Application of high-precision enhanced radial point interpolation meshless calculation method in acoustic problem calculation

Abstract

The invention discloses application of a high-precision enhanced radial point interpolation meshless calculation method in acoustic problem calculation, and relates to application of a grid calculation method in the field of acoustic problem calculation, firstly, a wave propagation problem domain is dispersed into a series of scatter points, and an interpolation format of a general scalar field is constructed based on a radial basis function; deducing to obtain an interpolation primary function of each scatter point; in order to improve the interpolation precision of the obtained interpolation format, a new node degree of freedom is constructed at each scatter point, and the node degree of freedom is a local numerical value approximation composed of a local enhanced interpolation primary function and a coefficient to be solved. And based on the obtained local numerical approximation, constructing and obtaining a global interpolation format of a general scalar field on the premise of meeting unit decomposition characteristics. And obtaining a final discrete system matrix equation, and solving the matrix equation to obtain the sound pressure of any point in the whole acoustic problem computational domain. According to the method, high-order interpolation is realized under the condition of not increasing unit nodes, and numerical calculation errors can be reduced.

Description

[0001] Methodology Area

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

[0003] Background Methods

[0004] In today's society, noise pollution has increasingly developed into a serious environmental and social problem. Noise pollution not only seriously affects people's daily life, work and study, but also threatens people's physical and mental health. In engineering applications, acoustic problems are also ubiquitous. In the field of mechanical engineering, with the improvement of people's daily living standards, the requirements for the quality and performance of mechanical products are getting higher and higher. Therefore, how to design low-noise, high-performance products is an issue that mechanical engineers are committed to focusing on; in the field of architectural acoustics, how to ensure that the local part of the building has the best acoustic effect is a key issue that architectural engineers should be concerned about when designing buildings; in the field of petrochemicals, the vibration and sound propagation of infusion pipelines are also the focus of people's attention.

[0005] For acoustic problems, analytical solutions can only be obtained under extremely simple and special circumstances. However, in most engineering problems in reality, the topological structures of the problem domain are diverse, and the boundary conditions are even more complex and changeable. For this situation, there is generally no analytical solution; in this case, only numerical methods can be used to solve it. Among the several types of numerical methods for solving acoustic problems, the finite element method (FEM) is the most widely used numerical method. However, due to the influence of discrete error (dispersion error) and pollution error (pollution error), the wavelength of the finite element solution is always greater than the actual wavelength. At the same time, as the calculation frequency increases, this error will increase dramatically.

[0006] When the finite element method is actually used to solve acoustic problems, the finite element method can obtain relatively accurate calculation results in the low-frequency region, but 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 grid 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 computing 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, and to use a suitable basis function to strengthen the original interpolation space, so as to obtain a higher-order interpolation format than the standard radial basis function meshless method without adding nodes, and to obtain more accurate numerical results than the standard radial basis function point interpolation meshless method when performing acoustic problem simulation calculations.

[0009] To achieve the above object, the present invention provides an application of a high-precision enhanced radial point interpolation meshless calculation method in computational acoustic problems, discretizing the acoustic problem domain into a series of scattered points, and deriving the node interpolation basis function of the standard radial point interpolation meshless algorithm;

[0010] Step S2: Select a suitable local enhanced interpolation basis function, construct a node degree of freedom composed of the local enhanced interpolation basis function and the coefficient to be determined at the node, 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 of a general scalar field is constructed under the premise of satisfying the unit decomposition characteristic;

[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 discrete system matrix equation;

[0014] S6: using 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 sound field global interpolation format constructed in step S3;

[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 unknown 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 It means that the local enhanced interpolation basis function and the coefficients to be determined are constructed at the nodes;

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

[0024]

[0025] The local enhanced interpolation basis function is constructed by dimensionless relative coordinate values:

[0026]

[0027] In the formula, is the dimensionless relative coordinate value, and h represents the average spacing 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] Among them, 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 obtained as follows:

[0037]

[0038] Where k is 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 represent Dirichlet boundary condition, Newman boundary condition and Robin boundary condition respectively, n represents the external normal unit vector on the corresponding boundary; ρ represents the density of the ideal fluid medium, v n and A n 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 re-expressed 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 three different directions: x, y, and z;

[0053] Applying the three boundary conditions of Dirichlet boundary condition, Newman boundary condition and Robin boundary condition, it is 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 pipeline is water with a density of 1000kg / m3 and a sound propagation speed of 1500m / s. The Neumann boundary condition (i.e., velocity boundary condition) vn=1m / s is applied to the left end of the pipeline. Three different calculation frequencies are set: f=1100Hz in the low-frequency region, f=2200Hz in the medium-frequency region, and f=4400Hz in the high-frequency region. The distribution of sound pressure along the pipeline 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 numerical calculation error of acoustics. When performing numerical calculations of acoustic problems, it can significantly reduce the numerical calculation error. 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 embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0072] Figure 2 A schematic diagram of an integration point support domain in an 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 provided by an embodiment of the present invention;

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

[0076] Figure 6 A diagram 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 A diagram 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 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 drawings and embodiments.

[0080] Unless otherwise defined, method terms or scientific terms used in the present invention shall have the common meanings understood by one of ordinary skill in the art to which the present invention belongs.

[0081] The words "include" or "comprises" and the like 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 drawings, which 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 specified and limited, the terms "attachment" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral body; 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 specific circumstances.

[0082] Example

[0083] like Figure 1 As shown, the present invention provides an application of a high-precision enhanced radial point interpolation gridless computing method in computing 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 function of the standard radial point interpolation meshless algorithm;

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

[0086]

[0087] Where x represents the position vector of the interpolation point, and m is the number of field points involved in the interpolation. 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) with the integration point as the center. Figure 3 As shown in the figure, R(x) is the radial basis function used, S(x) is the Lagrangian polynomial basis function used, and linear basis functions are often used for interpolation; n is the number of terms of the Lagrangian 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] In the formula, r i Represents 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] In the formula, R M is the matrix associated with 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 involved 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 a suitable local enhanced interpolation basis function, construct a node degree of freedom composed of the local enhanced interpolation basis function and the coefficient to be determined at the node, 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 It means that the local enhanced interpolation basis function and the coefficients to be determined are constructed at the nodes;

[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 dimensionless relative coordinate values:

[0121]

[0122] In the formula, is the dimensionless relative coordinate value, and h represents the average spacing 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 of a general scalar field is constructed under the premise of satisfying the unit decomposition characteristic;

[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:

[0134]

[0135] Where k is 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 represent Dirichlet boundary condition, Newman boundary condition and Robin boundary condition respectively, n represents the external normal unit vector on the corresponding boundary; ρ represents the density of the ideal fluid medium, v n and A n 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 re-expressed 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 three different directions: x, y, and z;

[0150] Applying the three boundary conditions of Dirichlet boundary condition, Newman boundary condition and Robin boundary condition, it is 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 discrete system matrix equation;

[0161]

[0162] S6: using the software tool 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 sound field global interpolation format constructed in step S3;

[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 calculated by the above method using the standard radial basis function meshless algorithm with the same node distribution;

[0165] The sound propagation medium inside the pipeline is water with a density of 1000kg / m3 and a sound propagation speed of 1500m / s. The Neumann boundary condition (i.e., velocity boundary condition) vn=1m / s is applied to the left end of the pipeline. Three different calculation frequencies are set: f=1100Hz in the low-frequency region, f=2200Hz in the medium-frequency region, and f=4400Hz in the high-frequency region. The distribution of sound pressure along the pipeline 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 given in this scheme for acoustic problem simulation calculation and its ability to control the error of acoustic numerical calculation, 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 at 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] Consider 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 calculated 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 finally 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 the calculation of acoustic problems, realizes high-order interpolation without increasing unit nodes, and compared with the standard radial point interpolation gridless method, the enhanced radial point interpolation gridless algorithm that can greatly reduce the acoustic numerical calculation error 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 rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, ordinary method personnel in the 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 a suitable local enhanced interpolation basis function, construct a node degree of freedom composed of the local enhanced interpolation basis function and the coefficient to be determined at the node, 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 of a general scalar field is constructed under the premise of satisfying the unit decomposition characteristic; 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 discrete system matrix equation; S6: using 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 of 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 in 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 unknown 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 in 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 It means that the local enhanced interpolation basis function and the coefficients to be determined are constructed at the nodes; The Lagrange polynomial basis function is used as the local enhanced interpolation basis function: The local enhanced interpolation basis function is constructed by dimensionless relative coordinate values: In the formula, and is the dimensionless relative coordinate value, and h represents the average spacing between field points.

4. The application of a high-precision enhanced radial point interpolation meshless computing method in 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 according to claim 4 to computational acoustic problems, 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 ; Among them, 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 obtained as follows: Where k is 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 represent Dirichlet boundary condition, Newman boundary condition and Robin boundary condition respectively, n represents the external normal unit vector on the corresponding boundary; ρ represents the density of the ideal fluid medium, v n and A n 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 re-expressed 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 three different directions: x, y, and z; Applying the three boundary conditions of Dirichlet boundary condition, Newman boundary condition and Robin boundary condition, it is 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. The application of a high-precision enhanced radial point interpolation meshless computing method in computational acoustics problems according to claim 5, characterized in that: In step S5, the final discrete system matrix equation is obtained as follows:

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

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