis functions, so that a higher-order interpolation format than the standard radial basis function meshless method can be obtained without adding nodes. When performing acoustic problem simulation calculations, more accurate numerical results can be obtained than the standard radial basis function point interpolation meshless method.

[0009] To achieve the above objectives, the present invention provides an application of a high-precision enhanced radial point interpolation meshless calculation method to computational acoustic problems. The acoustic problem domain is discretized into a series of scattered points, and the node interpolation basis functions of the standard radial point interpolation meshless algorithm are derived.

[0010] Step S2: Select appropriate local enhanced interpolation basis functions, construct node degrees of freedom at the nodes consisting of the local enhanced interpolation basis functions and the coefficients to be determined, and complete the local numerical approximation of the enhanced radial point interpolation meshless algorithm;

[0011] Step S3: Based on the node interpolation basis functions of the standard radial point interpolation meshless algorithm obtained in step S1 and the local numerical approximation obtained in step S2, a global interpolation format for the general scalar field is constructed under the premise of satisfying the unit decomposition property;

[0012] S4: Based on the global interpolation format of the general scalar field obtained in step S3, the basic system matrix equation of the acoustic problem is obtained by combining the partial differential governing equation of the acoustic problem and the Galerkin weighted residual method;

[0013] S5: Based on the given field point distribution, apply external loads and appropriate boundary conditions to the system matrix equation in step S4, and obtain the final discretized system matrix equation;

[0014] S6: Using the tool software MATLAB, the discrete system matrix equation obtained in step S5 is solved to obtain the unknown coefficients at the nodes. Based on the global interpolation format of the sound field constructed in step S3, the sound pressure at any point within the entire acoustic problem calculation domain is calculated.

[0015] S7: Based on the sound pressure at any point within the entire acoustic problem calculation domain obtained in step S6, the sound field calculation results obtained by different calculation methods are compared to complete the calculation and analysis of the acoustic problem.

[0016] Preferably, in step S1, the global interpolation of the sound pressure at any point in the acoustic calculation domain is expressed as:

[0017]

[0018] Where N represents the node interpolation basis function matrix of the standard radial point interpolation meshless algorithm, x represents the position vector of the interpolation point, R(x) is the radial basis function used, S(x) is the Lagrange polynomial basis function used, and a and b represent the undetermined coefficient vectors related to the radial basis function and the polynomial basis function, respectively.

[0019] Preferably, step S2 specifically includes the following steps:

[0020] p(x) represents the interpolation format of the standard radial point interpolation meshless algorithm. In the enhanced radial point interpolation meshless algorithm, the enhanced interpolation format is expressed as:

[0021]

[0022] Where N i represents the number of field points involved in the interpolation of the enhanced radial point interpolation meshless algorithm, represents the local numerical approximation of the enhanced radial point interpolation meshless algorithm, ψ(x) and a i Indicates that the local enhanced interpolation basis function and the coefficients to be determined are constructed at the node;

[0023] The Lagrange polynomial basis function is used as the local enhanced interpolation basis function:

[0024]

[0025] Construct the local enhanced interpolation basis function through dimensionless relative coordinate values:

[0026]

[0027] Where, is the dimensionless relative coordinate value, and h represents the average distance between field points.

[0028] Preferably, in step S3, the global interpolation format in the final enhanced radial point interpolation gridless algorithm is expressed as:

[0029]

[0030] Preferably, step S4 specifically includes the following steps:

[0031] The governing equation for small amplitude waves in an ideal static uniform fluid medium is expressed as:

[0032]

[0033] in, represents the Laplace operator, P represents the variable in the wave propagation problem domain, c represents the propagation speed of the sound wave, and t represents time;

[0034] The sound pressure distribution in the acoustic problem domain is expressed as:

[0035] P(x)=p(x)e jωt ;

[0036] Where p(x) is the spatial distribution of the sound pressure amplitude, j is the imaginary unit, and ω is the angular frequency. According to the above two formulas, the small amplitude wave equation under the frequency condition of the ideal fluid medium is:

[0037]

[0038] Where k represents the wave number and:

[0039]

[0040] Acoustic problems involve three acoustic boundary conditions: Dirichlet boundary condition DBC, Newman boundary condition NBC and Robin boundary condition RBC. The specific expressions of the three boundary conditions are:

[0041] p=p D onΓ D ;

[0042]

[0043] Among them, Γ D , Γ N and Γ R Denote the Dirichlet boundary condition, the Newman boundary condition, and the Robin boundary condition, respectively; n denotes the outer normal unit vector on the corresponding boundary; ρ denotes the density of the ideal fluid medium; v n and A n They represent the vibration velocity of the particle under the Newman boundary condition and the admittance coefficient under the Robin boundary condition respectively;

[0044] When a small amplitude wave propagates in an ideal static fluid, the relationship between the particle vibration velocity v and the sound pressure gradient ▽p is expressed as:

[0045]

[0046] In the ideal fluid medium, the small amplitude wave equation under the frequency condition is multiplied by a weight function w on both sides and integrated over the entire problem domain Ω. The corresponding control equation is expressed as:

[0047]

[0048] The corresponding control equation is integrated by integration by parts, and the control equation is reformulated as:

[0049]

[0050] Where Γ represents the boundary of the problem domain Ω, and n represents the external normal unit vector on the boundary Γ;

[0051]

[0052] Among them, n i (i=x,y,z) represents the projection of the external normal unit vector n along the three different directions of x, y, and z respectively;

[0053] Applying the Dirichlet boundary condition, Newman boundary condition and Robin boundary condition, it can be expressed as:

[0054]

[0055] Substituting the global interpolation format of the enhanced radial point interpolation meshless algorithm into the above formula, we get:

[0056]

[0057] The matrix form is expressed as:

[0058] [Kk 2 M+jρωC]a=-jρωF;

[0059]

[0060] M=∫ Ω N T NdΩ;

[0061]

[0062] Among them, a is the node coefficient to be calculated, K, M, C and F respectively represent the stiffness matrix, mass matrix, damping matrix and node force vector in the finite element calculation model of an acoustic problem, and B is the gradient matrix.

[0063] Preferably, in step S5, the final discrete system matrix equation obtained is:

[0064]

[0065] Preferably, the acoustic pressure calculation result along the liquid-filled pipe is calculated by the above method using a standard radial basis function meshless algorithm with the same node distribution;

[0066] The sound propagation medium inside the pipe is water with a density of 1000 kg / m3 and a sound propagation velocity of 1500 m / s. The Neumann boundary condition (i.e., velocity boundary condition) vn = 1 m / s is applied to the left end of the pipe. Three different calculation frequencies are set: low-frequency region f = 1100 Hz, medium-frequency region f = 2200 Hz, and high-frequency region f = 4400 Hz. The distribution of sound pressure along the pipe at different calculation frequencies is calculated.

[0067] Therefore, the present invention adopts a high-precision enhanced radial point interpolation gridless calculation method of the above structure for application in computational acoustic problems, which has the following beneficial effects:

[0068] (1) The present invention realizes high-order interpolation without increasing unit nodes. Compared with the standard radial point interpolation meshless method, the enhanced radial point interpolation meshless algorithm can significantly reduce the error of acoustic numerical calculations. When performing numerical calculations of acoustic problems, it can significantly reduce the error of numerical calculations. Therefore, it can obtain more accurate numerical results when performing numerical calculations of acoustic problems.

[0069] (2) The enhanced radial point interpolation gridless calculation method proposed in this invention has great potential application value in engineering practice.

[0070] The method scheme of the present invention is further described in detail below through the drawings and examples. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 This is a flow chart of the application of a high-precision enhanced radial point interpolation gridless calculation method of the present invention to computational acoustic problems;

[0072] Figure 2 Schematic diagram of the integration point support domain in the enhanced radial point interpolation meshless algorithm in an embodiment of the present invention;

[0073] Figure 3 Schematic diagram of the field point influence domain in the enhanced radial point interpolation meshless algorithm in an embodiment of the present invention;

[0074] Figure 4 A schematic diagram of the sound propagation problem in a liquid-filled pipe according to an embodiment of the present invention;

[0075] Figure 5 Schematic diagram of field point distribution in the standard radial basis function meshless method and enhanced radial basis function meshless algorithm for acoustic numerical calculations provided in an embodiment of the present invention;

[0076] Figure 6 Graph showing the sound pressure calculation results of the standard radial basis function meshless method and the enhanced radial basis function meshless algorithm provided in an embodiment of the present invention at a calculation frequency of f=1100 Hz;

[0077] Figure 7 Graph showing the sound pressure calculation results of the standard radial basis function meshless method and the enhanced radial basis function meshless algorithm provided in an embodiment of the present invention at a calculation frequency of f=2200 Hz;

[0078] Figure 8 This is a diagram of the sound pressure calculation results of the standard radial basis function meshless method and the enhanced radial basis function meshless algorithm provided in an embodiment of the present invention at a calculation frequency of f=4400 Hz. DETAILED DESCRIPTION

[0079] The method scheme of the present invention is further described below through the drawings and examples.

[0080] Unless otherwise defined, technical terms or scientific terms used in the present invention shall have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

[0081] The words “include” or “comprising” and similar words used in the present invention mean that the elements before the word include the elements listed after the word, and do not exclude the possibility of also including other elements. The orientation or position relationship indicated by the terms “inside”, “outside”, “upper”, “lower”, etc. is based on the orientation or position relationship shown in the accompanying drawings. It is only for the convenience of describing the present invention and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it cannot be understood as a limitation of the present invention. When the absolute position of the described object changes, the relative position relationship may also change accordingly. In the present invention, unless otherwise clearly stipulated and limited, the terms such as “attachment” should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral whole; it can be directly connected or indirectly connected through an intermediate medium, and it can be the internal connection of two elements or the interaction relationship between two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to the specific circumstances.

[0082] Example

[0083] like Figure 1 As shown, the present invention provides an application of a high-precision enhanced radial point interpolation meshless computing method to computational acoustic problems, comprising the following steps:

[0084] Step S1: Discretize the wave propagation problem domain into a series of scattered points and derive the node interpolation basis functions of the standard radial point interpolation meshless algorithm;

[0085] In step S1, for the sound field to be considered, the numerical interpolation value p of the sound pressure at any point in the acoustic calculation domain is calculated based on the standard radial basis function meshless method. h (x) can be expressed as:

[0086]

[0087] Where x represents the position vector of the interpolation point, m is the number of field points involved in the interpolation, and the number of field points involved in the interpolation is determined by the support domain of the integration point during numerical integration. The support domain of the integration point is defined as a circular area or a rectangular area centered on the integration point (such as Figure 2 As shown in the figure, the present invention adopts a rectangular area, the size of which is 1.5h (h is the average spacing of the field point distribution) with the integration point as the center. When performing numerical integration, the area that each field point can affect is called the field point influence domain. The size of the field point influence domain is closely related to the integration point support domain. In the present invention, the influence domain of each field point is also a rectangular area with a size of 1.5h (as shown in the figure). Figure 3 As shown in the figure), R(x) is the radial basis function used, S(x) is the Lagrange polynomial basis function used, and linear basis functions are often used for interpolation; n is the number of terms of the Lagrange polynomial basis function used, and a and b represent the unknown coefficient vectors related to the radial basis function and the polynomial basis function, respectively.

[0088] For one-dimensional, two-dimensional and three-dimensional problems, the Lagrangian linear basis functions used can be expressed as:

[0089]

[0090] In formula (1), the radial basis function R(x) used can be expressed as:

[0091]

[0092] Where r i Indicates the distance between the point to be interpolated and the field point involved in the interpolation, α c and q are two unknown coefficients, here we take α c =2 and q = 1.03, d c Indicates the average spacing between field points involved in interpolation.

[0093] In order to determine the unknown coefficient vectors a and b, we must first ensure that the interpolation in equation (1) is valid at the field nodes involved in the interpolation. Then

[0094]

[0095] Where R M is the matrix related to the radial basis function, S M is a matrix related to the polynomial basis function, and p represents the sound pressure vector at all field points participating in the interpolation.

[0096]

[0097] Taking the two-dimensional problem as an example, S M It can be expressed as

[0098]

[0099] In order to ensure the uniqueness of the solution, the polynomial basis function used needs to meet the following additional constraints:

[0100]

[0101] Combining equations (4) and (7), we get the following matrix equation:

[0102]

[0103] Substitute the coefficient vectors a and b obtained by equation (8) into the global interpolation represented by equation (1):

[0104]

[0105] According to formula (9), the interpolation function at the field point involved in the interpolation can be expressed as

[0106]

[0107] Since there are actually only m field points involved in the interpolation, we only need to use the first m terms in equation (10) as the field point interpolation basis functions.

[0108] According to equations (8) and (9), the unknown coefficient vectors a and b can be obtained by the following formulas:

[0109]

[0110] Finally, the global interpolation of any scalar field is expressed as:

[0111]

[0112] Where N represents the node interpolation basis function matrix of the standard radial point interpolation meshless algorithm.

[0113] Step S2: Select appropriate local enhanced interpolation basis functions, construct node degrees of freedom at the nodes consisting of the local enhanced interpolation basis functions and the coefficients to be determined, and complete the local numerical approximation of the enhanced radial point interpolation meshless algorithm;

[0114] Step S2 specifically includes the following steps:

[0115] In formula (13), p(x) represents the interpolation format of the standard radial point interpolation meshless algorithm. In the enhanced radial point interpolation meshless algorithm, the enhanced interpolation format is expressed as:

[0116]

[0117] Where N i represents the number of field points involved in the interpolation of the enhanced radial point interpolation meshless algorithm, represents the local numerical approximation of the enhanced radial point interpolation meshless algorithm, ψ(x) and a i Indicates that the local enhanced interpolation basis function and the coefficients to be determined are constructed at the node;

[0118] The Lagrange polynomial basis function is used as the local enhanced interpolation basis function:

[0119]

[0120] In order to ensure that the obtained system matrix equation has sufficient stability, the local enhanced interpolation basis function is constructed through the dimensionless relative coordinate values:

[0121]

[0122] Where, is the dimensionless relative coordinate value, and h represents the average distance between field points.

[0123] Step S3: Based on the node interpolation basis functions of the standard radial point interpolation meshless algorithm obtained in step S1 and the local numerical approximation obtained in step S2, a global interpolation format for the general scalar field is constructed under the premise of satisfying the unit decomposition property;

[0124] In step S3, the global interpolation format in the final enhanced radial point interpolation meshless algorithm is expressed as:

[0125]

[0126] Based on the global interpolation format of the general scalar field obtained in step S3, the basic system matrix equation of the acoustic problem is obtained by combining the partial differential governing equation of the acoustic problem and the Galerkin weighted residual method;

[0127] Step S4 specifically includes the following steps:

[0128] For acoustic problems in an ideal static uniform fluid medium, the governing equation for small amplitude waves is expressed as:

[0129]

[0130] in, represents the Laplace operator, P represents the variable in the wave propagation problem domain, c represents the propagation speed of the sound wave, and t represents time;

[0131] The sound pressure distribution in the acoustic problem domain is expressed as:

[0132] P(x)=p(x)e jωt; (19)

[0133] Where p(x) is the spatial distribution of the sound pressure amplitude, j is the imaginary unit, and ω is the angular frequency. Substituting Equation (19) into Equation (18), the small amplitude wave equation under the frequency condition of the ideal fluid medium is obtained as follows:

[0134]

[0135] Where k represents the wave number and:

[0136]

[0137] Acoustic problems involve three acoustic boundary conditions: Dirichlet boundary condition DBC, Newman boundary condition NBC, and Robin boundary condition RBC. The specific expressions of the three boundary conditions are:

[0138] p=p D onΓ D ; (twenty two)

[0139]

[0140] Among them, Γ D , Γ N and Γ R Denote the Dirichlet boundary condition, the Newman boundary condition, and the Robin boundary condition, respectively; n denotes the outer normal unit vector on the corresponding boundary; ρ denotes the density of the ideal fluid medium; v n and A n They represent the vibration velocity of the particle under the Newman boundary condition and the admittance coefficient under the Robin boundary condition respectively;

[0141] When a small amplitude wave propagates in an ideal static fluid, the particle vibration velocity v and the sound pressure gradient The relationship is expressed as:

[0142]

[0143] In the ideal fluid medium, the small amplitude wave equation under the frequency condition is multiplied by a weight function w on both sides and integrated over the entire problem domain Ω. The corresponding control equation is expressed as:

[0144]

[0145] The corresponding control equation is integrated by integration by parts, and the control equation is reformulated as:

[0146]

[0147] Where Γ represents the boundary of the problem domain Ω, and n represents the external normal unit vector on the boundary Γ;

[0148]

[0149] Among them, n i (i=x,y,z) represents the projection of the external normal unit vector n along the three different directions of x, y, and z respectively;

[0150] Applying the Dirichlet boundary condition, Newman boundary condition and Robin boundary condition, it can be expressed as:

[0151]

[0152] Substituting the global interpolation format of the enhanced radial point interpolation meshless algorithm into the above formula, we get:

[0153]

[0154] The matrix form of formula (30) is expressed as:

[0155] [Kk 2 M+jρωC]a=-jρωF;(31)

[0156]

[0157] M=∫ Ω N T NdΩ; (33)

[0158]

[0159] Among them, a is the node coefficient to be calculated, K, M, C and F respectively represent the stiffness matrix, mass matrix, damping matrix and node force vector in the finite element calculation model of an acoustic problem, and B is the gradient matrix.

[0160] S5: Based on the given field point distribution, apply external loads and appropriate boundary conditions to the system matrix equation in step S4, and obtain the final discretized system matrix equation;

[0161]

[0162] S6: Using the software tool MATLAB, the discrete system matrix equation obtained in step S5 is solved to obtain the unknown coefficients at the nodes. Based on the global interpolation format of the sound field constructed in step S3, the sound pressure at any point within the entire acoustic problem calculation domain is calculated.

[0163] S7: Based on the sound pressure at any point within the entire acoustic problem calculation domain obtained in step S6, the sound field calculation results obtained by different calculation methods are compared to complete the calculation and analysis of the acoustic problem.

[0164] The acoustic pressure calculation results along the liquid-filled pipe are obtained by using the standard radial basis function meshless algorithm with the same node distribution as above;

[0165] The sound propagation medium inside the pipe is water with a density of 1000 kg / m3 and a sound propagation velocity of 1500 m / s. The Neumann boundary condition (i.e., velocity boundary condition) vn = 1 m / s is applied to the left end of the pipe. Three different calculation frequencies are set: low-frequency region f = 1100 Hz, medium-frequency region f = 2200 Hz, and high-frequency region f = 4400 Hz. The distribution of sound pressure along the pipe at different calculation frequencies is calculated.

[0166] Comparative Example

[0167] In order to compare and verify the effectiveness and correctness of the enhanced radial point interpolation meshless calculation method proposed in this scheme for acoustic simulation calculations and its ability to control the errors of acoustic numerical calculations, the standard radial basis function point interpolation meshless method and the enhanced radial basis function point interpolation meshless method disclosed in this scheme are used to solve the sound propagation problem of a liquid-filled pipe (such as Figure 4 As shown), the sound propagation medium inside the pipe is water with a density of 1000kg / m 3 , the sound propagation speed is 1500m / s, and the Neumann boundary condition (i.e. velocity boundary condition) is applied to the left end of the pipe. n =1m / s, the node distribution used by the two different calculation methods is as follows Figure 5 shown.

[0168] Considering three different calculation frequencies (f = 1100 Hz, f = 2200 Hz and f = 4400 Hz), Figure 6-Figure 8 The distribution of sound pressure along the pipeline obtained by two different calculation methods is given. It can be seen from the figure that in the low-frequency region (f=1100Hz), the calculation results of the two different calculation methods, the standard radial basis function point interpolation meshless method and the enhanced radial basis function point interpolation meshless method disclosed in this scheme, are consistent with the analytical solution very well; however, with the increase of the calculation frequency, the error of the result calculated by the standard radial basis function point interpolation meshless method will become larger and larger, while the enhanced radial basis function point interpolation meshless method disclosed in this scheme can still calculate very accurate numerical calculation results, indicating that the enhanced radial point interpolation meshless calculation method given in this scheme has a more powerful ability to perform acoustic problem simulation calculations, so that it can greatly reduce the numerical error of acoustic calculations, and ultimately obtain more accurate calculation results when performing numerical calculations of acoustic problems. Therefore, the enhanced radial point interpolation meshless calculation method proposed in this scheme has great potential application value in engineering practice.

[0169] Therefore, the present invention adopts the above-mentioned high-precision enhanced radial point interpolation gridless calculation method to apply in computational acoustic problems, and realizes high-order interpolation without increasing unit nodes. Compared with the standard radial point interpolation gridless method, the enhanced radial point interpolation gridless algorithm that can greatly reduce the error of acoustic numerical calculation can significantly reduce the numerical calculation error when performing numerical calculation of acoustic problems, so it can obtain more accurate numerical results when performing numerical calculation of acoustic problems.

[0170] Finally, it should be noted that the above embodiments are only used to illustrate the method scheme of the present invention and not to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, ordinary method personnel in this field should understand that they can still modify or replace the method scheme of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified method scheme to deviate from the spirit and scope of the method scheme of the present invention.

Claims

1. A high-precision enhanced radial point interpolation meshless computing method is applied to computational acoustics problems, characterized by: The following steps are involved: Step S1: Discretize the acoustic problem domain into a series of scattered points and derive the node interpolation basis function of the standard radial point interpolation meshless algorithm; Step S2: Select appropriate local enhanced interpolation basis functions, construct node degrees of freedom at the nodes consisting of the local enhanced interpolation basis functions and the coefficients to be determined, and complete the local numerical approximation of the enhanced radial point interpolation meshless algorithm; Step S3: Based on the node interpolation basis functions of the standard radial point interpolation meshless algorithm obtained in step S1 and the local numerical approximation obtained in step S2, a global interpolation format for the general scalar field is constructed under the premise of satisfying the unit decomposition property; S4: Based on the global interpolation format of the general scalar field obtained in step S3, the basic system matrix equation of the acoustic problem is obtained by combining the partial differential governing equation of the acoustic problem and the Galerkin weighted residual method; S5: Based on the given field point distribution, apply external loads and appropriate boundary conditions to the system matrix equation in step S4, and obtain the final discretized system matrix equation; S6: Use the tool software MATLAB to solve the discrete system matrix equation obtained in step S5, calculate the unknown coefficients at the nodes, and calculate the sound pressure at any point in the entire acoustic problem calculation domain based on the global interpolation format of the sound field constructed in step S3; S7: Based on the sound pressure at any point within the entire acoustic problem calculation domain obtained in step S6, the sound field calculation results obtained by different calculation methods are compared to complete the calculation and analysis of the acoustic problem.

2. The application of a high-precision enhanced radial point interpolation meshless computing method to computational acoustics problems according to claim 1, characterized in that: In step S1, the global interpolation of the sound pressure at any point in the acoustic calculation domain is expressed as: Where N represents the node interpolation basis function matrix of the standard radial point interpolation meshless algorithm, x represents the position vector of the interpolation point, R(x) is the radial basis function used, S(x) is the Lagrange polynomial basis function used, and a and b represent the undetermined coefficient vectors related to the radial basis function and the polynomial basis function, respectively.

3. The application of a high-precision enhanced radial point interpolation meshless computing method to computational acoustics problems according to claim 2, characterized in that: Step S2 specifically includes the following steps: p(x) represents the interpolation format of the standard radial point interpolation meshless algorithm. In the enhanced radial point interpolation meshless algorithm, the enhanced interpolation format is expressed as: Where N i represents the number of field points involved in the interpolation of the enhanced radial point interpolation meshless algorithm, represents the local numerical approximation of the enhanced radial point interpolation meshless algorithm, ψ(x) and a i Indicates that the local enhanced interpolation basis function and the coefficients to be determined are constructed at the node; The Lagrange polynomial basis function is used as the local enhanced interpolation basis function: Construct the local enhanced interpolation basis function through dimensionless relative coordinate values: Where, and is the dimensionless relative coordinate value, and h represents the average distance between field points.

4. The application of a high-precision enhanced radial point interpolation meshless computing method to computational acoustics problems according to claim 3, characterized in that: In step S3, the global interpolation format in the final enhanced radial point interpolation meshless algorithm is expressed as:

5. The application of a high-precision enhanced radial point interpolation meshless computing method to computational acoustics problems according to claim 4, characterized in that: Step S4 specifically includes the following steps: The governing equation for small amplitude waves in an ideal static uniform fluid medium is expressed as: in, represents the Laplace operator, P represents the variable in the wave propagation problem domain, c represents the propagation speed of the sound wave, and t represents time; The sound pressure distribution in the acoustic problem domain is expressed as: P(x)=p(x)e jωt ; Where p(x) is the spatial distribution of the sound pressure amplitude, j is the imaginary unit, and ω is the angular frequency. According to the above two formulas, the small amplitude wave equation under the frequency condition of the ideal fluid medium is: Where k represents the wave number and: Acoustic problems involve three acoustic boundary conditions: Dirichlet boundary condition DBC, Newman boundary condition NBC and Robin boundary condition RBC. The specific expressions of the three boundary conditions are: p=p D onΓ D ; Among them, Γ D , Γ N and Γ R Denote the Dirichlet boundary condition, the Newman boundary condition, and the Robin boundary condition, respectively; n denotes the outer normal unit vector on the corresponding boundary; ρ denotes the density of the ideal fluid medium; v n and A n They represent the vibration velocity of the particle under the Newman boundary condition and the admittance coefficient under the Robin boundary condition respectively; When a small amplitude wave propagates in an ideal static fluid, the particle vibration velocity v and the sound pressure gradient The relationship is expressed as: In the ideal fluid medium, the small amplitude wave equation under the frequency condition is multiplied by a weight function w on both sides and integrated over the entire problem domain Ω. The corresponding control equation is expressed as: The corresponding control equation is integrated by integration by parts, and the control equation is reformulated as: Where Γ represents the boundary of the problem domain Ω, and n represents the external normal unit vector on the boundary Γ; Among them, n i (i=x,y,z) represents the projection of the external normal unit vector n along the three different directions of x, y, and z respectively; Applying the Dirichlet boundary condition, Newman boundary condition and Robin boundary condition, it can be expressed as: Substituting the global interpolation format of the enhanced radial point interpolation meshless algorithm into the above formula, we get: The matrix form is expressed as: [Kk 2 M+jρωC]a=-jρωF; M=∫ Ω N T NdΩ; Among them, a is the node coefficient to be calculated, K, M, C and F respectively represent the stiffness matrix, mass matrix, damping matrix and node force vector in the finite element calculation model of an acoustic problem, and B is the gradient matrix.

6. Application of a high-precision enhanced radial point interpolation meshless computing method to computational acoustics problems according to claim 5, characterized in that: In step S5, the final discrete system matrix equation is obtained as follows:

7. Application of a high-precision enhanced radial point interpolation meshless computing method according to claim 6 to computational acoustics problems, characterized in that: The acoustic pressure calculation results along the liquid-filled pipe are obtained by using the standard radial basis function meshless algorithm with the same node distribution as above; The sound propagation medium inside the pipe is water, with a density of 1000 kg / m 3 , the sound propagation speed is 1500m / s, and the velocity boundary condition Neumann is applied to the left end of the pipe, v n =1m / s, set three different calculation frequencies, low frequency region f = 1100Hz, medium frequency region f = 2200Hz, high frequency region f = 4400Hz, and calculate the distribution of sound pressure along the pipeline at different calculation frequencies.

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