CN117875098A - Curved surface feature structure simulation method and system - Google Patents
Curved surface feature structure simulation method and system Download PDFInfo
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Abstract
The invention relates to a curved surface characteristic structure simulation method and a curved surface characteristic structure simulation system. The method comprises the following steps: acquiring electric field information and magnetic field information in a nondestructive free space; and obtaining electric field information and magnetic field information with curved surface characteristic structures by adopting a method of combining conformal grids with CDI-FDTD according to the electric field information and the magnetic field information. The method can combine the conformal grid technology with the CDI-FDTD method to simulate the electromagnetic characteristics of the PEC target with the curved surface structure, thereby further improving the numerical calculation precision.
Description
Technical Field
The invention relates to the field of curved surface feature structure simulation, in particular to a curved surface feature structure simulation method and system.
Background
The time domain finite difference method performs a second order center difference approximation to the time and space partial derivatives so that the electric and magnetic field components are scattered and sampled in an alternating fashion in time and space. Advantages of the FDTD method include, but are not limited to, simple numerical implementation, visual physical process description, easy parallel calculation, capability of obtaining broadband information through single calculation, and the like. Through development in recent decades, the FDTD method has been widely used in various aspects of the electromagnetic field, such as electromagnetic compatibility, antenna radiation, target scattering, and simulation and design of microwave circuits. However, two problems that have to be faced by users of the FDTD method are: (1) The traditional FDTD method needs to meet the steady condition of the Courant-Friedrich-Levy (CFL), and a smaller time step is required to ensure convergence of the numerical results. (2) When an electromagnetic model with a curved surface and an irregular structure is modeled by adopting an orthogonal hexahedral mesh, a step error exists.
In order to eliminate or weaken the limitation of the grid size in the computation space on the time step, some unconditionally stable and weakly conditional stable FDTD methods are proposed successively for electromagnetic simulation, and common implicit unconditional stabilization algorithms are: an alternate direction implicit FDTD (ADI-FDTD) method, a single step ADI-FDTD method, a local one-dimensional FDTD method, a mixed explicit HIE-FDTD method, a CN-FDTD method, and the like. In addition, the explicit unconditional stabilization algorithm is mainly a spatial filtering method and eigenvalue filtering algorithm based on the FDTD method. The time step adopted by the optimized FDTD method does not need to meet the CFL condition specified by the traditional FDTD, so that under the condition that the physical simulation time is unchanged, the larger time step means that the required steady-state condition can be achieved with fewer iteration times, and the numerical value is improved even though the efficiency is improved.
In order to solve the ladder problem caused by the orthorhombic hexahedral mesh, some common mesh processing methods include a hybrid sub-mesh technique, a non-uniform mesh technique, and a conformal mesh technique. The main principle of the hybrid subgrid technology is that a fine grid subdivision is adopted for an area with an electrical small structure and an irregular structure, and a coarse grid subdivision is adopted for the rest part, so that unified fine grid subdivision of the whole calculation area is avoided, the calculation efficiency can be effectively improved, and the calculation memory can be reduced. However, the subgrid technique requires complex time-space field value exchange processing at the boundaries and the vicinity of the coarse and fine grids, and false reflection occurs at the boundaries of the coarse and fine grids due to the influence of interpolation calculation accuracy, which affects the numerical calculation accuracy and even causes divergence of numerical results. Meanwhile, the space-time interpolation operation existing in the subgrid technology increases the difficulty in realizing a numerical algorithm and the complexity of code programming. The non-uniform grid technique is also suitable for modeling electromagnetic models with complex media characteristics or locally containing fine structures. Non-uniform grid techniques adapt to the media characteristics by changing the size of the grid cells. In the area with complex medium characteristics or rapid electromagnetic phenomenon change, smaller grid units are used to increase the resolution of the space grid, so that the numerical calculation accuracy is improved. The remaining simulation space uses larger grid cells to reduce memory and increase computational efficiency. However, since different grid cells have different sizes and shapes, the propagation speed of electromagnetic waves in the different grid cells may also be different, resulting in a large numerical dispersion error, and in numerical simulation, it is necessary to make the dimensional change between the different grid cells as gentle as possible.
During the development of the FDTD method, different types of conformal methods have been proposed to reduce the step error introduced in Yee modeling. Conformal mesh technology was developed for both types of media targets and PEC targets, depending on the nature of the material media. The prior art relates to area-averaging conformal techniques for Debye media, and also relates to conformal techniques for plasma media, which are based on area-averaging conformal techniques for adjacent dispersive interfaces. The common grid technology effectively improves the numerical calculation precision of the FDTD method for simulating the electromagnetic structure with the curved surface. Meanwhile, the conformal technology aiming at the medium target is combined with an unconditional stabilization method in the prior art, so that the calculation efficiency of a numerical method is further improved.
Conformal grid techniques for media targets are essentially numerical averages of media parameters, often without late instability. The conformal grid technique for PEC targets is relatively complex and the numerical implementation varies from medium targets. The prior art is concerned with conformal techniques for processing two-dimensional and three-dimensional PEC targets. In addition, the prior art also describes a conformal mesh technique based on the higher order FDTD (2, 4) approach to simulate the electromagnetic properties of PEC structures. It should be noted that if the PEC part in the Yee cell occupies a smaller proportion, the range of the time step in the FDTD method needs to be reduced to ensure the stability of the numerical simulation result. However, a smaller time step results in an increased simulation time and reduced computational efficiency. In order to overcome the defect that the value range of the time step is too small in the conformal FDTD method, some conformal grid technologies based on unconditionally stable FDTD methods, such as a C-ADI-FDTD method, are proposed, and although the method can take a larger time step, the method has the phenomenon of instability at a later time. Recently, a LOD-FDTD method incorporating conformal mesh technology was used for electromagnetic simulation involving curved electromagnetic structures and electrically large targets. The method employs partially filled cells to accurately model a curved PEC target and has unconditionally stable properties, but conventional LOD-FDTDs do not have compliant divergent properties.
Recently, a new CDI-FDTD method has been proposed, which has not only the feature of unconditional stability, but also satisfies the compliance divergence property as the conventional FDTD. The application of the CDI-FDTD method in the aspect of electromagnetic characteristic simulation of a complex target shows that compared with an implicit FDTD algorithm which does not meet compliance divergence attribute, the method has higher numerical calculation efficiency and calculation accuracy. However, no relevant effort has been made to combine conformal mesh techniques with CDI-FDTD methods for simulating the electromagnetic properties of PEC targets with curved structures, thereby further improving the accuracy of numerical calculations.
Disclosure of Invention
The invention aims to provide a curved surface characteristic structure simulation method and system, which combines a conformal grid technology with a CDI-FDTD method to simulate the electromagnetic characteristics of a PEC target with a curved surface structure, thereby further improving the numerical calculation precision.
In order to achieve the above object, the present invention provides the following solutions:
the curved surface characteristic structure simulation method comprises the following steps:
acquiring electric field information and magnetic field information in a nondestructive free space;
and obtaining electric field information and magnetic field information with curved surface characteristic structures by adopting a method of combining conformal grids with CDI-FDTD according to the electric field information and the magnetic field information.
Optionally, the acquiring electric field information and magnetic field information in the lossless free space specifically includes:
acquiring maxwell's equations in a lossless free space;
and determining electric field information and magnetic field information according to the Maxwell equation.
Optionally, the method for combining the conformal grid and the CDI-FDTD according to the electric field information and the magnetic field information to obtain electric field information and magnetic field information with curved surface features specifically includes:
and correcting the Ye grid region containing the curved surface structure in the electromagnetic model by adopting a method of combining conformal grids and CDI-FDTD according to the electric field information and the magnetic field information to obtain electric field information and magnetic field information with curved surface characteristic structures.
Optionally, the method for combining the conformal grid and the CDI-FDTD according to the electric field information and the magnetic field information corrects a Yee grid area including a curved surface structure in the electromagnetic model to obtain electric field information and magnetic field information having a curved surface feature structure, which specifically includes:
and processing the Maxwell equation by adopting a numerical discrete strategy which is the same as that of the LOD-FDTD method and combining a conformal grid method to obtain a numerical iteration formula of an electric field and a numerical iteration formula of a magnetic field, wherein the numerical iteration formula of the electric field and the numerical iteration formula of the magnetic field respectively comprise electric field information and magnetic field information with curved surface characteristic structures.
Optionally, the method further comprises:
and performing stability analysis on the electric field information and the magnetic field information with the curved surface characteristic structure by using a Von Neumann method.
Optionally, the method further comprises:
and carrying out numerical simulation on three electromagnetic models, namely the PEC cavity with the circular seam, the fighter plane model and the unmanned plane model, according to the electric field information and the magnetic field information with the curved surface characteristic structure.
A curved surface feature modeling system comprising:
the electromagnetic information acquisition module is used for acquiring electric field information and magnetic field information in a nondestructive free space;
and the curved surface characteristic structure determining module is used for obtaining the electric field information and the magnetic field information with the curved surface characteristic structure by adopting a method of combining the conformal grid and the CDI-FDTD according to the electric field information and the magnetic field information.
Optionally, the electromagnetic information acquisition module specifically includes:
a maxwell's equations acquisition unit for acquiring maxwell's equations in a lossless free space;
and the electromagnetic information acquisition unit is used for determining electric field information and magnetic field information according to the Maxwell equation.
Optionally, the curved surface feature structure determining module specifically includes:
and the curved surface characteristic structure determining unit is used for correcting the Ye grid area containing the curved surface structure in the electromagnetic model by adopting a method of combining the conformal grid and the CDI-FDTD according to the electric field information and the magnetic field information to obtain electric field information and magnetic field information with the curved surface characteristic structure.
Optionally, the curved surface feature structure determining unit specifically includes:
the curved surface characteristic structure determining subunit is used for processing the Maxwell equation by adopting a numerical discrete strategy which is the same as that of the LOD-FDTD method and combining a conformal grid method to obtain a numerical iteration formula of an electric field and a numerical iteration formula of a magnetic field, wherein the numerical iteration formula of the electric field and the numerical iteration formula of the magnetic field respectively comprise electric field information and magnetic field information with curved surface characteristic structures.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a curved surface characteristic structure simulation method. The method comprises the following steps: acquiring electric field information and magnetic field information in a nondestructive free space; and obtaining electric field information and magnetic field information with curved surface characteristic structures by adopting a method of combining conformal grids with CDI-FDTD according to the electric field information and the magnetic field information. The method can combine the conformal grid technology with the CDI-FDTD method to simulate the electromagnetic characteristics of the PEC target with the curved surface structure, thereby further improving the numerical calculation precision.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a curved surface feature structure simulation method of the present invention;
FIG. 2 is a diagram of a curved surface feature modeling system of the present invention;
FIG. 3 is a schematic diagram of a cell with a partially curved PEC object;
fig. 4 is a graph showing the results of stability analysis of the C-CDI-FDTD method, wherein (a) cfln=1; (b) cfln=4; (c) cfln=8; (d) cfln=10;
fig. 5 is a CFDTD method stability analysis result, wherein (a) cfln=1; (b) cfln=0.2b compliant divergence analysis;
fig. 6 is at t=t 0 When D is a plot of the sampled surface results, where (a) FDTD method, cfln=1; (b) C-FDTD method cfln=0.2;
fig. 7 is at t=t 0 When D is scattered on the sample surface result plot. (a) CDI-FDTD method cfln=1; (b) cfln=1 for the C-CDI-FDTD method; (c) Cfln=4 (d) cfln=8 for C-CDI-FDTD method;
FIG. 8 is a schematic diagram of a cavity model;
FIG. 9 is a graph showing comparison of time domain results at detection points for different methods;
FIG. 10 is a graph showing the comparison of the Shielding Effectiveness (SE) results at the detection points for different methods in the frequency domain;
FIG. 11 is a schematic view of a fighter plane model;
FIG. 12 is a schematic diagram of a different method modeling, wherein (a) a conventional Yee grid model; (b) modeling of conformal techniques;
FIG. 13 is a graph showing the results of a two-station RCS at 300MHz for the different methods, wherein (a) the CFLN values for the CDI-FDTD method and the C-CDI-FDTD method are 1, and the CFLN value for the FDTD method is 1; (b) The CFLN value of the CDI-FDTD method and the CFLN value of the C-CDI-FDTD method are 4, and the CFLN value of the FDTD method is 1;
FIG. 14 is a diagram showing a comparison of time domain waveforms at detection points in different methods;
FIG. 15 is a schematic diagram of the surface current distribution of electromagnetic targets obtained by different calculation methods, wherein (a) the fine-grid FDTD method; (b) coarse grid C-CDI-FDTD process; (c) CDI-FDTD process.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a curved surface characteristic structure simulation method and system, which combines a conformal grid technology with a CDI-FDTD method to simulate the electromagnetic characteristics of a PEC target with a curved surface structure, thereby further improving the numerical calculation precision.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
Example 1:
FIG. 1 is a flow chart of a method for simulating a curved surface feature structure according to the present invention. As shown in fig. 1, a curved surface feature structure simulation method includes:
step 101: the method for acquiring the electric field information and the magnetic field information in the nondestructive free space specifically comprises the following steps:
acquiring maxwell's equations in lossless free space:
wherein E is electric field strength, H is magnetic field strength, epsilon and mu are dielectric constant and magnetic permeability in vacuum.
And determining electric field information and magnetic field information according to the Maxwell equation.
Step 102: and obtaining electric field information and magnetic field information with a curved surface characteristic structure by adopting a method of combining conformal grids with CDI-FDTD according to the electric field information and the magnetic field information, wherein the method specifically comprises the following steps:
and correcting a Ye grid region containing a curved surface structure in an electromagnetic model according to the electric field information and the magnetic field information by adopting a method of combining a conformal grid and CDI-FDTD to obtain electric field information and magnetic field information with curved surface feature structures, and specifically, adopting a numerical discrete strategy which is the same as that of an LOD-FDTD method and combining a conformal grid method to process the Maxwell equation to obtain a numerical iteration formula of an electric field and a numerical iteration formula of a magnetic field, wherein the numerical iteration formula of the electric field and the numerical iteration formula of the magnetic field respectively contain the electric field information and the magnetic field information with the curved surface feature structures.
Processing (1) and (2) using the same numerical discrete strategy as the LOD-FDTD method in combination with conformal grid techniques can result in:
wherein I is n×n For n-order identity matrix, u= [ E, H] T Coefficient matrix A, B is
lx,ly,lz,S yz ,S xz ,S xy The location of each cell is shown in fig. 3. lx, ly, lz are the edge length ratio of the non-PEC part of the YEE cell along the x, y, z directions, S yz ,S xz ,S xy The area ratio projected onto the yoz, xoz, xoy plane for the non-PEC regions. When the calculation region is free space, lx, ly, lz, S yz ,S xz ,S xy And (2) are 1, and in contrast, lx, ly, lz, S when the calculation area is PEC yz ,S xz ,S xy The values of the above coefficients are all 0, so that the value ranges of the above coefficients are [0,1 ]]。
Next, defineAnd->The forms of (a) are respectively as follows:
wherein u is c ＝[E c ,H c ] T . Next, equations (8), (9) are respectively brought intoEquations (3), (4) can be obtained:
let u in formula (9) c And u from n+1 to n and brings it into equation (10), it can be obtained:
e can be obtained according to the formula (12) c Iterative formula at time n+1/2:
similarly, u in equation (8) c And u is changed from n+1/2 to n-1/2 and substituted into the formula (11) (note that, u in (11) c And u is changed from n+1 to n), and finally E c The iterative formula at time n-1/2 is:
further, equation (14) is subtracted from equation (13) to obtain E c The numerical iterative formula of (2) is:
similarly, H can be derived c The iterative formula of (2) is:
finally, for convenience of numerical solutions equations (15) and (16), an auxiliary variable h is defined c ,e c
Simultaneously, equations (17) and (18) are substituted into equations (15) and (16). Can obtain
Thus, equations (17) - (20) are numerical iterative equations for the C-CDI-FDTD method with curved PEC structure, ec and Hc are the output electric and magnetic fields, respectively. Taking the x direction as an example, a specific numerical iteration formula of the C-CDI-FDTD method is as follows:
wherein,
in addition to the above steps, the present invention further includes:
and performing stability analysis on the electric field information and the magnetic field information with the curved surface characteristic structure by using a Von Neumann method.
Firstly, writing a numerical iteration formula of the C-CDI-FDTD method into the following matrix form:
M L P n+1 ＝M R P n (25)
wherein P= [ E x ,E y ,E z ,H x ,H y ,H z ] T In E x For example, E x ＝[E x (1,1,1),E x (1,1,2),…,E x (m,n+1,q+1)] T The expression of the other field components is similar. Meanwhile, m, n and q are the maximum values of indexes of the field components in the x, y and z directions respectively. Here, the
Defining the field component form of electromagnetic waves in the spatial domain is:
wherein, phi=e, H,zeta represents the time growth factor, k p (p=x, y, z) represents the fourier wave number in the p direction. The subscript i, j, k denotes the node position of the Yee grid, and Δp (p=x, y, z) denotes the discretized grid size.
The space first-order partial derivative is approximated by second-order central difference discrete approximation to obtain
Wherein,substituting equation (29) into equation (27) to obtain
MP n ＝(ζM L -M R )P n ＝0 (28)
To ensure that equation (28) has a non-zero solution, the determinant of the coefficient matrix M must be 0. Meanwhile, in order to ensure that the numerical method maintains stability during the iteration, the modulus value of the growth factor ζ must be less than or equal to 1. The expression of ζ can be obtained by solving the determinant of the matrix M. However, ζ is expressed in too complex an expression, and lx, ly, lz, S yz ,S xz ,S xy The value of (2) will vary with the shape of the PEC target. For computational purposes, taking example a as an example, the relevant parameters are brought into a matrix M to determine the modulus of the growth factor ζ. Since the wave number k is not involved in the example A p In the actual calculation, the wave number k p A random array is defined.
Figure 4 shows the values of the corresponding growth factor ζ for the C-CDI-FDTD method under different CFLN conditions. (cfln=Δt C-CDI-FDTD /Δt FDTD ，Δt C-CDI-FDTD Time step, Δt, for the C-CDI-FDTD method FDTD Representing the maximum time step of the conventional FDTD method under CFL conditions). The abscissa and ordinate in figure 4 represent the real and imaginary parts of the growth factor zeta,all growth factors ζ can be found to have a modulus value of no more than 1, which indicates that the C-CDI-FDTD process has unconditionally stable behavior.
Also, taking example a as an example, the modulus of the growth factor ζ of the CFDTD method under different CFLN conditions is calculated. As shown in fig. 5 (a), in the case of cfln=1, the modulus value of the partial growth factor ζ appears to be greater than 1, and the result of fig. 5 (b) shows that in the case of cfln=0.2, the modulus value of the growth factor ζ is not greater than 1. This suggests that conformal mesh techniques may further reduce the CFL stability conditions of the FDTD process. However, as can be seen from fig. 4, the stability conditions of the proposed C-CDI-FDTD method are not affected by the conformal grid technique.
Both the traditional FDTD method and the CDI-FDTD method meet the compliance divergence attribute, and whether the conformal grid technology can influence the compliance divergence attribute of the FDTD method and the CDI-FDTD method is analyzed below.
According to the differential gaussian law:
wherein D is an electric displacement vector, ρ v Is the charge density. Equation (29) shows that in the inactive region, the divergence of the electrical displacement vector should be zero. Thus, the divergence of D in the numerical method can be solved to verify whether the C-FDTD method and the C-CDI-FDTD method also satisfy the compliance divergence attribute. The divergence of the electrical displacement vector D can be expressed as
Fig. 6 (a) is a graph showing the result of the dispersion of D on the sampling surface in the conventional FDTD method, and fig. 6 (b) is a graph showing the result of the dispersion of D on the sampling surface in the C-FDTD method. It can be found that the calculation result of the CFDTD method is identical to that of the conventional FDTD method. Fig. 7 (a) shows the result of D scattering on the sampling surface (cfln=1) in the conventional CDI-FDTD method, and fig. 7 (b) - (D) show the result of D scattering on the sampling surface when cfln=1, 4,8, respectively. Similarly, the calculation result of the C-CDI-FDTD method is consistent with the calculation result of the CDI-FDTD method. Comparison of the above results shows that the conformal grid technique employed by the present invention does not affect the divergent-compliant properties of the numerical method.
In addition to the above steps, the present invention further includes:
and carrying out numerical simulation on three electromagnetic models, namely the PEC cavity with the circular seam, the fighter plane model and the unmanned plane model, according to the electric field information and the magnetic field information with the curved surface characteristic structure.
In order to verify the accuracy and effectiveness of the C-CDI-FDTD method provided by the invention, numerical simulation is carried out on three electromagnetic models, including a PEC cavity with circular seams, a fighter plane model and an unmanned plane model.
A PEC cavity with circular slits:
as shown in fig. 8, the simulation space has a size of 0.35m×0.5m×0.35m, and is truncated using 10 layers. The PEC cavity size was 0.25m x 0.225m x 0.25m, and the circular seam radius size was 0.06m. The position of the excitation point is 0.1m away from the circle center of the circular seam, and the time domain form is as follows:
wherein t is 0 =4τ, τ= 1.0618ns. The probe point is the center of the PEC cavity.
The calculation example adopts a fine grid CFDTD method, a coarse grid C-CDI-FDTD method and a coarse grid CDI-FDTD method to carry out electromagnetic simulation of the models, and simultaneously takes the calculation result of the fine grid CFDTD method as a reference solution, and the space step sizes of the coarse grid and the fine grid are 5 multiplied by 10 respectively -3 m and 2.5X10 -3 m. In order to ensure convergence of the calculation result of the C-FDTD method, cfln=0.2 was taken. Fig. 9 shows time domain waveform results obtained at detection points by different methods, when cfln=1, the calculation result of the C-CDI-FDTD method is better matched with the calculation result of the fine-grid CFDTD method, and the result of the CDI-FDTD method has a certain error with the result of the fine-grid CFDTD method. Similarly, when cfln=4, the C-CDI-FDTD method is also closer to the reference solution than the CDI-FDTD method. In addition, lead toThe inset from the figures shows that the C-CDI-FDTD method gives results closer to the reference solution when cfln=4 than when CDI-FDTD gives cfln=1.
Meanwhile, according to a calculation formula of Shielding Effectiveness (SE): :
wherein F is represented as a Fourier transform,representing the time domain results at the probe point in free space and with the cavity model, respectively. Fig. 10 is a graph showing the variation of SE results with frequency calculated by different methods, and the difference between the calculated results of the different methods is similar to that shown in fig. 9, so as to verify the correctness of the C-CDI-FDTD method according to the present invention.
And B, fighter plane model:
in order to further verify the correctness of the C-CDI-FDTD method provided by the invention, a fighter plane model with a more complex structure is considered. Fig. 11 is a schematic view of a fighter plane model, the maximum lengths of the model in three directions being 1.57m×2.05m×0.49m, respectively. The whole computation space size is 2.2m×2.6m×1.4m, also truncated with CPML. The spatial step sizes of the coarse mesh and the fine mesh adopted in the numerical calculation are respectively 0.02m and 0.01m. In the calculation example, a fine grid FDTD method, a coarse grid C-CDI-FDTD method and a coarse grid CDI-FDTD method are adopted to carry out numerical simulation. The excitation source used in the computation space is a differential Gaussian pulse, where t 0 ＝5τ，τ＝1.0618ns。
Fig. 12 (a) and (b) show mesh models established using conventional Yee mesh technology and conformal mesh technology, respectively, according to the fighter plane model of fig. 11. Comparing the two modeling methods, it can be found that in some areas containing curved surface structures, the electromagnetic model established by using the conformal grid technology is smoother than the electromagnetic model established by using the Yee grid technology, because the Yee grid modeling technology can directly equivalent some curved surface structure parts into regular rectangular structures, and the conformal grid technology can realize smooth approximate treatment of the curved surface structures.
According to the simulation environment established by the present example, fig. 13 shows the results of the two-station RCS of the fighter plane model at 300 MHz. Wherein (a) is the result of the C-CDI-FDTD method and CDI-FDTD method when cfln=1 and (b) is the result of the C-CDI-FDTD method and CDI-FDTD method when cfln=4, while the result of the fine-grid FDTD method when cfln=1 is given. It can be found that when cfln=1, the result obtained by the coarse grid C-CDI-FDTD method is closer to the calculation result of the fine grid FDTD method than the coarse grid CDI-FDTD method. When cfln=4, although the calculation result of the coarse grid C-CDI-FDTD method is different from the calculation result of the fine grid FDTD method to some extent, the calculation accuracy is still higher than that of the coarse grid CDI-FDTD method.
FIG. 14 shows E obtained at the detection point (1.2 m,0.8m,0.4 m) by various methods z Time domain waveform diagrams of (a). As can be seen from fig. 13, in both cases cfln=1 and cfln=4, the coarse-grid C-CDI-FDTD method obtains a calculation result of the time-domain waveform at the detection point that is closer to the fine-grid FDTD method than the coarse-grid CDI-FDTD method, which is consistent with the result obtained in fig. 12.
In addition, fig. 15 shows current distributions on the surface of the electromagnetic model calculated by different methods, wherein (a), (b) and (C) correspond to the fine-grid FDTD method, the coarse-grid C-CDI-FDTD method and the coarse-grid CDI-FDTD method, respectively. By comparing the calculation results of the fine grid FDTD method, the calculation result of the coarse grid C-CDI-FDTD method is clear, the calculation result of the CDI-FDTD method is very fuzzy, and the difference between the calculation result of the coarse grid C-CDI-FDTD method and the calculation result of the fine grid FDTD method is larger. The modeling scheme of the C-CDI-FDTD method can better capture the curved surface structural characteristics of the electromagnetic target.
An unmanned aerial vehicle model is used for verifying the correctness and the validity of the C-CDI-FDTD method. The computational space size is 0.65m by 0.275m by 0.45m. In numerical calculation, the size of the coarse mesh is 5×10 -3 m, the size of the fine mesh is 2.5X10 - 3 m. The time domain form of the incident plane wave is the same as equation (33), where t 0 ＝4τ，τ＝0.5309ns。
According to the double-station RCS results calculated by the fine grid FDTD method, the coarse grid C-CDI-FDTD method and the coarse grid CDI-FDTD method at 650MHz, it can be found that the calculation results of the C-CDI-FDTD method are closer to the reference solution than the CDI-FDTD method in the case of cfln=1, 4. Meanwhile, in a partial frequency range, the result obtained by the coarse grid C-CDI-FDTD method at CFLN=4 is almost identical with the result obtained by the coarse grid CDI-FDTD method at CFLN=1.
Finally, table 1 compares the calculation efficiency of the different methods, and it can be found that the coarse grid C-CDI-FDTD has higher calculation efficiency when cfln=1 than the fine grid FDTD method, and is more obvious when cfln=4. This is because the time step size corresponding to the coarse mesh when cfln=1 is larger than the time step size corresponding to the fine mesh when cfln=1. Meanwhile, the fine-grid FDTD method requires iteratively solving values of more field components. Although the CDI-FDTD method is slightly more computationally efficient than the C-CDI-FDTD method, this advantage is difficult to remedy its disadvantage in terms of larger computational errors.
TABLE 1 simulation time for different methods under different conditions
Example 2:
FIG. 2 is a diagram of a curved surface feature simulation system according to the present invention, as shown in FIG. 2, the curved surface feature simulation system includes:
an electromagnetic information acquisition module 201 for acquiring electric field information and magnetic field information in a free space without damage;
the curved surface feature structure determining module 202 is configured to obtain electric field information and magnetic field information with a curved surface feature structure according to the electric field information and the magnetic field information by adopting a method of combining a conformal grid and CDI-FDTD.
The electromagnetic information acquisition module 201 specifically includes:
a maxwell's equations acquisition unit for acquiring maxwell's equations in a lossless free space;
and the electromagnetic information acquisition unit is used for determining electric field information and magnetic field information according to the Maxwell equation.
The curved surface feature structure determining module 202 specifically includes:
and the curved surface characteristic structure determining unit is used for correcting the Ye grid area containing the curved surface structure in the electromagnetic model by adopting a method of combining the conformal grid and the CDI-FDTD according to the electric field information and the magnetic field information to obtain electric field information and magnetic field information with the curved surface characteristic structure.
The curved surface characteristic structure determining unit specifically comprises:
the curved surface characteristic structure determining subunit is used for processing the Maxwell equation by adopting a numerical discrete strategy which is the same as that of the LOD-FDTD method and combining a conformal grid method to obtain a numerical iteration formula of an electric field and a numerical iteration formula of a magnetic field, wherein the numerical iteration formula of the electric field and the numerical iteration formula of the magnetic field respectively comprise electric field information and magnetic field information with curved surface characteristic structures.
Example 3:
the present embodiment provides an electronic device, including a memory and a processor, where the memory is configured to store a computer program, and the processor is configured to execute the computer program to cause the electronic device to execute the curved surface feature structure simulation method of embodiment 1.
Alternatively, the electronic device may be a server.
In addition, the embodiment of the present invention also provides a computer readable storage medium storing a computer program, which when executed by a processor, implements the curved surface feature structure simulation method of embodiment 1.
Embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The principles and embodiments of the present invention have been described in detail with reference to specific examples, which are provided to facilitate understanding of the method and core ideas of the present invention; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (10)
1. A method for simulating a curved surface feature structure, comprising:
acquiring electric field information and magnetic field information in a nondestructive free space;
and obtaining electric field information and magnetic field information with curved surface characteristic structures by adopting a method of combining conformal grids with CDI-FDTD according to the electric field information and the magnetic field information.
2. The curved surface feature structure simulation method according to claim 1, wherein the acquiring electric field information and magnetic field information in a lossless free space specifically includes:
acquiring maxwell's equations in a lossless free space;
and determining electric field information and magnetic field information according to the Maxwell equation.
3. The method for simulating a curved surface feature structure according to claim 2, wherein the method for combining the CDI-FDTD with the conformal grid is adopted according to the electric field information and the magnetic field information to obtain the electric field information and the magnetic field information with the curved surface feature structure, specifically comprising:
and correcting the Ye grid region containing the curved surface structure in the electromagnetic model by adopting a method of combining conformal grids and CDI-FDTD according to the electric field information and the magnetic field information to obtain electric field information and magnetic field information with curved surface characteristic structures.
4. The curved surface feature structure simulation method according to claim 3, wherein the method for combining the conformal grid and the CDI-FDTD according to the electric field information and the magnetic field information corrects a Yee grid region including a curved surface structure in an electromagnetic model to obtain electric field information and magnetic field information having a curved surface feature structure, and specifically includes:
and processing the Maxwell equation by adopting a numerical discrete strategy which is the same as that of the LOD-FDTD method and combining a conformal grid method to obtain a numerical iteration formula of an electric field and a numerical iteration formula of a magnetic field, wherein the numerical iteration formula of the electric field and the numerical iteration formula of the magnetic field respectively comprise electric field information and magnetic field information with curved surface characteristic structures.
5. The curved surface feature modeling method of claim 1, further comprising:
and performing stability analysis on the electric field information and the magnetic field information with the curved surface characteristic structure by using a Von Neumann method.
6. The curved surface feature modeling method of claim 1, further comprising:
and carrying out numerical simulation on three electromagnetic models, namely the PEC cavity with the circular seam, the fighter plane model and the unmanned plane model, according to the electric field information and the magnetic field information with the curved surface characteristic structure.
7. A curved surface feature modeling system, comprising:
the electromagnetic information acquisition module is used for acquiring electric field information and magnetic field information in a nondestructive free space;
and the curved surface characteristic structure determining module is used for obtaining the electric field information and the magnetic field information with the curved surface characteristic structure by adopting a method of combining the conformal grid and the CDI-FDTD according to the electric field information and the magnetic field information.
8. The curved surface feature modeling system of claim 7, wherein the electromagnetic information acquisition module specifically comprises:
a maxwell's equations acquisition unit for acquiring maxwell's equations in a lossless free space;
and the electromagnetic information acquisition unit is used for determining electric field information and magnetic field information according to the Maxwell equation.
9. The surface feature modeling system of claim 8, wherein the surface feature determination module specifically comprises:
and the curved surface characteristic structure determining unit is used for correcting the Ye grid area containing the curved surface structure in the electromagnetic model by adopting a method of combining the conformal grid and the CDI-FDTD according to the electric field information and the magnetic field information to obtain electric field information and magnetic field information with the curved surface characteristic structure.
10. The curved surface feature modeling system of claim 9, wherein the curved surface feature determination unit specifically comprises:
the curved surface characteristic structure determining subunit is used for processing the Maxwell equation by adopting a numerical discrete strategy which is the same as that of the LOD-FDTD method and combining a conformal grid method to obtain a numerical iteration formula of an electric field and a numerical iteration formula of a magnetic field, wherein the numerical iteration formula of the electric field and the numerical iteration formula of the magnetic field respectively comprise electric field information and magnetic field information with curved surface characteristic structures.
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