A non-divergent interpolation method of fluid motion control equation in sea surface oil spill simulation

Abstract

The application discloses a non-divergence interpolation method for fluid motion control equation in sea surface oil spill simulation, which comprises the following steps: solving initial velocity field; performing non-divergence interpolation; updating particle position; if the running time of simulation meets the requirement, ending, otherwise turning to step A to continue simulation. The application can realize oil spill dynamic simulation based on fluid mechanics NS equation, which is a physical-based method, thus effectively improving the real feeling of oil spill behavior. Since the application combines the continuity equation of fluid mechanics, the divergence of velocity field is gradually reduced through multi-step iteration solving method; therefore, the application can guarantee that the interpolation result meets the continuity equation, so that the calculation result is more stable. Since the application meets the continuity equation, the number of iterations required for calculation is less.

Description

Technical Field

[0001] This invention belongs to the field of computer simulation of marine oil spills, and relates to a non-scattered interpolation method for fluid motion control equations in marine oil spill simulation, which can be applied to marine oil spill emergency simulation. Background Technology

[0002] The threat of oil spills at sea is severe, and improving emergency response capabilities and strengthening emergency training for personnel involved in such incidents have become urgent issues. Using simulators for maritime emergency simulation training has proven to be a feasible method. However, currently, oil spill models in simulators generally lack realistic behavior and are not sufficiently interactive.

[0003] In computer graphics simulation of fluid motion in an oil spill model within a simulator, the fluid motion control equations need to be solved discretely. The main solution methods include the mesh method, the particle method, and a hybrid mesh-particle method.

[0004] In mesh-particle hybridization methods, information exchange between the mesh and particles is necessary. Previous methods typically employed interpolation techniques, such as second-order interpolation, for this information exchange. However, commonly used interpolation methods do not satisfy the continuity equation, thus failing to guarantee zero divergence in the interpolation results. This can easily lead to divergent calculations, making simulations impossible and rendering the simulation results meaningless.

[0005] The references involved in this invention are as follows:

[0006] [1] Zou Changjun, Emergency Simulation and Visualization of Ship Oil Spill in Navigation Simulation [D], (Doctoral Dissertation), Dalian: Dalian Maritime University, 2018.

[0007] [2] Zou Changjun, Yin Yong, Liu Xiuwen, et al. Research and implementation of a new method for visualizing oil spills on the sea surface [J], Journal of Chongqing Jiaotong University (Natural Science Edition), 2017, 36(6):103-108.

[0008] [3] Zou Changjun, Yin Yong, Liu Xiuwen, et al. Research on key technologies for visualizing oil spills on the sea surface [J], Journal of System Simulation, 2018, 30(6):2109-2116. Summary of the Invention

[0009] To address the issue of insufficient realism in existing oil spill simulation technologies, this invention proposes a divergence-free interpolation method for the fluid motion control equations in marine oil spill simulation, thereby further enhancing the realism of the behavior in marine oil spill simulations.

[0010] A divergence-free interpolation method for the fluid motion control equations in marine oil spill simulation includes the following steps:

[0011] A. Solving the initial velocity field

[0012] The fluid motion control equations based on the particle mesh mixing method are as follows:

[0013]

[0014] In the formula, p is pressure; V is velocity vector; ρ is density; μ is viscosity coefficient; f is external force; t is time; ▽ is divergence; Equation (1) consists of two equations, the first of which is the momentum equation and the second equation is the fluid continuity equation;

[0015] When solving the momentum equation (1), the oil spill area is first divided into rectangular grids, and the velocity field is solved using a grid-based method. The solution process includes calculating the pressure gradient term and the divergence term; then the velocity field is corrected, and the updated velocity field at the grid nodes is obtained.

[0016] B. Perform discrepancy-free interpolation

[0017] After obtaining the velocity field of the grid nodes, the velocity of the grid nodes is interpolated to obtain the velocity field of the particle position. The specific steps are as follows:

[0018] B1. First, interpolate using the following interpolation method to obtain the initial values ​​of the velocity field:

[0019]

[0020] In the formula, u' and v' are the interpolated initial velocities in the horizontal and vertical directions, respectively. Let p i Let i represent the position of the i-th particle at the current moment, where i is the particle's index. Sort the four nodes of the grid containing this particle's position clockwise: bottom left is numbered 1, top left 2, top right 3, and bottom right 4. Divide the grid into four rectangular regions: with the i-th particle as the center point, draw horizontal and vertical lines. The crosshairs formed by these lines and the four edges of the grid form four rectangular regions, A1, A2, A3, and A4 representing the areas of the top right, bottom right, bottom left, and top left rectangular regions, respectively. u1, u2, u3, u4 and v1, v2, v3, v4 represent the x- and y-direction velocities of the corresponding nodes 1, 2, 3, and 4, respectively.

[0021] Discretize the fluid dynamics continuity equation, where Δx and Δy are the widths of the grid in the horizontal and vertical directions, respectively:

[0022]

[0023] B2. The velocity field divergence is obtained after interpolation according to the continuity equation (4), where the divergence obtained by the first calculation of div1 is:

[0024]

[0025] B3. Calculate the first correction value of u according to equation (5), where u” is the first correction speed:

[0026]

[0027] B4. Calculate the new divergence according to equation (6), where div2 is the divergence obtained from the second calculation:

[0028]

[0029] B5. Update the speed v according to equation (7), where v” is the speed after the second correction:

[0030]

[0031] B6. Determine whether the divergence value is lower than the threshold according to formula (4). If it is lower than the threshold, proceed to step B7; otherwise, proceed to step B2.

[0032] B7. End interpolation.

[0033] C. Particle position update

[0034] The updated velocity field is used to calculate particle position convection.

[0035] D. Conditional Loop

[0036] If the simulation runtime meets the requirements, the simulation ends; otherwise, proceed to step A to continue the simulation.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] 1. This invention can realize dynamic simulation of oil spills based on the Navier-Stokes equations of fluid dynamics. This is a physics-based approach, which can effectively improve the realism of oil spill behavior.

[0039] 2. Because this invention incorporates the continuity equation of fluid mechanics and gradually reduces the divergence of the velocity field through a multi-step iterative solution, this invention can ensure that the interpolation results satisfy the continuity equation, making the calculation results more stable.

[0040] 3. Because this invention satisfies the continuity equation, fewer iterations are required for the calculation. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the interpolation process of the present invention. Detailed Implementation

[0042] The present invention will now be described in further detail with reference to the accompanying drawings. Figure 1 The diagram illustrates the divergence-free interpolation process in step B of this invention. After obtaining the velocity field of the grid nodes, the velocity of the grid nodes needs to be interpolated to obtain the velocity field of the particle positions. This process requires the use of a divergence-free interpolation method. In this process, an initial velocity field is first obtained using a distance-based interpolation method, such as a second-order interpolation method. Then, the velocity field is corrected using a continuity equation, and the corrected velocity field satisfies the divergence condition. The specific process is the same as step B in the invention description and will not be repeated here.

[0043] This invention is not limited to this embodiment. Any equivalent concept or modification within the technical scope disclosed in this invention shall be included within the protection scope of this invention.

Claims

1. A divergence-free interpolation method for the fluid motion control equations in marine oil spill simulation, characterized in that: Includes the following steps: A. Solving the initial velocity field The fluid motion control equations based on the particle mesh mixing method are as follows: In the formula, p is pressure; V is velocity vector; ρ is density; μ is viscosity coefficient; f is external force; and t is time. For divergence; Equation (1) consists of two equations, where the first equation is the momentum equation and the second equation is the fluid continuity equation; When solving the momentum equation (1), the oil spill area is first divided into rectangular grids, and the velocity field is solved using a grid-based method. The solution process includes calculating the pressure gradient term and the divergence term; then the velocity field is corrected, and the updated velocity field at the grid nodes is obtained. B. Perform discrepancy-free interpolation After obtaining the velocity field of the grid nodes, the velocity of the grid nodes is interpolated to obtain the velocity field of the particle position. The specific steps are as follows: B1. First, interpolate using the following interpolation method to obtain the initial values ​​of the velocity field: In the formula, u' and v' are the interpolation results of the initial velocities in the horizontal and vertical directions, respectively; let pi be the position of the i-th particle at the current moment, and i be the particle number; the four nodes of the grid where the particle position is located are sorted clockwise, i.e., the bottom left corner is numbered 1, the top left corner is numbered 2, the top right corner is numbered 3, and the bottom right corner is numbered 4; the grid where the particle position is located is divided into four rectangular regions, the division method is as follows: with the i-th particle as the center point, draw horizontal and vertical lines respectively, and the cross line formed by the horizontal and vertical lines forms four rectangular regions between the four sides of the grid, A1, A2, A3, A4 are the areas of the top right, bottom right, bottom left, and top left rectangular regions, respectively; u1, u2, u3, u4 and v1, v2, v3, v4 are the x-direction and y-direction velocities of the corresponding nodes 1, 2, 3, 4, respectively; Discretize the fluid dynamics continuity equation, where Δx and Δy are the widths of the grid in the horizontal and vertical directions, respectively: B2. The velocity field divergence is obtained by interpolation according to the continuity equation (4), where div1 is the divergence obtained in the first calculation: B3. Calculate the first correction value of u according to equation (5), where u” is the first correction speed: B4. Calculate the new divergence according to equation (6), where div2 is the divergence obtained from the second calculation: B5. Update the speed v according to equation (7), where v” is the speed after the second correction: B6. Determine whether the divergence value is lower than the threshold according to formula (4). If it is lower than the threshold, proceed to step B7. Otherwise, proceed to step B2; B7. End interpolation; C. Particle position update The updated velocity field is used to calculate particle position convection. D. Conditional Loop If the simulation runtime meets the requirements, the simulation ends; otherwise, proceed to step A to continue the simulation.

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