CN113744358B - Three-dimensional particle field and speed field reconstruction method based on GPU acceleration - Google Patents
Three-dimensional particle field and speed field reconstruction method based on GPU acceleration Download PDFInfo
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Abstract
The invention relates to a three-dimensional particle field and speed field reconstruction method based on GPU acceleration, which comprises the following steps: acquiring two groups of multi-camera image data with a certain time interval and a weight matrix searching curve of each camera; performing three-dimensional particle field chromatographic reconstruction based on the multi-camera image data and the weight matrix search curve by adopting a GPU (graphics processing unit), and obtaining a reconstructed three-dimensional particle field, wherein in the chromatographic reconstruction process, the light intensity reconstruction of all voxels is calculated in parallel by using the thread number which is equal to the voxel number; and partitioning the reconstructed three-dimensional particle field, extracting two diagnosis window data of each data block, performing three-dimensional cross-correlation calculation by adopting a GPU concurrence process to obtain the average speed of all windows, and reconstructing to obtain a three-dimensional speed field. Compared with the prior art, the method has the advantages of effectively reducing the expenditure of calculation time, improving the efficiency and the like.
Description
Technical Field
The invention relates to the technical field of particle image velocimetry, in particular to a three-dimensional particle field and velocity field reconstruction method based on GPU acceleration.
Background
The particle image velocimetry (Particle Image Velocimetry, PIV) technology is a non-contact and non-interference quantitative measurement means for a space flow field. The PIV technology utilizes trace particles with even scattered tiny particle diameters to follow the movement of fluid, records the movement of the trace particles in a continuous 'polishing' and 'photographing' mode, extracts the movement information of the particles from continuous trace particle images based on an image processing algorithm, and obtains the approximation of the space movement speed of the fluid. The tomographic particle image velocimetry (Tomographic Particle Image Velocimetry, tomo-PIV) technology combines PIV technology with computed tomography technology (Computed Tomography, CT), simultaneously photographs and records illuminated particle fields using multiple viewing angles (at least three cameras), and reconstructs a three-dimensional distribution of light intensity by an optical tomographic method, obtaining a three-dimensional spatial distribution of trace particles; and reconstructing the three-dimensional velocity field distribution of the flow field through a cross-correlation algorithm according to the particle field.
Compared with the traditional two-dimensional PIV technology, the Tomo-PIV technology can realize instantaneous three-dimensional flow field speed measurement and full-field quantitative measurement of a space flow field, and can provide great convenience for research on a flow field structure with complex flow fields (such as a turbulent flow and a three-dimensional vortex structure). The Tomo-PIV technology has the advantages of simple operation, high measurement precision, simple equipment, wide application range, more information acquisition quantity and the like; however, there are limitations in that higher volume illumination energy is required, huge data storage amount is required, and calculation efficiency is low.
The core step of acquiring the three-dimensional particle field in the Tomo-PIV technology is a particle field chromatography reconstruction algorithm based on an image, the calculation of a weight matrix in the calculation process needs more than 12 hours, and the calculation needs to occupy 200-500GB of storage space, so that the method consumes great calculation cost and becomes a main technical bottleneck of measuring the flow field in the PIV technology. Secondly, the speed field reconstruction after obtaining the particle distribution is also a core step of the Tomo-PIV technology, and since each particle of two frames of particle field distribution (each particle is approximately a cube grid and called a voxel) needs to be compared in detail, the number of voxels obtained by the Tomo-reconstruction is also extremely large, so that the problem of the efficiency of the speed field reconstruction is also one of application obstacles of the Tomo-PIV technology.
In recent years, research on particle field chromatography reconstruction at home and abroad focuses on improving the calculation precision of the Tomo-PIV technology, and numerous reconstruction algorithms including a multiplication algebraic reconstruction algorithm (Multiplicative Algebraic Reconstruction Techniques, MART), a self-calibration technology, a Multiplicative First Guess (MFG) algorithm, an MLOS-MART algorithm, an IntE-MART algorithm and the like are provided, so that the quality of three-dimensional particle field reconstruction and the precision of three-dimensional velocity field reconstruction are improved. But since these algorithms run on the CPU, the improvement in efficiency is not significant. In the speed field reconstruction of the PIV technology, students at home and abroad already start to accelerate the cross-correlation algorithm of the traditional two-dimensional PIV or the three-dimensional PIV by using a GPU (Graphics Processing Unit, image processor), and reconstruct a speed field; however, these researches do not further optimize the GPU thread design, only rely on the CUFFT module in the GPU function library to replace the fast fourier transform in the cross-correlation algorithm, and do not further study the multi-thread concurrency mode, so that the speed field reconstruction module cannot fully exert the advantages of the GPU.
In summary, the efficiency problems of particle field reconstruction and velocity field reconstruction severely hamper the large-scale application of the Tomo-PIV technique, requiring improvements over the prior art.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a three-dimensional particle field and speed field reconstruction method based on GPU acceleration, which effectively reduces the calculation time cost and improves the efficiency.
The aim of the invention can be achieved by the following technical scheme:
a three-dimensional particle field and speed field reconstruction method based on GPU acceleration comprises the following steps:
acquiring two groups of multi-camera image data with a certain time interval and a weight matrix searching curve of each camera;
performing three-dimensional particle field chromatographic reconstruction based on the multi-camera image data and the weight matrix search curve by adopting a GPU (graphics processing unit), and obtaining a reconstructed three-dimensional particle field, wherein in the chromatographic reconstruction process, the light intensity reconstruction of all voxels is calculated in parallel by using the thread number which is equal to the voxel number;
and partitioning the reconstructed three-dimensional particle field, extracting two diagnosis window data of each data block, performing three-dimensional cross-correlation calculation by adopting a GPU concurrence process to obtain the average speed of all windows, and reconstructing to obtain a three-dimensional speed field.
Further, the weight matrix search curve is obtained by:
calibrating a plurality of cameras to obtain a camera calibration matrix;
based on the camera calibration matrix, mapping the experimental image coordinates into a space three-dimensional real coordinate system;
and according to the space three-dimensional real coordinates obtained by mapping, approximating the line of sight of each image pixel point under the space three-dimensional real coordinates to be a cylinder, approximating each voxel under the three-dimensional real coordinates to be a sphere, approximating the contribution value of each voxel corresponding to the image pixel point to be the ratio of the volume intersected by the cylinder and the voxel to the whole voxel volume, and fitting the contribution value of each voxel corresponding to each pixel, namely, a weight matrix searching curve.
Further, the camera calibration matrix is obtained based on control constants and calibration data, the control constants including a particle field tomography reconstruction parameter and a velocity field reconstruction parameter.
Further, the particle field tomography reconstruction parameters include image data number, image data type, image data size, image data storage path, number of cameras, measurement region size and number of voxels per millimeter,
the velocity field reconstruction parameters include a diagnostic window size and a window overlap ratio.
Furthermore, in the three-dimensional particle field chromatographic reconstruction, the space distribution of the three-dimensional particle field is obtained by using the GPU-based parallel MART algorithm chromatographic reconstruction.
Further, the MART algorithm has the following calculation formula:
where k is the number of iterations, μ is the relaxation parameter, E (x j ,y j ,z j ) For voxel gray value, I (x i ,y j ) For camera image pixel values, W i,j A contribution weight matrix for each voxel j to the gray value of each pixel i, the contribution weight matrix being obtained from the multi-camera image data and a weight matrix look-up curve, N i Is the total number of voxels.
Further, the reconstructed three-dimensional particle field is segmented based on the diagnostic window size and the window overlap ratio, and two diagnostic window data of each data block are extracted through an adaptive window selection technology.
Further, the three-dimensional cross-correlation calculation specifically includes:
performing three-dimensional Fourier transform on the two diagnostic window data based on CUFFT fast Fourier transform of the GPU respectively to obtain frequency domain transform results of the two diagnostic windows;
the energy spectrums of two diagnostic window particle fields are obtained based on CUFFT convolution calculation of the GPU;
performing inverse Fourier transform based on CUFFT (inverse fast Fourier transform) of the GPU to obtain cross-correlation functions of two diagnostic window particle fields;
and (3) calculating the peak value of the cross-correlation function and the index of the three-dimensional array where the peak value is located, and calculating to obtain the average speed of the trace particles in the diagnosis window.
Further, after obtaining the average speeds of all windows, searching whether an error speed vector exists in the average speeds, and if so, performing replacement processing.
Further, the time interval is 0.001s.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention applies the novel GPU hardware to accelerate the particle field chromatography reconstruction algorithm and the three-dimensional cross-correlation algorithm of the speed field reconstruction process in the Tomo-PIV technology, can greatly improve the calculation efficiency of the Tomo-PIV technology, reduces the complicated data processing work of a user when using the related hardware equipment of the Tomo-PIV technology, saves a great deal of time, accelerates the experimental hydrodynamic research speed, provides a foundation for the wide application of the Tomo-PIV technology in the flow field reconstruction, and has important significance for accelerating the experimental fluid research.
2. The invention can greatly improve the efficiency of particle field reconstruction based on GPU parallel chromatography reconstruction and reduce the time cost of most of the chromatography particle image velocimetry technology.
3. Based on the multi-task concurrent thinking, the three-dimensional cross-correlation calculation of a large number of diagnostic windows of the particle field is decomposed into multi-process concurrent calculation, so that the calculation time cost of speed field reconstruction is greatly reduced.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a flow chart of a three-dimensional particle field chromatography reconstruction method according to the invention;
FIG. 3 is a flow chart of three-dimensional velocity field reconstruction in accordance with the present invention;
FIG. 4 is a graph of a calculated weight matrix lookup in an embodiment of the present invention;
FIG. 5 is 8 images read in an embodiment of the present invention;
FIG. 6 is a three-dimensional particle field at two moments obtained based on GPU-based accelerated reconstruction in an embodiment of the present invention;
FIG. 7 is a diagram of two temporal diagnostic window data extracted based on a three-dimensional particle field in an embodiment of the present invention;
FIG. 8 is a concurrent 4-pass, 4 sets of two-time diagnostic window data extracted based on three-dimensional particle fields in an embodiment of the present invention;
FIG. 9 is a cross-correlation function distribution obtained based on GPU-accelerated three-dimensional cross-correlation in an embodiment of the invention;
FIG. 10 is a three-dimensional velocity field result in an embodiment of the present invention.
Detailed Description
The invention will now be described in detail with reference to the drawings and specific examples. The present embodiment is implemented on the premise of the technical scheme of the present invention, and a detailed implementation manner and a specific operation process are given, but the protection scope of the present invention is not limited to the following examples.
The invention provides a three-dimensional particle field and speed field reconstruction method based on GPU acceleration, which adopts GPU to carry out three-dimensional particle field chromatography reconstruction based on multi-camera image data and a weight matrix search curve, so as to obtain a reconstructed three-dimensional particle field, and in the chromatography reconstruction process, the thread quantity equivalent to the voxel quantity is used for calculating the light intensity reconstruction of all voxels in parallel; and partitioning the reconstructed three-dimensional particle field, extracting two diagnosis window data of each data block, performing three-dimensional cross-correlation calculation by adopting a GPU concurrence process to obtain the average speed of all windows, and reconstructing to obtain a three-dimensional speed field. The method is based on GPU parallel chromatography reconstruction, so that the efficiency of particle field reconstruction can be greatly improved, and the time cost of the vast majority of the chromatography particle image velocimetry technology is reduced; meanwhile, based on the concurrent thought of multiple tasks, the three-dimensional cross-correlation calculation of a large number of diagnostic windows of the particle field is decomposed into multiple processes of concurrent calculation, so that the calculation time cost of speed field reconstruction is greatly reduced.
Referring to fig. 1-3, a flow chart of a three-dimensional particle field and velocity field reconstruction method based on GPU-accelerated tomographic particle image velocimetry according to the present invention specifically includes the following steps:
1) And reading the calculated control constant and calibration data from the input file, and calibrating the camera to obtain a camera calibration matrix.
11 Reading control constants of the present embodiment including an image data number, an image data type, an image data size, an image data storage path, the number of cameras, an actual size of a measurement area, the number of voxels per millimeter, and the like, which are required for tomographic reconstruction; parameters including the diagnostic window size, window overlap ratio, etc., required for velocity field reconstruction are shown in table 1.
TABLE 1 control parameters
12 Reading calibration data including all calibration data required to perform camera calibration and calculate the calibration matrix a.
13 Calibration of the camera, solving to obtain 12 unknowns a in the camera calibration matrix A according to the control constant data and the calibration data of the step 11) and the step 12) 11 ，a 12 ，a 13 ，a 14 ，a 21 ，a 22 ，a 23 ，a 24 ，a 31 ，a 32 ，a 33 ，a 34 The calibration function relation between the constructed space three-dimensional real coordinate system and the image plane pixel coordinate system is as follows:
wherein lambda is a scale factor, (u, v) is a pixel coordinate of the image point P, and (X, Y, Z) is a three-dimensional real coordinate of the three-dimensional real space voxel point P; a is a camera projective transformation matrix.
2) And (3) according to the camera calibration matrix obtained by calculation in the step (1), mapping the experimental image coordinates to the space three-dimensional real coordinates through a calibration function relation, and establishing a weight matrix searching curve.
21 Reading two experimental images according to the camera calibration matrix A obtained in the step 1), and mapping the coordinates of the experimental images into a space three-dimensional real coordinate system through a calibration function relation.
22 According to the space three-dimensional real coordinate result obtained in the step 21), the sight line of each image pixel point under the space three-dimensional real coordinate system is approximately a cylinder, each pixel under the three-dimensional real coordinate system is approximately a sphere, the contribution value of each pixel corresponding to the image pixel point is approximately the ratio of the intersecting volume of the sight line cylinder and the pixel to the whole voxel volume, and the contribution value of each pixel corresponding to each pixel is fitted, namely a weight matrix searching curve.
In this embodiment, the number of cameras is 4, each camera needs to calculate a weight matrix searching curve, 4 weight matrix searching curves are calculated, the data length of each table is 18000 points, and the result of the 4 weight matrix searching curves is shown in fig. 4.
3) Three-dimensional particle field chromatography reconstruction based on GPU.
As shown in fig. 2, the three-dimensional particle field tomographic reconstruction specifically includes:
31 Two sets of multi-camera image data with a time interval of 0.001s are read, including the number of cameras required by the tomographic reconstruction process, the images recorded by each camera, and the coordinates and gray values of each pixel of each image, and transferred to the memory of the GPU device.
In this embodiment, the number of cameras is 4, the shooting time interval is 0.001s, the four cameras at two moments each shoot one image, the total number of images is 8, the image size is 1000×2000pixel, the numbers of the images are 1-4 and 5-8, 1-4 are 4 images at the first moment, 5-8 are 4 images at the second moment, and all the read images are shown in fig. 5.
32 And (3) transferring the weight matrix searching curve copy of each camera obtained in the step (2) to the GPU memory.
33 Voxel gray value E (X) based on all voxel center coordinates in three-dimensional space j ,Y j ,Z j ) All pixels I (x) i ,y i ) According to step 31) the camera image data of the incoming GPU, and step 32) the weight matrix look-up curve calculation of the incoming GPU to obtain the contribution weight matrix W of each voxel j to the gray value of each pixel i of each camera image i,j 。
In this example, the measurement area size is 50mm×100mm, and the number of voxels per millimeter is11voxels. Simultaneously calculating contribution weight matrix W of all voxels j at two moments to all image pixels i of image numbers 1-8 using GPU multithreading i,j 。
34 A contribution weight matrix W) calculated according to step 33) i,j And performing chromatographic reconstruction by using a GPU-based parallel MART algorithm to obtain the gray value spatial distribution of the three-dimensional particle field. And (3) performing chromatographic reconstruction calculation based on the GPU, wherein the light intensity reconstruction process of each voxel j and all camera pixels is calculated by adopting one GPU thread, and the light intensity reconstruction process of all voxels is calculated in parallel by using the thread number equivalent to the voxel number by utilizing the characteristic of huge thread number in GPU equipment. Before acceleration, the three-dimensional particle field is obtained by reconstructing the chromatography reconstruction calculation flow based on the CPU with higher calculation efficiency.
The MART algorithm has the following calculation formula:
where k is the number of iterations, μ is the relaxation parameter, E (x j ,y j ,z j ) For voxel gray value, I (x i ,y j ) For camera image pixel values, W i,j A contribution weight matrix for each voxel j to the gray value of each pixel i, the contribution weight matrix being obtained from the multi-camera image data and a weight matrix look-up curve, N i Is the total number of voxels.
In the embodiment, the number of cameras is 4, the shooting time interval is 0.001s, four cameras at two moments shoot one image respectively, the total number of images is 8, the size of the images is 1000×2000pixel, the numbers of the images are 1-4 and 5-8, 1-4 are 4 images at the first moment, and 5-8 are 4 images at the second moment; the measurement area size was 50mm×100mm, and the number of voxels per millimeter was 11voxels. The gray values of all particles (voxels) at two moments are simultaneously calculated using GPU simultaneous multithreading, the three-dimensional particle field at two moments is shown in fig. 6.
4) Three-dimensional speed field reconstruction based on GPU.
As shown in fig. 2, the three-dimensional velocity field reconstruction specifically includes:
41 According to the three-dimensional particle field data at two moments obtained in the step 3), based on the size of the diagnostic window obtained in the step 1), the particle field data are segmented, two diagnostic window data for three-dimensional cross-correlation calculation in each data block are extracted through an adaptive window selection technology, and the two diagnostic window data are stored in a GPU memory.
In this embodiment, the diagnostic window size is 32voxel×32voxel, the window overlapping rate is 50%, and the total number of diagnostic windows in three dimensions of the measurement region is 32×64×32; the diagnostic window data a with voxel (particle) coordinates (17 voxel ) at the first moment is extracted, and the diagnostic window data b with voxel coordinates (17 voxel ) at the second moment is extracted, as shown in fig. 7, and is copied into the GPU memory.
42 According to the size of the GPU memory of the computing device, the number of concurrent processes is adaptively designed, each process can complete the diagnosis window data selection of the step 41), a three-dimensional cross-correlation calculation module is independently processed, and the maximum concurrent process simultaneously processes all three-dimensional cross-correlation calculation of the diagnosis window.
In the embodiment, the number of concurrent processes is set to be 4 according to the size of the GPU memory of the computing device; 4 processes respectively extract diagnostic window data a1, a2, a3 and a4 at the first moment; and diagnostic window data b1, b2, b3, b4 at a second time instant, as shown in fig. 8, are copied into the GPU memory.
43 For each process of step 42), according to the two diagnostic window data extracted in step 41), performing three-dimensional fourier transform based on the CUFFT fast fourier transform module of the GPU, respectively, to obtain frequency domain transform results of the two diagnostic windows.
44 Performing CUFFT convolution calculation based on the GPU on the frequency domain transformation results of the two diagnostic windows obtained by the calculation in the step 43) to obtain energy spectrums of particle fields of the two diagnostic windows; then, the CUFFT inverse fast Fourier transform module based on the GPU performs inverse Fourier transform once to obtain cross-correlation functions of the particle fields of the two diagnostic windows of the 4 processes as shown in fig. 9.
45 According to the cross-correlation function of the two diagnostic windows obtained in the step 44), the peak value of the cross-correlation function and the three-dimensional array index of the peak value are obtained, and the average speed of the trace particles in the diagnostic windows is calculated.
In this embodiment, the peak coordinates, the peak values and the average speeds of the three dimensions are shown in table 2 according to the cross-correlation function distribution shown in the four processes of fig. 9.
Table 2 four processes calculate the peak coordinates, peak values, and average speed in three dimensions of the cross-correlation function
45 Repeating step 42), step 43), step 44) until the average speed calculation for all diagnostic windows is completed.
In this embodiment, the diagnostic window size is 32voxel×32voxel, the window overlapping rate is 50%, and the total number of diagnostic windows in three dimensions of the measurement region is 32×64×32; a total of 32×64×32=65536 cross-correlation cycles are performed.
46 The average velocity of the trace particles in all diagnostic windows obtained in step 45) is analyzed to replace the erroneous velocity vector therein.
5) And (3) outputting and storing the three-dimensional particle field and the three-dimensional velocity field obtained by the calculation in the step (2), the step (3) and the step (4), and ending the calculation.
The three-dimensional velocity field results of this embodiment are shown in fig. 10.
The performance improvement of this embodiment using a CPU and a different GPU is shown in table 3.
TABLE 3 Performance analysis
The foregoing describes in detail preferred embodiments of the present invention. It should be understood that numerous modifications and variations can be made in accordance with the concepts of the invention by one of ordinary skill in the art without undue burden. Therefore, all technical solutions which can be obtained by logic analysis, reasoning or limited experiments based on the prior art by the person skilled in the art according to the inventive concept shall be within the scope of protection defined by the claims.
Claims (9)
1. The three-dimensional particle field and speed field reconstruction method based on GPU acceleration is characterized by comprising the following steps of:
acquiring two groups of multi-camera image data with a certain time interval and a weight matrix searching curve of each camera;
performing three-dimensional particle field chromatographic reconstruction based on the multi-camera image data and the weight matrix search curve by adopting a GPU (graphics processing unit), and obtaining a reconstructed three-dimensional particle field, wherein in the chromatographic reconstruction process, the light intensity reconstruction of all voxels is calculated in parallel by using the thread number which is equal to the voxel number;
partitioning the reconstructed three-dimensional particle field, extracting two diagnostic window data of each data block, performing three-dimensional cross-correlation calculation by adopting a GPU concurrency process to obtain average speeds of all windows, and reconstructing to obtain a three-dimensional speed field;
the three-dimensional cross-correlation calculation specifically comprises the following steps:
performing three-dimensional Fourier transform on the two diagnostic window data based on CUFFT fast Fourier transform of the GPU respectively to obtain frequency domain transform results of the two diagnostic windows;
the energy spectrums of two diagnostic window particle fields are obtained based on CUFFT convolution calculation of the GPU;
performing inverse Fourier transform based on CUFFT (inverse fast Fourier transform) of the GPU to obtain cross-correlation functions of two diagnostic window particle fields;
and (3) calculating the peak value of the cross-correlation function and the index of the three-dimensional array where the peak value is located, and calculating to obtain the average speed of the trace particles in the diagnosis window.
2. The GPU acceleration based three-dimensional particle field and velocity field reconstruction method of claim 1, wherein the weight matrix look-up curve is obtained by:
calibrating a plurality of cameras to obtain a camera calibration matrix;
based on the camera calibration matrix, mapping the experimental image coordinates into a space three-dimensional real coordinate system;
and according to the space three-dimensional real coordinates obtained by mapping, approximating the line of sight of each image pixel point under the space three-dimensional real coordinates to be a cylinder, approximating each voxel under the three-dimensional real coordinates to be a sphere, approximating the contribution value of each voxel corresponding to the image pixel point to be the ratio of the volume intersected by the cylinder and the voxel to the whole voxel volume, and fitting the contribution value of each voxel corresponding to each pixel, namely, a weight matrix searching curve.
3. The GPU acceleration based three dimensional particle field and velocity field reconstruction method according to claim 2, wherein the camera calibration matrix is obtained based on control constants and calibration data, the control constants comprising particle field tomography reconstruction parameters and velocity field reconstruction parameters.
4. The method for reconstructing a three-dimensional particle field and velocity field based on GPU acceleration according to claim 3, wherein the particle field tomographic reconstruction parameters include an image data number, an image data type, an image data size, an image data storage path, a number of cameras, a measurement region size, and a number of voxels per millimeter,
the velocity field reconstruction parameters include a diagnostic window size and a window overlap ratio.
5. The three-dimensional particle field and velocity field reconstruction method based on GPU acceleration according to claim 1, wherein in the three-dimensional particle field tomographic reconstruction, a MART algorithm tomographic reconstruction based on GPU parallelism is used to obtain the spatial distribution of the three-dimensional particle field.
6. The GPU acceleration based three-dimensional particle field and velocity field reconstruction method of claim 5, wherein the MART algorithm has a computational formula as follows:
where k is the number of iterations, μ is the relaxation parameter, E (x j ,y j ,z j ) For voxel gray value, I (x i ,y j ) For camera image pixel values, W i,j A contribution weight matrix for each voxel j to the gray value of each pixel i, the contribution weight matrix being obtained from the multi-camera image data and a weight matrix look-up curve, N i Is the total number of voxels.
7. The GPU acceleration based three-dimensional particle field and velocity field reconstruction method of claim 4, wherein the reconstructed three-dimensional particle field is partitioned based on the diagnostic window size and window overlap ratio, and two diagnostic window data for each data block are extracted by an adaptive window selection technique.
8. The GPU acceleration based three-dimensional particle field and velocity field reconstruction method according to claim 1, wherein after obtaining the average velocity of all windows, searching for whether there is an erroneous velocity vector therein, and if so, performing a replacement process.
9. The GPU acceleration based three dimensional particle field and velocity field reconstruction method according to claim 1, wherein the time interval is 0.001s.
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