Floating ice water surface oil spill influence range prediction method based on color gradient LBM model

Abstract

The invention provides a floating ice water surface oil spill influence range prediction method based on a color gradient LBM model, which organically links a lattice Boltzmann method with an immersion boundary method, a free interface model and a color gradient model, and comprises the following steps: firstly, processing coupling of oil and water two-phase complementary miscible fluids by adopting the lattice Boltzmann color gradient model; an ice phase is added, the fluid-solid coupling problem is solved by adopting an immersed boundary method, and finally the severe sea surface flowing problem is solved by adopting a free liquid level model, so that the diffusion process of oil in a polar region ice layer and water is fully considered; the problem of inaccurate simulation at the fluid-structure interaction boundary and the situation of numerical instability of the fluid boundary with large density and viscosity difference are solved, and accurate prediction of polar region oil spill can be achieved by combining relevant detection data and the calculation result of the model.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of oil spill influence range prediction in the state of sea broken ice, in particular, especially relates to a floating ice water surface oil spill influence range prediction method based on a color gradient LBM model. BACKGROUND

[0002] The state of sea broken ice in the polar environment has a significant impact on oil spill diffusion behavior, and accurate prediction of its influence range is crucial for ecological protection. The polar ecosystem is characterized by high vulnerability and low recovery capacity, and oil spill accidents can cause long-term ecological damage. Due to the low temperature and insufficient light in the polar region, the natural degradation of oil is extremely slow, and oil pollutants may persist for a long time, causing irreversible damage to the biological community. Therefore, rapid and accurate prediction of oil spill diffusion range can help optimize emergency response measures, improve oil spill cleanup efficiency, and reduce ecological losses. In recent years, with the improvement of computing power and the development of numerical simulation technology, numerical method-based oil spill prediction has become a research hotspot, but multi-phase flow simulation in the polar broken ice environment still faces many challenges, such as insufficient fluid-structure coupling accuracy, numerical stability problems in high-density difference fluid simulation, etc.

[0003] Currently, numerical simulation methods for oil spill diffusion in broken ice environments mainly include the boundary element method (BEM), volume fraction method (VOF), and smoothed particle hydrodynamics method (SPH). BEM is based on potential flow theory and has high computational efficiency, but it ignores fluid viscosity effects and is difficult to simulate complex free surface phenomena (such as splashing, cavity closure, etc.). The VOF method can better maintain mass conservation, but it requires a large amount of computing resources and has difficulty in estimating interface physical quantities (such as normal vectors). The SPH method is suitable for particle simulation of free surface motion, but the computational cost is high and difficult to meet actual engineering needs. In addition, existing methods have insufficient accuracy in handling fluid-structure boundary information exchange, and numerical instability phenomena easily occur in the simulation of multi-phase flow with large density and viscosity differences, limiting their applicability in polar oil spill prediction. Therefore, there is an urgent need for an efficient and stable numerical simulation method to improve the accuracy of oil spill influence range prediction in the broken ice environment. SUMMARY

[0004] To address the aforementioned technical problems, this invention provides a method for predicting the impact range of oil spills on floating ice surfaces based on a color gradient LBM model. This invention organically integrates the lattice Boltzmann method with the submerged boundary method, the free interface model, and the color gradient model. First, the lattice Boltzmann color gradient model is used to handle the coupling between oil and water, two complementary miscible fluids. Then, the ice phase is added, and the submerged boundary method is used to handle the fluid-structure interaction problem. Finally, the free surface model is used to handle the problem of violent sea surface flow. This method fully considers the diffusion process of oil in polar ice and water, solves the problems of inaccurate simulation at fluid-structure interaction boundaries and numerical instability at fluid boundaries with large differences in density and viscosity. Combined with relevant detection data and the solution results of this model, accurate prediction of polar oil spills can be achieved.

[0005] The technical means employed in this invention are as follows: A method for predicting the impact range of oil spills on floating ice surfaces based on a color gradient LBM model includes: S1. The color gradient model is used to capture the interface of the water-oil two-phase immiscible liquid. The interface is kept sharp and numerical diffusion is suppressed by the recoloring operator to obtain the spatiotemporal evolution data of the oil-water interface. S2. Using the spatiotemporal evolution data of the oil-water interface obtained in step S1 as initial conditions, the lattice Boltzmann method is used to perform fluid dynamics simulation to obtain the oil-water mixed flow field. S3. In the oil-water mixed flow field obtained in step S2, the ice fragmentation boundary is discretized into Lagrange points by the submerged boundary method. The solid ice boundary force is coupled to the Eulerian seawater grid by force correction interpolation to realize the fluid-structure coupling between ice fragmentation and seawater, and the ice-water-oil three-phase coupled flow field is obtained. S4. Based on the ice-water-oil three-phase coupled flow field obtained in step S3, the volume fraction of the air layer on the sea surface is described by a single-phase free liquid surface model. Only the seawater phase is solved, and the liquid surface position is updated by interface reconstruction and overfill / overfill cell conversion rules to complete the coupled simulation of complex flow between the liquid surface and the gas. S5. Repeat steps S1-S4 until the oil film area, center of gravity and leading edge position converge, and output the spatiotemporal distribution results of the oil spill impact range for emergency response to oil spills in polar ice cap areas.

[0006] Further, step S1 includes: S11. For the oil-water immiscibility model, the D3Q19 model is adopted, with velocity vector... The definition is as follows:

[0007] in, The number representing the discrete velocity; S12. Define the colors of oil and water as... oil ,water The evolution equation is as follows:

[0008] in, This is the sum of the distribution functions of the two fluids, oil and water. ; For collision operators, ,in This represents a one-way collision operator. This represents the perturbation two-phase collision operator. This represents the recoloring two-phase collision operator; S13. The evolution equation in step S12 is solved by decomposing it using the one-way collision operator, perturbation operator, recoloring operator, and flow operator, as follows:

[0009]

[0010]

[0011]

[0012] S14. Formula based on one-way collision operator The distribution function is obtained as follows:

[0013] in, The relaxation coefficient; S15. The first torque of the distribution function gives the oil-water mixture fluid. Density:

[0014] in, For total density, ; S16. The second torque of the distribution function is defined by the total momentum, as follows:

[0015] in, The weighted average velocity representing the density of the oil-water mixture; Represents the equilibrium function. , Indicates the weighting coefficient. ; S17. To obtain a stable interface, calculate the density ratio and color. The pressure of an oil-water mixture is given by the following formula:

[0016]

[0017] in, , Indicates free parameters, It's a color Speed ​​of sound in fluids; S18. When the two fluids have different viscosities, interpolation is used to define the relaxation coefficient. Therefore, a color field is introduced, as follows:

[0018] Color field It is a function between -1 and 1, and its specific value depends on the proportion of red or blue fluid being evaluated. The relaxation coefficient, defined using interpolation, is expressed as follows:

[0019] in, It is a free parameter; ; Ultimately, the spatiotemporal evolution data of the oil-water interface were obtained.

[0020] Further, step S2 includes: S21. According to the lattice Boltzmann method, the evolution equation of the multiple relaxation time model (MRT) is as follows:

[0021] The above evolution equation represents the first evolution for each lattice. velocity distribution function of velocity components The evolutionary pattern; among which, This represents the distribution function of the combined oil and water two-phase flow in the color gradient method. Represents the particle discrete velocity. Represents a spatial position vector. Represents a moment vector. Represents the equilibrium moment. This represents a diagonal matrix consisting of relaxation rates. Indicates the time step. This represents volumetric force terms, including submerged boundary forces and surface tension. S22. Based on the multiple relaxation time model, the collision step is performed as follows:

[0022] S23. Based on the multiple relaxation time model, the transition steps are performed as follows:

[0023] The final result is an oil-water mixed flow field.

[0024] Furthermore, the D3Q19 model used in step S1, where D3 represents the spatial dimension and Q19 represents the number of discrete microvelocities, is used in the evolution equation of the multiple relaxation time model (MRT) in step S21: The moment space is as follows:

[0025] The equilibrium moments are as follows:

[0026] The particle discrete velocities are as follows:

[0027] in, , It is the lattice length. For time step; The diagonal matrix composed of relaxation rates is as follows: .

[0028] Further, step S3 includes: S31. The fluid velocity at the Lagrange midpoint is obtained by interpolating the seawater points within a certain range near the sea ice boundary point:

[0029] in, express Time of the first The intermediate fluid velocity at each Lagrange point This indicates the fluid velocity without considering boundary forces. Indicates the grid size. Represents a smooth Delta function; S32. Since the intermediate velocity and the velocity at that point are generally not equal, it is necessary to... When fluid forces are applied nearby, they are considered as solid-ice boundary forces. The formula for calculating solid-ice boundary forces is as follows:

[0030] in, Indicates sea ice speed; This represents the interpolated seawater velocity; Indicates the force correction factor. ,in The total number of Lagrange points, This represents the arc length between two adjacent Lagrange points; S33. Couple the boundary forces of solid ice to the Euler seawater mesh, as shown in the following formula:

[0031] in, Indicates the boundary force vector; S34. Correct the seawater velocity as follows:

[0032] The corrected seawater velocity was output, and the fluid-structure interaction between the ice fragments and the seawater was finally achieved, resulting in a three-phase coupled flow field of ice-water-oil.

[0033] Further, step S4 includes: S41. The volume fraction of the sea surface air layer is described using a single-phase free liquid surface model, as follows:

[0034] in, Indicates fluid mass; Indicates fluid density; This represents the volume fraction, i.e., the proportion of a cell that is filled. Its value is between 0 and 1, based on... The values ​​determine their respective types, for example, the sea surface and air grids. The value is 0, representing the seawater grid. The value is 1, if A value between 0 and 1 indicates that the grid is located at the boundary between the air and seawater at the sea surface, and belongs to the interface grid. S42. The inflow-outflow distribution function is used to calculate the mass change of the lattice within a time step. The calculation formula is as follows:

[0035] in, ,if If it is a liquid lattice, then ,if If it is a grid, then ,if If it is a gas lattice, then ; S43. At the interface, artificially reconstruct the distribution function between the interface grid and the adjacent sea surface air grid. The reconstruction equation is as follows:

[0036] in, Indicates the atmospheric pressure at the interface; S44. The distribution function of the interface normal is artificially reconstructed, and the reconstructed equation is as follows:

[0037] S45. During the calculation process, the following may occur: or In these cases, these two types of cells are called overfilled cells and overfilled cells, respectively. The excess mass is the mass difference between an overfilled or overfilled cell and a standard type cell. The rules for allocating excess mass after cell type conversion are as follows:

[0038] Among them, for the grid that is too full, For spaces, ; Indicates all directions Summation; Indicates excess mass. Finally, the coupled simulation of the complex flow between the liquid surface and the gas was completed.

[0039] Furthermore, in step S45, the conversion rules for overfilled cells and overfilled cells are as follows: Transform overfilled cells into seawater cells, and simultaneously transform the surrounding gas cells into interface cells; transform overfilled cells into surface air cells, and simultaneously transform the nearby seawater cells into interface cells; initialize the resulting interface cells, seawater cells, and surface air cells with the equilibrium distribution functions corresponding to the average density and velocity of their adjacent interface cells.

[0040] Compared with the prior art, the present invention has the following advantages: 1. At the boundary between floating sea ice and the sea surface, the submerged boundary method is used to realize the information transmission at the sea ice and sea surface boundary by interpolation through the force correction method. At the same time, the submerged boundary lattice Boltzmann method is a non-body-fitted mesh method with higher computational efficiency.

[0041] 2. Different treatments are applied to fluids with large differences in density and viscosity. In the coupling of air and seawater on the sea surface, a single-term free liquid surface model is adopted, which cleverly ignores the gas phase dynamics and only solves the seawater term, thus fundamentally avoiding the numerical difficulties caused by the low density of the gas phase.

[0042] 3. For the simulation of oil-water coupling, a color gradient model was adopted. This model can stably simulate flow with higher viscosity ratios and lower capillary number by accurately introducing surface tension terms in the moment space (within the MRT framework) and using an optimized recoloring algorithm. Attached Figure Description

[0043] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0044] Figure 1 This is a flowchart of the method of the present invention.

[0045] Figure 2 A detailed flowchart of the lattice Boltzmann method provided in an embodiment of the present invention.

[0046] Figure 3 A detailed flowchart of the single-phase free liquid surface model provided in the embodiments of the present invention.

[0047] Figure 4 A flowchart illustrating the application of the method of this invention to predict the impact range of oil spills on floating ice surfaces, provided as an embodiment of this invention. Detailed Implementation

[0048] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0049] It should be noted that the terms "comprising" and "having" and any variations thereof in the specification, claims and accompanying drawings of this invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such processes, methods, products or devices.

[0050] like Figure 1 As shown, this invention provides a method for predicting the impact range of oil spills on floating ice surfaces based on a color gradient LBM model, including: S1. The color gradient model is used to capture the interface of the water-oil two-phase immiscible liquid. The interface is kept sharp and numerical diffusion is suppressed by the recoloring operator to obtain the spatiotemporal evolution data of the oil-water interface. S2. Using the spatiotemporal evolution data of the oil-water interface obtained in step S1 as initial conditions, the lattice Boltzmann method is used to perform fluid dynamics simulation to obtain the oil-water mixed flow field. S3. In the oil-water mixed flow field obtained in step S2, the ice fragmentation boundary is discretized into Lagrange points by the submerged boundary method. The solid ice boundary force is coupled to the Eulerian seawater grid by force correction interpolation to realize the fluid-structure coupling between ice fragmentation and seawater, and the ice-water-oil three-phase coupled flow field is obtained. S4. Based on the ice-water-oil three-phase coupled flow field obtained in step S3, the volume fraction of the air layer on the sea surface is described by a single-phase free liquid surface model. Only the seawater phase is solved, and the liquid surface position is updated by interface reconstruction and overfill / overfill cell conversion rules to complete the coupled simulation of complex flow between the liquid surface and the gas. S5. Repeat steps S1-S4 until the oil film area, center of gravity and leading edge position converge, and output the spatiotemporal distribution results of the oil spill impact range for emergency response to oil spills in polar ice cap areas.

[0051] In a specific implementation, as a preferred embodiment of the present invention, step S1 includes: S11. For the oil-water immiscibility model, the D3Q19 model is adopted, with velocity vector... The definition is as follows:

[0052] in, The number representing the discrete velocity; S12. Define the colors of oil and water as... oil ,water The evolution equation is as follows:

[0053] in, This is the sum of the distribution functions of the two fluids, oil and water. ; For collision operators, ,in This represents a one-way collision operator. This represents the perturbation two-phase collision operator. This represents the recoloring two-phase collision operator; S13. The evolution equation in step S12 is solved by decomposing it using the one-way collision operator, perturbation operator, recoloring operator, and flow operator, as follows:

[0054]

[0055]

[0056]

[0057] S14. Formula based on one-way collision operator The distribution function is obtained as follows:

[0058] in, The relaxation coefficient; S15. The first torque of the distribution function gives the oil-water mixture fluid. Density:

[0059] in, For total density, ; S16. The second torque of the distribution function is defined by the total momentum, as follows:

[0060] in, The weighted average velocity representing the density of the oil-water mixture; Represents the equilibrium function. , Indicates the weighting coefficient. ; S17. To obtain a stable interface, calculate the density ratio and color. The pressure of an oil-water mixture is given by the following formula:

[0061]

[0062] in, , Indicates free parameters, It's a color Speed ​​of sound in fluids; S18. When the two fluids have different viscosities, interpolation is used to define the relaxation coefficient. Therefore, a color field is introduced, as follows:

[0063] Color field It is a function between -1 and 1, and its specific value depends on the proportion of red or blue fluid being evaluated. The relaxation coefficient, defined using interpolation, is expressed as follows:

[0064] in, It is a free parameter; ; Ultimately, the spatiotemporal evolution data of the oil-water interface were obtained.

[0065] In a specific implementation, as a preferred embodiment of the present invention, step S2 includes: S21. According to the lattice Boltzmann method, the evolution equation of the multiple relaxation time model (MRT) is as follows:

[0066] The above evolution equation represents the first evolution for each lattice. velocity distribution function of velocity components The evolutionary pattern; among which, This represents the distribution function of the combined oil and water two-phase flow in the color gradient method. Represents the particle discrete velocity. Represents a spatial position vector. Represents a moment vector. Represents the equilibrium moment. This represents a diagonal matrix consisting of relaxation rates. Indicates the time step. This represents volumetric force terms, including submerged boundary forces and surface tension. S22. Based on the multiple relaxation time model, the collision step is performed as follows:

[0067] S23. Based on the multiple relaxation time model, the transition steps are performed as follows:

[0068] The final result is an oil-water mixed flow field.

[0069] In this embodiment, as Figure 2 As shown, the specific calculation steps of the lattice Boltzmann method are given below: Step 1: Initialize seawater density and velocity, and calculate the particle distribution function; Step 2: Perform the collision step; Step 3: Perform the migration step; Step 4: Execute boundary conditions; Step 5: Calculation Macroscopic quantity at any given moment; Step 6: Repeat steps 2 through 5 until the output values ​​converge.

[0070] In specific implementation, as a preferred embodiment of the present invention, the D3Q19 model used in step S1, where D3 represents the spatial dimension and Q19 represents the number of discrete microvelocities, is used in the evolution equation of the multiple relaxation time model (MRT) in step S21: The moment space is as follows:

[0071] The equilibrium moments are as follows:

[0072] The particle discrete velocities are as follows:

[0073] in, , It is the lattice length. For time step; The diagonal matrix composed of relaxation rates is as follows: .

[0074] In a specific implementation, as a preferred embodiment of the present invention, step S3 includes: S31. The fluid velocity at the Lagrange midpoint is obtained by interpolating the seawater points within a certain range near the sea ice boundary point:

[0075] in, express Time of the first The intermediate fluid velocity at each Lagrange point This indicates the fluid velocity without considering boundary forces. Indicates the grid size. Represents a smooth Delta function; S32. Since the intermediate velocity and the velocity at that point are generally not equal, it is necessary to... When fluid forces are applied nearby, they are considered as solid-ice boundary forces. The formula for calculating solid-ice boundary forces is as follows:

[0076] in, Indicates sea ice speed; This represents the interpolated seawater velocity; Indicates the force correction factor. ,in The total number of Lagrange points, This represents the arc length between two adjacent Lagrange points; S33. Couple the boundary forces of solid ice to the Euler seawater mesh, as shown in the following formula:

[0077] in, Indicates the boundary force vector; S34. Correct the seawater velocity as follows:

[0078] The corrected seawater velocity was output, and the fluid-structure interaction between the ice fragments and the seawater was finally achieved, resulting in a three-phase coupled flow field of ice-water-oil.

[0079] In this embodiment, the submerged boundary method is used to perform fluid-structure interaction on water and ice. The solid boundary, i.e., the sea ice boundary, is discretized using Lagrange points, and the fluid domain, i.e., the sea area, is discretized using Eulerian networks. To solve the problem of non-fitting between the sea ice and seawater boundaries, an interpolation method is used to solve the boundary problem between seawater particles and sea ice particles. In this embodiment, a force correction method is used for processing.

[0080] In a specific implementation, as a preferred embodiment of the present invention, step S4 includes: S41. The volume fraction of the sea surface air layer is described using a single-phase free liquid surface model, as follows:

[0081] in, Indicates fluid mass; Indicates fluid density; This represents the volume fraction, i.e., the proportion of a cell that is filled. Its value is between 0 and 1, based on... The values ​​determine their respective types, for example, the sea surface and air grids. The value is 0, representing the seawater grid. The value is 1, if A value between 0 and 1 indicates that the grid is located at the boundary between the air and seawater at the sea surface, and belongs to the interface grid. S42. The inflow-outflow distribution function is used to calculate the mass change of the lattice within a time step. The calculation formula is as follows:

[0082] in, ,if If it is a liquid lattice, then ,if If it is a grid, then ,if If it is a gas lattice, then ; S43. At the interface, artificially reconstruct the distribution function between the interface grid and the adjacent sea surface air grid. The reconstruction equation is as follows:

[0083] in, Indicates the atmospheric pressure at the interface; S44. The distribution function of the interface normal is artificially reconstructed, and the reconstructed equation is as follows:

[0084] S45. During the calculation process, the following may occur: or In these cases, these two types of cells are called overfilled cells and overfilled cells, respectively. The excess mass is the mass difference between an overfilled or overfilled cell and a standard type cell. The rules for allocating excess mass after cell type conversion are as follows:

[0085] Among them, for the grid that is too full, For spaces, ; Indicates all directions Summation; Indicates excess mass. Finally, the coupled simulation of the complex flow between the liquid surface and the gas was completed.

[0086] In this embodiment, as Figure 3 As shown, the specific calculation process for the single-phase free surface model is given, and the steps are as follows: Step 1: Enter the current time step; Step 2: Calculate the force correction factor; Step 3: Interpolate to obtain the seawater velocity at the Lagrange midpoint; Step 4: Calculate the sea ice boundary points; Step 5: Distribute the boundary force points to the nearby seawater boundary points; Step 6: Correct the seawater speed; Step 7: Proceed to the next time step and repeat steps 2 through 6 until completion; To accurately simulate the water surface situation while considering the influence of surface tension, this invention employs a single-phase flow free surface model. This model introduces the concept of volume fraction, classifying each cell into three types: liquid (seawater), gas (sea surface air), and solid (sea ice). At each time step, the volume fraction of each cell is updated according to a specific rule, thereby achieving cell type transformation. The single-phase flow free surface model ignores the sea surface air phase and only solves for the seawater phase.

[0087] Example like Figure 4 As shown, the method for predicting the impact range of oil spills on floating ice surfaces based on the color gradient LBM model provided by this invention is applied to a specific example, and the process is as follows: Collect data on weather, hydrology, and geographical factors in polar regions and create a database; The collected data from polar regions were categorized, and regions with similar data were divided. Numerical simulations were performed to predict the impact range of oil spills under the condition of floating ice at sea in the divided areas, and the simulation results were recorded. Analyze the simulation results, formulate a response plan for sudden oil spill accidents, and sort out the human and material resources required for different countries and regions; Based on the results of regional division and the established response plans for sudden oil spills, a strategy for corresponding sudden oil spills in global polar regions was developed.

[0088] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the impact range of oil spills on floating ice surfaces based on a color gradient LBM model, characterized in that, include: S1. The color gradient model is used to capture the interface of the water-oil two-phase immiscible liquid. The interface is kept sharp and numerical diffusion is suppressed by the recoloring operator to obtain the spatiotemporal evolution data of the oil-water interface. S2. Using the spatiotemporal evolution data of the oil-water interface obtained in step S1 as initial conditions, the lattice Boltzmann method is used to perform fluid dynamics simulation to obtain the oil-water mixed flow field. S3. In the oil-water mixed flow field obtained in step S2, the ice fragmentation boundary is discretized into Lagrange points by the submerged boundary method. The solid ice boundary force is coupled to the Eulerian seawater grid by force correction interpolation to realize the fluid-structure coupling between ice fragmentation and seawater, and the ice-water-oil three-phase coupled flow field is obtained. S4. Based on the ice-water-oil three-phase coupled flow field obtained in step S3, the volume fraction of the air layer on the sea surface is described by a single-phase free liquid surface model. Only the seawater phase is solved, and the liquid surface position is updated by interface reconstruction and overfill / overfill cell conversion rules to complete the coupled simulation of complex flow between the liquid surface and the gas. S5. Repeat steps S1-S4 until the oil film area, center of gravity and leading edge position converge, and output the spatiotemporal distribution results of the oil spill impact range for emergency response to oil spills in polar ice cap areas.

2. The method for predicting the impact range of oil spills on floating ice surfaces based on a color gradient LBM model according to claim 1, characterized in that, Step S1 includes: S11. For the oil-water immiscibility model, the D3Q19 model is adopted, with velocity vector... The definition is as follows: in, The number representing the discrete velocity; S12. Define the colors of oil and water as... oil ,water The evolution equation is as follows: in, This is the sum of the distribution functions of the two fluids, oil and water. ; For collision operators, ,in This represents a one-way collision operator. This represents the perturbation two-phase collision operator. This represents the recoloring two-phase collision operator; S13. The evolution equation in step S12 is solved by decomposing it using the one-way collision operator, perturbation operator, recoloring operator, and flow operator, as follows: S14. Formula based on one-way collision operator The distribution function is obtained as follows: in, The relaxation coefficient; S15. The first torque of the distribution function gives the oil-water mixture fluid. Density: in, For total density, ; S16. The second torque of the distribution function is defined by the total momentum, as follows: in, The weighted average velocity representing the density of the oil-water mixture; Represents the equilibrium function. , Indicates the weighting coefficient. ; S17. To obtain a stable interface, calculate the density ratio and color. The pressure of an oil-water mixture is given by the following formula: in, , Indicates free parameters, It's a color Speed ​​of sound in fluids; S18. When the two fluids have different viscosities, interpolation is used to define the relaxation coefficient. Therefore, a color field is introduced, as follows: Color field It is a function between -1 and 1, and its specific value depends on the proportion of red or blue fluid being evaluated. The relaxation coefficient, defined using interpolation, is expressed as follows: in, It is a free parameter; ; Ultimately, the spatiotemporal evolution data of the oil-water interface were obtained.

3. The method for predicting the impact range of oil spills on floating ice surfaces based on a color gradient LBM model according to claim 1, characterized in that, Step S2 includes: S21. According to the lattice Boltzmann method, the evolution equation of the multi-relaxation time model is as follows: The above evolution equation represents the first evolution for each lattice. velocity distribution function of velocity components The evolutionary pattern; among which, This represents the distribution function of the combined oil and water two-phase flow in the color gradient method. Represents the particle discrete velocity. Represents a spatial position vector. Represents a moment vector. Represents the equilibrium moment. This represents a diagonal matrix consisting of relaxation rates. Indicates the time step. This represents volumetric force terms, including submerged boundary forces and surface tension. S22. Based on the multiple relaxation time model, the collision step is performed as follows: S23. Based on the multiple relaxation time model, the transition steps are performed as follows: The final result is an oil-water mixed flow field.

4. The method for predicting the impact range of oil spills on floating ice surfaces based on a color gradient LBM model according to claim 3, characterized in that, The D3Q19 model used in step S1, where D3 represents the spatial dimension and Q19 represents the number of discrete micro-velocities, is used in the evolution equations of the multi-relaxation time model in step S21: The moment space is as follows: The equilibrium moments are as follows: The particle discrete velocities are as follows: in, , It is the lattice length. For time step; The diagonal matrix composed of relaxation rates is as follows: 。 5. The method for predicting the impact range of oil spills on floating ice surfaces based on a color gradient LBM model according to claim 1, characterized in that, Step S3 includes: S31. The fluid velocity at the Lagrange midpoint is obtained by interpolating the seawater points within a certain range near the sea ice boundary point: in, express Time of the first The intermediate fluid velocity at each Lagrange point This indicates the fluid velocity without considering boundary forces. Indicates the grid size. Represents a smooth Delta function; S32. Since the intermediate velocity and the velocity at that point are generally not equal, it is necessary to... When fluid forces are applied nearby, they are considered as solid-ice boundary forces. The formula for calculating solid-ice boundary forces is as follows: in, Indicates sea ice speed; This represents the interpolated seawater velocity; Indicates the force correction factor. ,in The total number of Lagrange points, This represents the arc length between two adjacent Lagrange points; S33. Couple the boundary forces of solid ice to the Euler seawater mesh, as shown in the following formula: in, Indicates the boundary force vector; S34. Correct the seawater velocity as follows: The corrected seawater velocity was output, and the fluid-structure interaction between the ice fragments and the seawater was finally achieved, resulting in a three-phase coupled flow field of ice-water-oil.

6. The method for predicting the impact range of oil spills on floating ice surfaces based on a color gradient LBM model according to claim 1, characterized in that, Step S4 includes: S41. The volume fraction of the sea surface air layer is described using a single-phase free liquid surface model, as follows: in, Indicates fluid mass; Indicates fluid density; This represents the volume fraction, i.e., the proportion of a cell that is filled. Its value is between 0 and 1, based on... The values ​​determine their respective types, for example, the sea surface and air grids. The value is 0, representing the seawater grid. The value is 1, if A value between 0 and 1 indicates that the grid is located at the boundary between the air and seawater at the sea surface, and belongs to the interface grid. S42. The inflow-outflow distribution function is used to calculate the mass change of the lattice within a time step. The calculation formula is as follows: in, ,if If it is a liquid lattice, then ,if If it is a grid, then ,if If it is a gas lattice, then ; S43. At the interface, artificially reconstruct the distribution function between the interface grid and the adjacent sea surface air grid. The reconstruction equation is as follows: in, Indicates the atmospheric pressure at the interface; S44. The distribution function of the interface normal is artificially reconstructed, and the reconstructed equation is as follows: S45. During the calculation process, the following may occur: or In these cases, these two types of cells are called overfilled cells and overfilled cells, respectively. The excess mass is the mass difference between an overfilled or overfilled cell and a standard type cell. The rules for allocating excess mass after cell type conversion are as follows: Among them, for the grid that is too full, For spaces, ; Indicates all directions Summation; Indicates excess mass. Finally, the coupled simulation of the complex flow between the liquid surface and the gas was completed.

7. The method for predicting the impact range of oil spills on floating ice surfaces based on a color gradient LBM model according to claim 6, characterized in that, In step S45, the conversion rules for overfilled cells and overfilled cells are as follows: Transform overfilled cells into seawater cells, and simultaneously transform the surrounding gas cells into interface cells; transform overfilled cells into surface air cells, and simultaneously transform the nearby seawater cells into interface cells; initialize the resulting interface cells, seawater cells, and surface air cells with the equilibrium distribution functions corresponding to the average density and velocity of their adjacent interface cells.

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