Improved method for identifying and predicting oil spill at sea
By constructing a convolutional neural network to automatically identify offshore oil spill areas, combined with Lagrangian model and data correction technology, the problem of insufficient accuracy in offshore oil spill identification and prediction is solved, and more accurate prediction of oil spill diffusion is achieved.
Patent Information
- Application Number
- CN202510016162.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-06
- Publication Date
- 2025-05-09
AI Technical Summary
The prior art has problems of insufficient accuracy and data anomalies in the identification and prediction of offshore oil spills, especially in cases where the boundaries of oil spills are irregular and environmental data predictions are inaccurate.
By constructing a convolutional neural network with encoder-decoder structure, the oil spilled area is automatically identified and segmented from satellite images, and Lagrangian particles are sown from the boundary profile of the oil spilled area. At the same time, the wind field, flow field, and wave field data are corrected, and the sea temperature data are predicted, and inputted into the Lagrangian model to obtain more accurate oil spill diffusion prediction results.
It realizes accurate identification of oil spilled areas from satellite images, and obtains more accurate oil spill spread prediction results through real simulation of initial state and data correction, improving the accuracy and reliability of identification and prediction.
Smart Images

Figure CN119963893A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of deep learning methods and neural network models, and in particular to an improved method for identifying and predicting offshore oil spills. Background Art
[0002] Oil spills at sea can cause serious damage to the marine environment and lead to subsequent high costs for treatment. Being able to promptly identify the oil spill area on the sea surface and predict the spread of the oil spill is crucial for relevant personnel to recover and clean up the oil in a timely manner.
[0003] For the identification of oil spills on the sea surface, image processing methods or deep learning methods are currently used. For traditional image processing methods, there are many difficulties in identifying oil spill areas from satellite remote sensing images. For example, due to factors such as lighting, sea conditions, and clouds, the imaging background is complex, and the extracted oil spill area is not accurate or even completely wrong. In the deep learning method, a specially designed image segmentation neural network is trained with a large number of artificially labeled data sets, which has the characteristics of high robustness and strong noise resistance, and can accurately segment the oil spill area at the pixel level.
[0004] The prediction of offshore oil spill diffusion is mainly achieved through numerical simulation methods. The choice of numerical models can be mainly divided into the Euler method and the Lagrangian method. The Euler method solves the trajectory of the oil spill by analyzing the amount of oil spill and the fluid dynamics equation. The advantage of this method is that the calculation is relatively simple, but the disadvantage is that when the numerical diffusion is large, the calculation results will be distorted. The Lagrangian method regards the oil spill as a large number of oil droplet particles, each of which undergoes Lagrangian drift motion under the influence of environmental physical factors (wind, current, and waves). This method solves the Lagrangian model equation. The Lagrangian method can not only simulate the deformation process of the oil film well, but also eliminate the problem of numerical divergence. It is currently a commonly used method for predicting oil spill diffusion.
[0005] When applying the Lagrangian method to predict offshore oil spills, the traditional method regards the initial oil spill area as a circle with a specified coordinate center and radius, and sows a large number of Lagrangian particles in a normal distribution within the circumference to simulate the initial state of the oil spill. However, in reality, when the sea area where the offshore oil spill accident occurred is photographed by a satellite, the oil spill area has spread to form an irregular shape. It is inaccurate to use only the circumference to represent the boundary of the oil spill area. The initial oil spill situation should be defined according to the outline of the oil spill area in the satellite image. And before predicting the spread of oil spills through the Lagrangian model, relevant environmental data in the future is required. At present, in the field of atmosphere and ocean, there are many dynamic numerical prediction models in the world, such as GFS (Global Forecast System), HYCOM (Hybrid Coordinate Ocean Model), FVCOM (Finite Volume Coastal Ocean Model), etc., through which high-resolution marine meteorological data for the next few dozen days can be obtained. Although the forecast data obtained through numerical models have the characteristics of high spatial resolution and temporal resolution, they often differ greatly from the actual observation values. If such abnormal data are input into the model, it will inevitably affect the final diffusion prediction results. Summary of the invention
[0006] The purpose of the present invention is to provide an improved method for identifying and predicting offshore oil spills, which can automatically identify and segment the oil spill area from satellite images, sow Lagrangian particles from the boundary contour of the oil spill area, truly simulate the initial state of the oil spill, correct the wind field, flow field, and wave field data, predict the sea temperature data, and input these data into the Lagrangian model to obtain more accurate oil spill diffusion prediction results.
[0007] To achieve the above object, the present invention provides an improved method for identifying and predicting marine oil spills, comprising the following steps:
[0008] S1. Identification of oil spill area;
[0009] Construct a neural network model for segmenting oil spill areas from satellite images, train the neural network model until the model loss begins to converge, and then verify the actual performance of the network through the test set. Continuously adjust the hyperparameters to repeatedly train the model until the model can accurately identify the oil spill area from the satellite image and segment its boundaries.
[0010] S2, using image processing methods to divide the boundary contour of the oil spill area;
[0011] S3. Obtain future environmental data of the oil spill area;
[0012] S4. Obtain the diffusion simulation results through the Lagrangian model and plot them.
[0013] Preferably, in S1, the main body of the neural network model is a convolutional neural network with an encoder-decoder structure.
[0014] Preferably, the encoder network is composed of ResNet-50, and the encoder downsamples the input original image and obtains deep semantic information therein through continuous feature extraction.
[0015] Preferably, the decoder is composed of a DeepLabV3+ decoder, which upsamples the extracted feature image to restore its original image size, captures the boundary information of the object by connecting the shallow and deep features of the image, and obtains accurate segmentation results.
[0016] Preferably, in S1, training the neural network model includes the following steps:
[0017] S101, manually calibrating the oil spill area from the oil spill satellite image and making a mask image as a data label;
[0018] S102, dividing the data set into a 90% training set for training the network and a 10% test set for testing network performance;
[0019] S103, when the network is trained until its loss begins to converge, the actual performance of the network is verified through the test set;
[0020] S104. Adjust the hyperparameters and perform repeated training to obtain the network model with the best performance as the oil spill recognition model.
[0021] Preferably, in S103, the loss function for determining whether the network has converged is:
[0022]
[0023] Among them, CE(c,p) represents the cross entropy loss, c i Indicates the category of the segmented object, p i Represents the probability of the class predicted by the model for each of the n classes in the dataset.
[0024] Preferably, in S103, the evaluation index of network performance is calculated by the formula To calculate, where A represents the predicted segmentation area and B is the actual segmentation area.
[0025] Preferably, in S3, the future environmental data is spatiotemporal data, and the future environmental data includes wind field, flow field and wave field data, and the future environmental data acquisition includes the following steps:
[0026] S301, the wind field data obtained from GFS, the flow field data obtained from HYCOM, and the wave field data obtained from FVCOM are input into the spatiotemporal prediction network. The convolutional loop structure in the spatiotemporal prediction network extracts both time and space information and fully considers the unity of time and space;
[0027] S302, calculating the loss of the output data of the spatiotemporal prediction network and the ERA5 wind field reanalysis data and the Copernicus flow field and wave field reanalysis data at the same time;
[0028] S303, until the spatiotemporal prediction network loss value converges, a wind field / flow field / wave field correction model is obtained.
[0029] Preferably, in S4, the Lagrangian method is used to calculate the position x of each oil particle. i The speed of movement is expressed as:
[0030]
[0031] Among them, v a is the sea surface advection velocity, affected by the flow field and wind field, v d is the turbulent velocity, affected by the wave field, v a The calculation formula is:
[0032]
[0033] in, is the sea surface velocity, It is a part of the sea surface wind speed, which is expressed as:
[0034]
[0035]
[0036] Among them, u and v are the components of the original wind speed in the longitude and latitude directions, α is the wind drift factor, β is the wind direction deflection angle, and the definition formula of α is:
[0037]
[0038] in, is the original value of the wind drift factor, usually set as an empirical constant to 0.01-0.04, z i is the current depth of the oil particle from the sea surface, d is the wind drift depth, indicating that within this depth range, α will change with the depth z of the oil particle. i decreases linearly with the increase of will become smaller, the depth of the oil particles z i Affected by the vertical speed, the specific formula is:
[0039]
[0040] Where w is the terminal velocity, K is the diffusion coefficient, and the current depth z i W is a standard Wiener process, that is, the Brownian motion of particles, which can be regarded as a random walk of oil particles in continuous time. The terminal velocity w is defined as:
[0041]
[0042] Among them, g is the acceleration of gravity, r is the radius of the oil particle, V is the viscosity of seawater, V is related to the temperature T and salinity S of seawater, ρ' is the density ratio, and the specific expressions of V and ρ' are as follows:
[0043] V~f(T(x i ,t),S);
[0044]
[0045] ρ w ~f(T(x i ,t),S);
[0046] Among them, ρ o is the density of oil, ρ w is the density of seawater. Affected by the temperature and salinity of seawater, the salinity S of seawater changes very little in adjacent sea areas and is set to a fixed value. The sea temperature T fluctuates greatly due to the day and night temperature difference of the atmosphere.
[0047] Preferably, the Lagrangian model is solved by using the fourth-order Runge-Kutta equation, which includes the following equation:
[0048]
[0049] The velocity v at the intermediate moment is calculated by the fourth-order interpolation method, using the flow velocity at moments n-2, n-1, n, and n+1. The calculation formula is:
[0050]
[0051] Therefore, the present invention adopts the above-mentioned improved method for identifying and predicting offshore oil spills, which can automatically identify and segment the oil spill area from satellite images, and sow Lagrangian particles from the boundary contour of the oil spill area, truly simulate the initial state of the oil spill, correct the wind field, flow field, and wave field data, predict the sea temperature data, and input these data into the Lagrangian model to obtain more accurate oil spill diffusion prediction results.
[0052] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS
[0053] Figure 1 It is a scheme flow chart of an embodiment of an improved method for identifying and predicting marine oil spills of the present invention;
[0054] Figure 2 It is a conventional oil spill diffusion prediction flow chart of an embodiment of an improved method for identifying and predicting offshore oil spills of the present invention;
[0055] Figure 3 It is a structural diagram of a neural network model for segmenting an oil spill area in an embodiment of an improved method for identifying and predicting oil spills at sea of the present invention;
[0056] Figure 4 It is a training flow chart of an oil spill identification model of an improved method for identifying and predicting offshore oil spills according to an embodiment of the present invention;
[0057] Figure 5 It is a segmented image of the oil spill area of an improved method for identifying and predicting offshore oil spills according to an embodiment of the present invention, wherein image a is the original image, and image b is the oil spill area mask obtained by the oil spill identification model;
[0058] Figure 6 It is a schematic diagram of extracting the oil spill contour through the mask boundary and seeding Lagrangian particles in an embodiment of an improved method for identifying and predicting offshore oil spills of the present invention;
[0059] Figure 7 It is a flow chart of wind field / flow field / wave field correction model training in an embodiment of an improved method for offshore oil spill identification and prediction of the present invention;
[0060] Figure 8 It is a prediction result diagram of an embodiment of an improved method for identifying and predicting marine oil spills of the present invention. DETAILED DESCRIPTION
[0061] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.
[0062] Unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.
[0063] Embodiment 1
[0064] The present invention adopts the above-mentioned improved method for identifying and predicting marine oil spills. The traditional oil spill diffusion prediction process is as follows: Figure 2 As shown, the overall solution process of the present invention is as follows Figure 1 As shown, the following steps are included:
[0065] S1. Identification of oil spill area;
[0066] First, the present invention constructs a neural network model for segmenting oil spill areas from satellite images. The network structure is as follows: Figure 3 As shown in the figure, its main body is a convolutional neural network with an encoder-decoder structure. The encoder network is composed of ResNet-50. ResNet is commonly used to solve the gradient vanishing and gradient exploding problems in deep networks. According to the number of layers, it is divided into different versions such as ResNet-18, ResNet-34, ResNet-50, and ResNet-101. Among them, the version with a smaller number of layers has insufficient number of neurons, which is easy to cause underfitting. If the number of layers is too large, the number of parameters is also large, which affects the reasoning speed and has the risk of overfitting. Therefore, ResNet-50 is finally selected to take into account both network performance and reasoning speed. The role of the encoder is to downsample the original input image and obtain the deep semantic information through continuous feature extraction.
[0067] The decoder is composed of the decoder of DeepLabV3+. The main feature of DeepLabV3+ is the use of the ASPP (AtrousSpatial Pyramid Pooling) module, which has four dilated convolution layers. The dilated convolution has a larger receptive field than ordinary convolution kernels, and contains an average pooling layer for processing feature maps in the encoder module to provide global context information. The decoder upsamples the extracted feature image to restore the size of its original image, and captures the boundary information of the object by connecting the shallow and deep features of the image, making the segmentation result more accurate. In addition, a 1×1 convolution is applied to the corresponding features from the encoder to balance the importance of shallow features and deep features.
[0068] Then the neural network model is trained. The training process is as follows Figure 4 As shown, the following steps are included:
[0069] S101. Artificially mark the oil spill area from the oil spill satellite image and create a mask image as a data label.
[0070] S102, dividing the data set into a 90% training set for training the network and a 10% test set for testing network performance.
[0071] S103. When the network is trained until its loss begins to converge, the actual performance of the network is verified by the test set. The loss function for judging whether the network has converged is the cross entropy loss (Cross Entropy Loss) shown in formula (1), where c i represents the category of the segmented object (the oil spill area and the background area in this invention), p i It represents the probability of the class predicted by the model for each of the n classes (n=2 in the present invention) in the data set.
[0072]
[0073] The evaluation index of network performance is calculated by IoU (Intersection over Union), as shown in formula (2), where A represents the predicted segmentation area and B is the actual segmentation area.
[0074]
[0075] S104. The hyperparameters are adjusted continuously according to the IoU and repeated training is performed to obtain the network model with the best performance as the oil spill recognition model.
[0076] S2, such as Figure 5 As shown in Figure 2, after obtaining the segmented image of the oil spill area, the image processing method is used to divide the boundary contour of the oil spill area. Based on the contour, Lagrangian particles representing a large number of oil droplets are seeded, as shown in Figure 2. Figure 6 shown.
[0077] S3. Obtain future environmental data of the oil spill area. The future environmental data is spatiotemporal data, including wind field, flow field and wave field data. The present invention corrects these original forecast data through a trained wind field / flow field / wave field correction model to obtain environmental data that is closer to the observed value. In addition, although the sea temperature will not directly affect the drift behavior of the oil spill, it will affect the weathering process of the oil droplets, resulting in changes in its physical properties such as density, which will indirectly affect its diffusion effect. Therefore, a sea temperature prediction model is also trained to obtain future sea temperature data as an additional parameter in the simulation process. The future environmental data is acquired using a spatiotemporal prediction network. The spatiotemporal prediction network is PredRNN. PredRNN is an improved version of the classic spatiotemporal prediction network ConvLSTM. Its improved network backbone structure enables it to have more accurate prediction capabilities. The convolutional loop structure in the spatiotemporal prediction network can extract time and space information at the same time, and fully considers the unity of time and space. The specific training process of the spatiotemporal prediction network is as follows: Figure 7 As shown, the following steps are included:
[0078] S301. The wind field forecast data obtained from GFS, the flow field forecast data obtained from HYCOM, and the wave field forecast data obtained from FVCOM are input into the spatiotemporal prediction network.
[0079] S302, calculating the loss of the output data of the spatiotemporal prediction network and the ERA5 wind field reanalysis data and the Copernicus flow field and wave field reanalysis data at the same time.
[0080] S303, until the loss value of the spatiotemporal prediction network converges, a wind field / flow field / wave field correction model is obtained. These models can correct the relevant forecast data to obtain data that is closer to the actual observation.
[0081] S4. Obtain the diffusion simulation results through the Lagrangian model and plot them.
[0082] The Lagrangian method is used to calculate the speed of each oil particle at a certain position. The expression formula is:
[0083]
[0084] Among them, v a is the sea surface advection velocity, affected by the flow field and wind field, v d is the turbulent velocity, affected by the wave field, v a The calculation formula is:
[0085]
[0086] in, is the sea surface velocity, It is a part of the sea surface wind speed, which is expressed as:
[0087]
[0088] Among them, u and v are the components of the original wind speed in the longitude and latitude directions, α is the wind drift factor, β is the wind direction deflection angle, and the definition formula of α is:
[0089]
[0090] in, is the original value of the wind drift factor, usually set as an empirical constant to 0.01-0.04, z i is the current depth of the oil particle from the sea surface, d is the wind drift depth, indicating that within this depth range, α will change with the depth z of the oil particle. i decreases linearly with the increase of will become smaller, the depth of the oil particles z i Affected by the vertical speed, the specific formula is:
[0091]
[0092] Where w is the terminal velocity, K is the diffusion coefficient, and the current depth z i W is a standard Wiener process, that is, the Brownian motion of particles, which can be regarded as a random walk of oil particles in continuous time. The terminal velocity w is defined as:
[0093]
[0094] Among them, g is the acceleration of gravity, r is the radius of the oil particle, V is the viscosity of seawater, V is related to the temperature T and salinity S of seawater, ρ' is the density ratio, and the specific expressions of V and ρ' are as follows:
[0095] V~f(T(x i ,t),S)#(10);
[0096]
[0097] ρ w ~f(T(x i ,t),S)#(12);
[0098] Among them, ρ o is the density of oil, ρ w is the density of seawater. Affected by the temperature and salinity of seawater, the salinity S of seawater changes very little in adjacent sea areas and is set to a fixed value. The sea temperature T fluctuates greatly due to the day and night temperature difference of the atmosphere.
[0099] The above process can be regarded as: the oil particles are affected by the sea temperature, and their density changes, which leads to changes in their buoyancy and vertical velocity, causing them to float up and down, and the degree of exposure to the sea surface also changes. In addition, the influence of wind speed (i.e., wind drift factor α) also changes continuously, which ultimately affects the drift and diffusion of oil particles. Therefore, the prediction of sea temperature is of great significance.
[0100] The fourth-order Runge-Kutta equation is used to solve formula (3). The fourth-order Runge-Kutta equation includes the following equations:
[0101]
[0102] The velocity v at the intermediate moment is calculated by the fourth-order interpolation method, using the flow velocity at moments n-2, n-1, n, and n+1. The calculation formula is:
[0103]
[0104] Finally, after solving the oil spill diffusion results through computer and plotting them, the effect is as follows: Figure 8 shown.
[0105] Therefore, the present invention adopts the above-mentioned improved method for identifying and predicting offshore oil spills, which can automatically identify and segment the oil spill area from satellite images, and sow Lagrangian particles from the boundary contour of the oil spill area, truly simulate the initial state of the oil spill, correct the wind field, flow field, and wave field data, predict the sea temperature data, and input these data into the Lagrangian model to obtain more accurate oil spill diffusion prediction results.
[0106] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.
Claims
1. An improved method for identifying and predicting marine oil spills, characterized in that: The following steps are involved: S1. Identification of oil spill area; Construct a neural network model for segmenting oil spill areas from satellite images, train the neural network model until the model loss begins to converge, and then verify the actual performance of the network through the test set. Continuously adjust the hyperparameters to repeatedly train the model until the model can accurately identify the oil spill area from the satellite image and segment its boundaries. S2, using image processing methods to divide the boundary contour of the oil spill area; S3. Obtain future environmental data of the oil spill area; S4. Obtain the diffusion simulation results through the Lagrangian model and plot them.
2. The improved method for identifying and predicting marine oil spills according to claim 1, characterized in that: In S1, the main body of the neural network model is a convolutional neural network with an encoder-decoder structure.
3. The improved method for identifying and predicting marine oil spills according to claim 2, characterized in that: The encoder network is composed of ResNet-50. The encoder downsamples the input original image and obtains the deep semantic information through continuous feature extraction.
4. The improved method for identifying and predicting marine oil spills according to claim 3, characterized in that: The decoder is composed of the DeepLabV3+ decoder. The decoder upsamples the extracted feature image to restore its original image size. By connecting the shallow and deep features of the image, it captures the boundary information of the object and obtains accurate segmentation results.
5. The improved method for identifying and predicting marine oil spills according to claim 1, characterized in that: In S1, training the neural network model includes the following steps: S101, manually calibrating the oil spill area from the oil spill satellite image and making a mask image as a data label; S102, dividing the data set into a 90% training set for training the network and a 10% test set for testing network performance; S103, when the network is trained until its loss begins to converge, the actual performance of the network is verified through the test set; S104. Adjust the hyperparameters and perform repeated training to obtain the network model with the best performance as the oil spill recognition model.
6. The improved method for identifying and predicting marine oil spills according to claim 5, characterized in that: In S103, the loss function for determining whether the network has converged is: Among them, CE(c,p) represents the cross entropy loss, c i Indicates the category of the segmented object, p i Represents the probability of the class predicted by the model for each of the n classes in the dataset.
7. The improved method for identifying and predicting marine oil spills according to claim 5, characterized in that: In S103, the evaluation index of network performance is calculated by the formula To calculate, where A represents the predicted segmentation area and B is the actual segmentation area.
8. The improved method for identifying and predicting marine oil spills according to claim 1, characterized in that: In S3, the future environmental data is spatiotemporal data, including wind field, flow field and wave field data. The acquisition of future environmental data includes the following steps: S301, the wind field data obtained from GFS, the flow field data obtained from HYCOM, and the wave field data obtained from FVCOM are input into the spatiotemporal prediction network. The convolutional loop structure in the spatiotemporal prediction network extracts both time and space information and fully considers the unity of time and space; S302, calculating the loss of the output data of the spatiotemporal prediction network and the ERA5 wind field reanalysis data and the Copernicus flow field and wave field reanalysis data at the same time; S303, until the spatiotemporal prediction network loss value converges, a wind field / flow field / wave field correction model is obtained.
9. The improved method for identifying and predicting marine oil spills according to claim 1, characterized in that: In S4, the Lagrangian method is used to calculate the position x of each oil particle. i The speed of movement is expressed as: Among them, v a is the sea surface advection velocity, affected by the flow field and wind field, v d is the turbulent velocity, affected by the wave field, v a The calculation formula is: in, is the sea surface velocity, It is a part of the sea surface wind speed, which is expressed as: Among them, u and v are the components of the original wind speed in the longitude and latitude directions, α is the wind drift factor, β is the wind direction deflection angle, and the definition formula of α is: in, is the original value of the wind drift factor, usually set as an empirical constant to 0.01-0.04, z i is the current depth of the oil particle from the sea surface, d is the wind drift depth, indicating that within this depth range, α will change with the depth z of the oil particle. i decreases linearly with the increase of will become smaller, the depth of the oil particles z i Affected by the vertical speed, the specific formula is: Where w is the terminal velocity, K is the diffusion coefficient, and the current depth z i W is a standard Wiener process, that is, the Brownian motion of the particles, which can be regarded as a random walk of the oil particles in continuous time. The terminal velocity w is defined as: Among them, g is the acceleration of gravity, r is the radius of the oil particle, V is the viscosity of seawater, V is related to the temperature T and salinity S of seawater, ρ' is the density ratio, and the specific expressions of V and ρ' are as follows: V~f(T(x i ,t),S); ρ w ~f(T(x i ,t),S); Among them, ρ o is the density of oil, ρ w is the density of seawater. Affected by the temperature and salinity of seawater, the salinity S of seawater changes very little in adjacent sea areas and is set to a fixed value. The sea temperature T fluctuates greatly due to the day and night temperature difference of the atmosphere.
10. An improved method for identifying and predicting marine oil spills according to claim 9, characterized in that: The Lagrangian model is solved by using the fourth-order Runge-Kutta equation, which includes the following equations: The velocity v at the intermediate moment is calculated by the fourth-order interpolation method, using the flow velocity at moments n-2, n-1, n, and n+1. The calculation formula is:
Citation Information
Cited By
Seaborne oil spill diffusion simulation method and device, storage medium and computer equipment
CN122023616A