Field line coupling simulation method under complex terrain

Abstract

The invention relates to a field line coupling simulation method under a complex terrain, belongs to the technical field of computational electromagnetism and electromagnetic compatibility, and solves the technical problem that the calculation precision is affected due to an edge effect existing in field line coupling calculation by a finite difference time domain method. The field line coupling simulation method comprises the following steps: establishing a layered irregular complex terrain and a closed TF / SF boundary; calculating an excitation field of a total field scattering field TF / SF boundary by adopting a fine line time domain finite difference method; and performing iterative calculation on field line coupling at the position of the cable by adopting a fine line time domain finite difference method to obtain a current I and a unit length charge Q at a cable sampling point. The method is used for field line coupling high-precision solution under the complex terrain.

Description

Technical Field

[0001] This invention belongs to the field of computational electromagnetics and electromagnetic compatibility technology, specifically relating to a field line coupling simulation method under complex terrain. Background Technology

[0002] The study of field-line coupling under complex terrain conditions is of significant value in both theory and practical applications. Strong electromagnetic pulses (SEMs) can induce strong currents in cables, posing a potential threat to electronic and electrical equipment, power systems, and communication systems. Therefore, to accurately assess the impact of SEMs on these devices and systems, it is necessary to conduct in-depth research on the coupling effect between SEMs and cables. However, complex terrain is a crucial background for cables, interacting with SEMs and causing phenomena such as reflection, scattering, and diffraction. This alters the frequency domain electromagnetic distribution characteristics, reconstructs the electromagnetic pulse waveform, and generates depolarization effects, resulting in changes in the spatial, frequency, temporal, and polarization domains of the electromagnetic environment, thereby affecting the current coupled by the SEM in the cables. Solving for cable coupling under complex terrain conditions faces technical challenges related to complex terrain and multi-scale analysis. Traditional studies on cable coupling in terrain generally equate the ground to an ideal horizontal surface. This simplification ignores the complex effects of actual terrain undulations, reducing the accuracy of coupling effect analysis and failing to meet the high-precision analysis requirements for field-line coupling effects. Therefore, in recent years, scholars have begun to focus on and dedicate themselves to developing methods capable of addressing field-line coupling problems under complex terrain conditions. However, to date, accurately calculating field line coupling under irregular terrain remains a challenging task, not to mention solving for field line coupling under complex layered terrain.

[0003] The FDTD method, based on time-domain differential equations, is a powerful tool for solving electromagnetic wave propagation, scattering, and coupling problems. FDTD directly discretizes the time-domain Maxwell equations, enabling simulation of time-harmonic continuous waves and non-time-harmonic pulse waves. However, when using FDTD to calculate cable coupling in rough terrain, the incident wave is typically applied to the rough ground and cable via the TF / SF boundary on the upper surface, with the sides directly connected to absorbing boundaries. This requires truncation of the ground, which generates spurious non-physical diffraction fields and edge effects, affecting computational accuracy. Currently, the academic community widely uses window functions or conical incident waves to eliminate edge effects, but neither method can truly introduce the actual incident wave source into the computational domain. Summary of the Invention

[0004] To overcome the shortcomings of the finite-difference time-domain method in calculating field line coupling, which has the disadvantage of edge effects affecting the calculation accuracy, this invention proposes a field line coupling simulation method under complex terrain.

[0005] The technical solution adopted by this invention to solve its technical problem is:

[0006] A field-line coupled simulation method for complex terrain includes the following steps:

[0007] Step 1: Establish a field-line coupling model for complex terrain.

[0008] Establish a layered, irregular, complex terrain; extend a horizontal structure at both ends of each truncated terrain layer, with the horizontal structures at both ends at the same height; the extended horizontal structure is used to provide an excitation source for the field line under the complex terrain.

[0009] Establish a closed total field scattering field (TF / SF) boundary; the upper boundary is located in the uppermost free space, the lower boundary is located in the lowermost ground, and the two side boundaries extend through the horizontal structure of the ground; the total field scattering field (TF / SF) boundary is used to introduce excitation sources for complex terrain and cables, so that the total field scattering field (TF / SF) boundary includes cables and complex terrain surfaces.

[0010] Step 2: Calculate the excitation field at the boundary of the total field scattering field.

[0011] The excitation field at the TF / SF boundary of the total field scattering field is calculated using the thin-line finite-difference time-domain method. The specific calculation is as follows:

[0012] For an incident wave with an azimuth angle of φ, the excitation field components of the total scattered field TF / SF boundary are calculated as follows:

[0013]

[0014] In equation (9), F' x 、F' y F represents the excitation field components in the x and y directions of the azimuth angle φ. x F y These are the excitation field components along the Z-axis in the x and y directions corresponding to a plane wave with an incident angle θ and an incident surface located on the XOZ plane.

[0015] Step 3, Field Line Coupling Calculation

[0016] Using the thin-line finite-difference time-domain method, the field-line coupling is iteratively calculated at the location of the cable to obtain the current I and the charge Q per unit length at the cable sampling point. The calculation formulas are as follows:

[0017]

[0018] In equations (16) and (17), L is the cellular inductance per unit length of the cable itself. <E ξ > represents the tangential electric field at the sampling point on the cable, Δ represents the spatial sampling interval on the cable, n represents the discrete point in time, k represents the discrete point in the z direction, and Δt represents the discrete time.

[0019] The above-mentioned field-line coupling simulation method for complex terrain, step 2, further includes:

[0020] When the incident angle is θ and the incident surface is a plane wave located on the XOZ plane, for any excitation field component F at any point (x, y, z) on the total scattered field TF / SF surface... w (x,y,z,t), represented by the excitation field components on the Z-axis, is as follows:

[0021]

[0022] In equation (8), F is the electric field E or the magnetic field H, w is the x, y, z direction of the coordinate axis, c is the speed of light, and t is time.

[0023] The above-mentioned field-line coupling simulation method for complex terrain, step 3, further includes:

[0024] The electric field E and magnetic field H in the x, y, and z directions at the location of the cable are calculated iteratively using the finite-difference time-domain method. The calculation formulas are as follows:

[0025]

[0026]

[0027] In the above formula, m is the discrete location of the electric or magnetic field, CA(m), CB(m), CP(m), and CQ(m) are the medium-related coefficients in the finite-difference time-domain (FDTD) iteration, i, j, and k are the discrete points in the x, y, and z directions, respectively, Δx, Δy, and Δz are the discrete intervals in the x, y, and z directions, respectively, n is the discrete point in time, and Δt is the discrete time.

[0028] The beneficial effects of this invention are:

[0029] A field-line coupling simulation method for complex terrain can more accurately simulate the impact of complex terrain on the electromagnetic environment and cable coupling, meeting the requirements of high-precision analysis.

[0030] A field-line coupling simulation method for complex terrain is proposed, applicable to various complex terrain conditions (including layered surface models), and has strong applicability. It can solve the problems faced by numerical methods in complex terrain and multi-scale scenarios. Attached Figure Description

[0031] Figure 1 It is a traditional field-line coupled FDTD simulation model for complex terrain. This model only loads the excitation source on the upper surface, resulting in low accuracy.

[0032] Figure 2 This is a field-line coupled FDTD simulation model under complex terrain according to an embodiment of the present invention;

[0033] Figure 3 This is a schematic diagram of loading a layered medium (LM) finite-difference time-domain (FDTD) plane wave excitation source;

[0034] Figure 4 These are the results of time-domain field line coupling on the horizontal ground, used to verify the correctness of the LM-TW FDTD mixing method;

[0035] Figure 5 The results show the coupling current amplitude at different locations of the cable under complex terrain. The results differ significantly from those on a horizontal plane, indicating the necessity of considering complex terrain. Detailed Implementation

[0036] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0037] Example 1

[0038] A method for simulating field-line coupling in complex terrain is proposed, which combines layered medium FDTD and thin-line FDTD, namely the LM-TW FDTD method, to effectively simulate field-line coupling in complex terrain environments. Existing methods typically assume an ideal horizontal surface, neglecting the impact of actual terrain variations on cable coupling, thus leading to decreased accuracy of the analysis results. To address the problems in existing technologies, this invention provides an LM-TW FDTD method for field-line coupling in complex terrain, which can solve field-line coupling problems with high accuracy in complex terrain.

[0039] This invention proposes an LM-TW FDTD method for field-line coupling under complex terrain, which specifically includes the following steps:

[0040] Step 1: Establish a field-line coupling solution model for complex terrain. For example... Figure 2 As shown, a layered, irregular, complex terrain is established. Figure 2 This example uses a two-layer irregular terrain (in practice, it can be a single layer or any number of layers). Each truncated layer extends horizontally from both ends, ensuring the horizontal structures at both ends are at the same height. The purpose of this horizontal extension is to provide an excitation source for the complex terrain and cables using the layered media (LM) finite-difference time-domain (FDTD) method. A closed total field scattering (TF / SF) boundary is then established, with the upper boundary located in the uppermost free space (above the ground) and the lower boundary in the lowermost ground layer, extending horizontally through the ground on both sides. The TF / SF boundary is used to introduce an excitation source for the complex terrain and cables, and it must ensure that the TF / SF boundary includes both the cables and the complex terrain surface.

[0041] Step 2: Calculate the excitation field on the boundary of the total field scattering field using the LM FDTD method. For example... Figure 3 As shown, for a plane wave with an incident angle of θ and an incident surface located at the XOZ plane, the formulas for the one-dimensional electric field E and magnetic field H along the Z-axis are:

[0042]

[0043]

[0044] in, For the auxiliary magnetic field component, μ0 is the free permeability, σ is the conductivity at the calculated location, ∈ r To calculate the relative permittivity at the location point, ∈ ro Let Y be the relative permittivity of the uppermost space, ∈0 be the permittivity of vacuum, Y0 be the characteristic admittance of vacuum, and Z0 be the characteristic impedance of vacuum. The LM FDTD iteration of the electric field components and magnetic field components on the Z-axis can be performed according to formulas (1)-(7).

[0045] For any point (x, y, z) on the TF / SF surface, any field component F w (x, y, z, t) can all be represented by field components on the Z-axis.

[0046]

[0047] Where F represents the electric field E or the magnetic field H, w represents the x, y, and z axes, and c represents the speed of light.

[0048] For an incident wave with an incident azimuth angle of φ, the corresponding field components can be obtained further through coordinate transformation.

[0049]

[0050] Among them, F' w This indicates the field component considering the azimuth angle φ.

[0051] Step 3: Perform standard FDTD calculations and thin-line FDTD calculations. Iterative formulas for the standard FDTD method.

[0052]

[0053]

[0054]

[0055] In the above formula, the label m is the discrete location of the electric or magnetic field; CA(m), CB(m), CP(m), and CQ(m) are the medium-related coefficients in the FDTD iteration, i, j, and k represent discrete points in the x, y, and z directions, respectively, with discrete intervals of Δx, Δy, and Δz, and n represents the discrete point in time, with a discrete time of Δt.

[0056] The location of the cable is determined using the thin-wire FDTD iterative formula proposed by Holland.

[0057]

[0058] Where I represents the current magnitude at the cable sampling point, Q represents the charge per unit length at the cable sampling point, and L represents the cellular inductance per unit length of the cable itself. <E ξ > represents the tangential electric field at the sampling point on the cable, and Δ represents the spatial sampling interval on the cable.

[0059] Experimental verification

[0060] To verify the correctness and effectiveness of this invention, electromagnetic simulation was performed on cables under rough ground. Without loss of generality, a strong electromagnetic pulse, represented by a high-altitude electromagnetic pulse (HEMP), was used as an example for the simulation.

[0061] E inc (t)=E0k(e -αt -e -βt (18)

[0062] Where, E0 = 5 × 10 4 V / m, k=1.3, α=4×10 7 s -1 β=6×10 8 s -1 .

[0063] First, the reliability of the method is verified using a horizontal lossy ground as an example. The horizontal ground is divided by the z=0 plane, with free space above and the ground below, and the ground is set as an ideal metallic ground. The incident angle is θ=60°, φ=0°, and the polarization direction is vertical; the cable is placed vertically, with one end open and the other end grounded, with a length of 1m, and the grounding resistances are 100Ω and 400Ω respectively. Figure 4 This presents the results of a comparison between the LM-TW FDTD method and CST commercial software. Figure 4 It can be seen that the LM-TW FDTD method proposed in this invention matches the calculation results of commercial software very well, verifying the effectiveness of the LM-TW FDTD hybrid method.

[0064] Subsequently, field-line coupling under complex terrain was simulated. The electromagnetic parameters of the complex terrain are ∈ r=10, σ=0.01S / m; The rough ground is selected as a Gaussian rough surface with a root mean square height h=0.5m and a correlation length l=2m; The incident angle is θ=30°, φ=0°, and the polarization direction is perpendicular; The cable is placed horizontally with a length of 60m, a radius of 0.001m, a height of 2m above the ground, and open at both ends. Figure 5 The figures show the current amplitude of cable coupling under rough terrain and level ground, demonstrating that complex terrain has a significant impact on the coupling current on the cable. This illustrates the importance of considering complex terrain.

Claims

1. A field-line coupling simulation method for complex terrain, characterized in that, Includes the following steps: Step 1, establish a field-line coupling model for complex terrain: Establish a layered, irregular, complex terrain; extend a horizontal structure at both ends of each truncated terrain layer, with the horizontal structures at both ends at the same height; the extended horizontal structure is used to provide an excitation source for the field line of the complex terrain; Establish a closed total field scattering field (TF / SF) boundary; the upper boundary is located in the uppermost free space, the lower boundary is located in the lowermost ground, and the two side boundaries extend through the horizontal structure of the ground; the total field scattering field (TF / SF) boundary is used to introduce excitation sources for complex terrain and cables, so that the total field scattering field (TF / SF) boundary includes cables and complex terrain surfaces; Step 2, calculate the excitation field at the boundary of the total field scattering field: The excitation field at the TF / SF boundary of the total field scattering field is calculated using the thin-line finite-difference time-domain method. The specific calculation is as follows: For an incident wave with an azimuth angle of φ, the excitation field components at the TF / SF boundary of the total field scattering field are calculated as follows: In equation (9), F' x 、F' y F represents the excitation field components in the x and y directions of the azimuth angle φ. x F y These are the excitation field components along the Z-axis in the x and y directions corresponding to the plane wave with an incident angle θ and an incident surface located on the XOZ plane; Step 3, Field Line Coupling Calculation: Using the thin-line finite-difference time-domain method, the field-line coupling is iteratively calculated at the location of the cable to obtain the current I and the charge Q per unit length at the cable sampling point. The calculation formulas are as follows: In equations (16) and (17), L is the cellular inductance per unit length of the cable itself. <E ξ > represents the tangential electric field at the sampling point on the cable, Δ represents the spatial sampling interval on the cable, n represents the discrete point in time, k represents the discrete point in the z direction, and Δt represents the discrete time.

2. The field-line coupling simulation method for complex terrain according to claim 1, characterized in that, Step 2 further includes: When the incident angle is θ and the incident surface is a plane wave located on the XOZ plane, for any excitation field component F at any point (x, y, z) on the total scattered field TF / SF surface... w (x,y,z,t), represented by the excitation field components on the Z-axis, is as follows: In equation (8), F is the electric field E or the magnetic field H, w is the x, y, z direction of the coordinate axis, c is the speed of light, and t is time.

3. The field-line coupling simulation method for complex terrain according to claim 1, characterized in that, Step 3 further includes: The finite-difference time-domain method is used to iteratively calculate the electric field E and magnetic field H in the x, y, and z directions at the location of the cable. The calculation formula is as follows: In the above formula, m is the discrete location of the electric or magnetic field, CA(m), CB(m), CP(m), and CQ(m) are the medium-related coefficients in the finite-difference time-domain (FDTD) iteration, i, j, and k are the discrete points in the x, y, and z directions, respectively, Δx, Δy, and Δz are the discrete intervals in the x, y, and z directions, respectively, n is the discrete point in time, and Δt is the discrete time.

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