Adaptive modeling method for atmospheric transport of gamma radiation under the influence of shock waves

Abstract

In order to solve the technical problem of the difficulty in achieving precise and efficient modeling in existing simulations of gamma radiation atmospheric transport under the influence of shock waves, the present invention provides a method for adaptive modeling of gamma radiation atmospheric transport under the influence of shock waves. Specifically, the method comprises the following steps: first, a model is established based on the atmospheric density distribution function and a uniform coarse grid is divided with a given step size; then, the grid is refined and interpolated according to the relative degree of change in atmospheric density; second, nodes with little change in atmospheric density are found in the refined grid and merged; finally, a precise and efficient adaptive grid model of gamma radiation atmospheric transport is obtained, and then a Monte Carlo program is used to carry out computational simulation. The present invention is suitable for adaptive grid division of atmospheric density distribution, and is also suitable for adaptive grid division of time, energy, etc. It is a new method for constructing a Monte Carlo simulation model of gamma radiation atmospheric transport under the influence of shock waves.

Description

Technical Field

[0001] The present invention belongs to the technical field of Monte Carlo numerical simulation of gamma radiation transport, and relates to an adaptive modeling method for gamma radiation atmospheric transport considering the influence of shock waves. Background Art

[0002] An aerial explosion refers to the explosion of explosives, artillery shells, etc. at a certain height above the ground. The shock wave generated by a strong aerial explosion has the characteristics of high initial pressure, slow attenuation with propagation distance, and long killing and destructive range. It will cause drastic changes in atmospheric density, causing the air mass to be mainly concentrated in a narrow area near the wave front and it will take a long time to return to normal atmosphere. During this period, the propagation of gamma radiation will be affected by the change in atmospheric density caused by the shock wave, which is a problem of gamma radiation transport in non-uniform and continuously changing media.

[0003] Monte Carlo methods can handle complex geometric problems and track the entire physical process of particle transport. Gamma radiation transport in the atmosphere is often simulated using Monte Carlo methods. Conventional modeling approaches for gamma radiation transport, where atmospheric density varies dramatically with altitude, divide the atmosphere into multiple layers of homogeneous media based on density variations (Byrd, RC, 1995, "Atmospheric transport of neutrons and gammarays from a high-altitude nuclear detonation."). To ensure reliable results, sufficiently precise atmospheric stratification along the altitude dimension is required, which increases the complexity of the geometric model and incurs a significant computational burden. Existing literature has used the mass distance sampling method instead of the traditional step sampling method to realize the Monte Carlo simulation of gamma-ray transport in an inhomogeneous atmosphere (Tao Yinglong, Zhu Jinhui, Wang Jianguo, et al., published in "Computational Physics", 2010, "Monte Carlo simulation method of gamma-ray transport in an inhomogeneous atmosphere"). This method has high computational efficiency, but the mass distance sampling method relies on the fact that the atmospheric density varies with altitude and has a uniform e-exponential function form.

[0004] The atmospheric density distribution under the influence of strong explosion shock waves is spherical. Its radial distribution is related to the explosion power and the time after the explosion. It is difficult to use a unified function to describe its density distribution, such as Figure 1As shown, it is difficult to use the mass distance sampling method. When the conventional multi-layer uniform medium combination method is used to construct the atmospheric transport model under the influence of shock waves, the equal step size layering method is generally adopted to facilitate modeling. The accuracy of the model depends on the selection of the step size. If the step size is large, it is difficult to accurately reflect the atmospheric density distribution, making the geometric model inaccurate; if the step size is small, it will lead to too many grid elements in the established geometric model, which will bring a large amount of calculation and thus affect the calculation efficiency. When performing Monte Carlo simulation calculations of gamma radiation transport under the influence of shock waves, in order to seek a balance between the accuracy of the Monte Carlo simulation geometric model and the calculation efficiency, it is urgent to establish a precise and efficient modeling method that can accurately describe the atmospheric density distribution while having as few geometric grid elements as possible. Summary of the Invention

[0005] The purpose of the present invention is to solve the technical problem of difficulty in fine and efficient modeling in the existing simulation of gamma radiation atmospheric transport under the influence of shock waves, and to provide an adaptive modeling method for gamma radiation atmospheric transport under the influence of shock waves.

[0006] The concept of the present invention is as follows: first, a model is established based on the atmospheric density distribution function and a uniform coarse grid is divided with a given step size; then, the grid is refined and interpolated according to the relative change in atmospheric density; secondly, nodes with little change in atmospheric density are found in the refined grid and merged; finally, a fine and efficient adaptive grid model of gamma radiation atmospheric transport is obtained, and then a Monte Carlo program is used to carry out computational simulation.

[0007] In order to achieve the above-mentioned purpose and complete the above-mentioned inventive concept, the technical solution adopted by the present invention is as follows:

[0008] A method for adaptive modeling of atmospheric transport of gamma radiation under the influence of shock waves is characterized in that it comprises the following steps:

[0009] Step 1) With the explosion point as the center, the entire area is uniformly meshed according to the atmospheric density radial distribution function and the time, and the given step size S0 is set to obtain a multi-layer uniform medium combination model, and the atmospheric density at each grid node is calculated;

[0010] Step 2), jump to the first grid node;

[0011] Step 3), calculate the relative error of atmospheric density at the first grid node and the second grid node;

[0012] Step 4) Determine whether the inter-grid step size between the first grid node and the second grid node is less than the minimum resolution S of the adaptive grid. N If yes, jump to the next grid node; if no, execute step 5);

[0013] Step 5) Determine whether the relative error is greater than the set maximum relative error A. If so, insert a new grid node in the middle of the two nodes, calculate the atmospheric density at the newly inserted grid node, use the newly inserted grid node as the second grid node, and postpone the original second grid node and the subsequent grid nodes in sequence, and return to step 3) until the relative error of the atmospheric density at the first grid node and the second grid node is less than the maximum relative error A, or the grid step size between the first grid node and the second grid node is less than the minimum resolution S of the adaptive grid. N ; If not, jump to the next grid node;

[0014] Step 6) Switch the grid nodes in turn, using the same method from step 3) to step 5) until the relative error of the atmospheric density at all grid nodes and the next adjacent grid node is less than the maximum relative error A, or the inter-grid step size between the next adjacent grid node is less than the minimum resolution S of the adaptive grid. N ;

[0015] Step 7) According to the final sorting number of all grid nodes, jump to the first grid node again;

[0016] Step 8), calculate the relative error of the atmospheric density at the first grid node and the second grid node, and determine whether the relative error is less than the set minimum relative error B. If so, merge the two grid nodes into one grid node, delete the second grid node, renumber the subsequent grid nodes in sequence, and execute step 9); if not, execute step 10);

[0017] Step 9), return to step 8), recalculate the relative error of atmospheric density at the first grid node and the next grid node, until the relative error of atmospheric density at the first grid node and its adjacent grid nodes is greater than the minimum relative error B; Step 10), switch the grid nodes in sequence, using the same method of steps 8)-9), until the relative error of atmospheric density at all grid nodes and their adjacent next grid nodes is greater than the set minimum relative error B;

[0018] Step 11) Based on the positions of all adaptive grid nodes finally obtained, a refined and efficient adaptive geometric model of gamma radiation atmospheric transport is established, detectors are set along the radial direction, and then a Monte Carlo simulation of gamma radiation atmospheric transport is carried out to calculate the gamma radiation tissue dose.

[0019] Furthermore, in step 1), the set given step length S0 can preliminarily reflect the changing trend of the atmospheric density distribution function.

[0020] Furthermore, in step 4), the minimum resolution of the adaptive grid S N for:

[0021] S N =S0 / 2 N

[0022] Where N is the maximum number of splits of the adaptive grid.

[0023] Furthermore, in step 3) and step 8), the calculation process of the relative error of atmospheric density is:

[0024] The relative error E between the atmospheric density at the i-th grid node and the i+1-th grid node rel for:

[0025]

[0026] Where i is the order number of the grid node, ρ i is the atmospheric density at the i-th grid node.

[0027] Furthermore, in step 5), the maximum relative error A=5%;

[0028] In step 9), the minimum relative error B=0.1%.

[0029] Furthermore, in step 1), the radial distribution function of the atmospheric density is a continuous function or a piecewise function.

[0030] Compared with the prior art, the present invention has the following beneficial technical effects:

[0031] 1. The adaptive modeling method for atmospheric transport of gamma radiation under the influence of shock waves proposed in the present invention automatically increases the step size and merges the layers in areas with small relative errors in atmospheric density (e.g., less than 0.1%), and increases the number of layers in areas with large atmospheric density errors, thereby avoiding the reduction in geometric model accuracy caused by excessively large step sizes in the equal-step multi-layer uniform medium combination method.

[0032] 2. The adaptive modeling method of gamma radiation atmospheric transport under the influence of shock waves proposed in the present invention avoids the increase in calculation amount caused by too many geometric grid elements in the equal-step multi-layer uniform medium combination method by automatically reducing the step size and increasing the number of layers in areas where the relative error of atmospheric density is too large (such as more than 5%), maintains sufficient model accuracy, and can effectively improve the model calculation efficiency.

[0033] 3. The adaptive modeling method for atmospheric transport of gamma radiation under the influence of shock waves proposed in the present invention is not only applicable to the adaptive grid division of atmospheric density distribution, but also to the adaptive grid division of time, energy, etc. It can be used as a new method for constructing a geometric model for Monte Carlo simulation of atmospheric transport of gamma radiation under the influence of shock waves. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is the one-dimensional atmospheric density distribution function diagram at different times under the same size shock wave;

[0035] Figure 2 This is a flow chart of an embodiment of the method for adaptive modeling of gamma radiation atmospheric transport under the influence of shock waves of the present invention;

[0036] Figure 3 Schematic diagram of division along the radial range of 0-2000m in an embodiment of the present invention using a uniform coarse grid with a step size of 64m, an adaptive grid based on a step size of 64m, and a uniform fine grid with a step size of 4m;

[0037] Figure 4 The curves of the relative deviations between the calculation results of the adaptive grid model and the uniform coarse grid model and the benchmark value vary with distance, respectively, based on the calculation results of the uniform fine grid model with a step size of 4m in the embodiment of the present invention. DETAILED DESCRIPTION

[0038] To further clarify the objectives, advantages, and features of the present invention, the following describes in further detail, with reference to the accompanying drawings and specific examples, a method for adaptively modeling atmospheric transport of gamma radiation under the influence of shock waves, as proposed by the present invention. Those skilled in the art should understand that these embodiments are intended only to illustrate the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0039] like Figure 2 As shown, the adaptive modeling method for atmospheric transport of gamma radiation under the influence of shock waves proposed in the present invention specifically includes the following steps:

[0040] Step 1) With the explosion point as the center, the entire area is uniformly meshed according to the radial distribution function of the atmospheric density and the time, and the given step size S0 is set to obtain a multi-layer uniform medium combination model, and the atmospheric density at each grid node is calculated.

[0041] The radial distribution function of atmospheric density can have any form, including but not limited to continuous function or piecewise function, such as Figure 1 The selection of a given step size S0 should be able to preliminarily reflect the changing trend of the atmospheric density distribution function.

[0042] Step 2) Jump to the first grid node.

[0043] Step 3) Calculate the relative error of atmospheric density between the first grid node and the second grid node.

[0044] Step 4) Determine whether the inter-grid step size between the first grid node and the second grid node is less than the minimum resolution S of the adaptive grid. N If yes, jump to the next grid node; if no, execute step 5).

[0045] Adaptive grid minimum resolution S N for:

[0046] S N =S0 / 2 N

[0047] Among them, N is the maximum number of splits of the adaptive grid, and S0 and N are both set manually.

[0048] Step 5) Calculate the relative error of the atmospheric density at the first grid node and the second grid node, and determine whether the relative error is greater than the set maximum relative error A (generally set to 5%). If so, insert a new node in the middle of the two nodes, calculate the atmospheric density at the newly inserted grid node, and execute step 6); if not, jump to the next grid node;

[0049] The relative error E between the atmospheric density at the i-th grid node and the i+1-th grid node rel for:

[0050]

[0051] Among them, ρ i is the atmospheric density at the i-th grid node.

[0052] Step 6) Repeat step 3) to calculate the relative error of atmospheric density between the first grid node and the newly inserted grid node until the relative error of atmospheric density between the first grid node and its adjacent grid nodes is less than the maximum relative error A, or the inter-grid step size between the first grid node and its adjacent grid nodes is less than the minimum resolution S of the adaptive grid. N .

[0053] Step 7) Switch the grid nodes in turn and repeat steps 3) to 6) until the relative error of the atmospheric density at all grid nodes and their adjacent grid nodes is less than the maximum relative error A, or the inter-grid step size between the first grid node and its adjacent grid nodes is less than the minimum resolution S of the adaptive grid. N .

[0054] Step 8) Reorder and number all grid nodes and jump to the first grid node again.

[0055] Step 9) Calculate the relative error of the atmospheric density at the first grid node and the second grid node, and determine whether the relative error is less than the set minimum relative error B (generally set to 0.1%). If so, merge the two grid nodes into one grid node and delete the second grid node; if not, execute step 10).

[0056] Step 10), repeat step 9), calculate the relative error of atmospheric density between the first grid node and the next grid node, until the relative error of atmospheric density between the first grid node and its adjacent grid nodes is greater than the minimum relative error B.

[0057] Step 11), switch the grid nodes in sequence, and repeat steps 9) to 10) until the relative error of atmospheric density at all grid nodes and their adjacent grid nodes is the minimum relative error B.

[0058] Step 12) Based on the final positions of all adaptive grid nodes, a refined and efficient adaptive geometric model of gamma radiation atmospheric transport is established, detectors are set along the radial direction, and then a Monte Carlo simulation of gamma radiation atmospheric transport is carried out to calculate the gamma radiation tissue dose.

[0059] The calculation model of gamma radiation tissue dose adopts the ring detector method and the dose-to-dose model.

[0060] The following is a specific example to illustrate the adaptive modeling method of gamma radiation atmospheric transport of the present invention.

[0061] First, a one-dimensional spherically symmetrical geometric model with a radius of 2000m is established. The atmosphere is an ideal uniform atmosphere with a density of 1.225kg / m 3 . Then, based on the atmospheric density distribution function at time 0.2s, the one-dimensional spherically symmetric geometry is adaptively meshed with a given step size S0 = 64m, and a fine and efficient adaptive geometric model of gamma radiation atmospheric transport is established. Secondly, an isotropic radiation source is set, and 20 detection points are evenly distributed in the radial range of 150m to 350m where the atmospheric density changes greatly. Finally, Monte Carlo simulation calculations are carried out for the fine and efficient adaptive geometric model of gamma radiation atmospheric transport, and a ring detector is used to count the measurement points. When the number of simulated particles reaches 1.0×10 7 The calculation terminates when the number of gamma-ray dose distributions is 0.000. Finally, the gamma-ray tissue dose distribution values under the adaptive grid model at the 20 measurement points are obtained. The maximum number of splits of the adaptive grid is set to 4, and accordingly, the minimum resolution of the adaptive grid is 4m.

[0062] For comparison, a uniform coarse grid model with a given step size S0 = 64m and a uniform fine grid model with a step size of 4m were constructed, and the Monte Carlo counting results at each measuring point were calculated under the conditions of the uniform coarse grid model and the uniform fine grid model. The radial grid node positions of the three models are as follows: Figure 3 So far, the gamma tissue dose distribution values under the three models are shown in Table 1.

[0063] Taking the gamma tissue dose distribution value under the uniform fine grid model with a step size of 4m as the benchmark, the gamma tissue dose distribution values calculated under the uniform coarse grid model and the adaptive grid model are compared with the benchmark value. It can be seen that the gamma tissue dose distribution value simulated under the adaptive grid model is basically consistent with the benchmark result, with a relative deviation within 0.5%, while the gamma tissue dose distribution value under the uniform coarse grid model has a relative deviation of about 5% from the benchmark value, as shown in Figure 2. Figure 4 shown.

[0064] Table 1 Gamma tissue dose distribution and relative deviation within the range of 150m to 350m from the explosion center

[0065]

[0066] At the same time, the use of the present invention for adaptive modeling of gamma radiation atmospheric transport can effectively reduce the number of geometric grid elements, thereby saving a large amount of memory space and computing time. After adopting the adaptive grid model, while ensuring the calculation accuracy, its simulation calculation time is reduced by 52.0% compared with the uniform fine grid benchmark model with a step size of 4m, as shown in Table 2.

[0067] Table 2 Computation time of three models

[0068]

[0069] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present invention.

Claims

1. A method for adaptive modeling of atmospheric transport of gamma radiation under the influence of shock waves, characterized in that: The following steps are involved: Step 1) With the explosion point as the center, the entire area is uniformly meshed according to the atmospheric density radial distribution function and the time, and the given step size S0 is set to obtain a multi-layer uniform medium combination model, and the atmospheric density at each grid node is calculated; Step 2), jump to the first grid node; Step 3) Calculate the relative error of atmospheric density between the first grid node and the second grid node; the calculation process of the relative error of atmospheric density is as follows: The relative error E between the atmospheric density at the i-th grid node and the i+1-th grid node rel for: Where i is the order number of the grid node, ρ i is the atmospheric density at the i-th grid node; Step 4) Determine whether the inter-grid step size between the first grid node and the second grid node is less than the minimum resolution S of the adaptive grid. N If yes, jump to the next grid node; if no, execute step 5); Step 5) Determine whether the relative error is greater than the set maximum relative error A. If so, insert a new grid node in the middle of the two nodes, calculate the atmospheric density at the newly inserted grid node, use the newly inserted grid node as the second grid node, and postpone the original second grid node and the subsequent grid nodes in sequence, and return to step 3) until the relative error of the atmospheric density at the first grid node and the second grid node is less than the maximum relative error A, or the grid step size between the first grid node and the second grid node is less than the minimum resolution S of the adaptive grid. N ; If not, jump to the next grid node; Step 6) Switch the grid nodes in turn, using the same method from step 3) to step 5) until the relative error of the atmospheric density at all grid nodes and the next adjacent grid node is less than the maximum relative error A, or the inter-grid step size between the next adjacent grid node is less than the minimum resolution S of the adaptive grid. N ; Step 7) According to the final sorting number of all grid nodes, jump to the first grid node again; Step 8), calculate the relative error of the atmospheric density at the first grid node and the second grid node according to the method of step 3), and determine whether the relative error is less than the set minimum relative error B. If so, merge the two grid nodes into one grid node, delete the second grid node, renumber the subsequent grid nodes in sequence, and execute step 9); if not, execute step 10); Step 9), return to step 8), recalculate the relative error of atmospheric density between the first grid node and the next grid node, until the relative error of atmospheric density between the first grid node and its adjacent grid nodes is greater than the minimum relative error B; Step 10), switching the grid nodes in sequence, using the same method from step 8) to step 9), until the relative error of the atmospheric density at all grid nodes and the next adjacent grid node is greater than the set minimum relative error B; Step 11) Based on the positions of all adaptive grid nodes finally obtained, a refined and efficient adaptive geometric model of gamma radiation atmospheric transport is established, detectors are set along the radial direction, and then a Monte Carlo simulation of gamma radiation atmospheric transport is carried out to calculate the gamma radiation tissue dose.

2. The method for adaptive modeling of atmospheric transport of gamma radiation under the influence of shock waves according to claim 1, characterized in that: In step 1), the set given step length S0 can preliminarily reflect the changing trend of the atmospheric density distribution function.

3. The method for adaptive modeling of atmospheric transport of gamma radiation under the influence of shock waves according to claim 2, characterized in that: In step 4), the minimum resolution of the adaptive grid S N for: S N =S0 / 2 N Where N is the maximum number of splits of the adaptive grid.

4. The method for adaptive modeling of atmospheric transport of gamma radiation under the influence of shock waves according to any one of claims 1 to 3, characterized in that: In step 5), the maximum relative error A=5%; In step 9), the minimum relative error B=0.1%.

5. The method for adaptive modeling of atmospheric transport of gamma radiation under the influence of shock waves according to claim 4, characterized in that: In step 1), the radial distribution function of atmospheric density is a continuous function or a piecewise function.

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