Shallow water dynamic process simulation method based on local time step length

Abstract

The invention relates to a shallow water dynamic process simulation method based on a local time step length, and the method comprises the steps: dividing a target region into a plurality of grids based on a shallow water dynamic process model, the target region comprising an ocean region and a land region adjacent to the ocean region; at least dividing the plurality of grids into a first grid set and a second grid set; determining a first time step length corresponding to the first grid set according to the first grid set; determining a second time step length corresponding to the second grid set according to the second grid set; determining a first simulation result of the shallow water dynamic process according to the first time step length and the second time step length; wherein the first grid set comprises a plurality of first grids, and the second grid set comprises a plurality of second grids; the first time step length is larger than the second time step length. The efficiency of the shallow water dynamic process simulation method is improved by respectively determining appropriate local time steps according to the precision requirements of different grid sets.

Description

Technical Field

[0001] The present invention relates to the technical field of hydrodynamic process simulation, and particularly relates to a shallow water hydrodynamic process simulation method based on local time steps. Background Art

[0002] The shallow water hydrodynamic process is a description of the water body movement where the water depth scale is significantly smaller than the flow horizontal scale, and can predict and evaluate disaster events such as storm surge water levels, water level rise amplitudes, and flood evolution, and is widely applied to scenarios such as estuaries, coasts, and coastal wetlands. However, since the time step of the shallow water hydrodynamic process is often uniformly global, there are problems with inaccurate simulation results in the shallow water hydrodynamic process. Summary of the Invention

[0003] To overcome the problems existing in the related art, the present invention provides a shallow water hydrodynamic process simulation method based on local time steps.

[0004] According to an embodiment of the present invention, there is provided a shallow water hydrodynamic process simulation method based on local time steps, the method comprising: Constructing a shallow water hydrodynamic process model to divide a target area into a plurality of grids, the target area including a marine area and a land area adjacent to the marine area; Dividing the plurality of grids into at least a first grid set and a second grid set; Determining a first time step corresponding to the first grid set according to the first grid set; Determining a second time step corresponding to the second grid set according to the second grid set; Determining a first simulation result of the shallow water hydrodynamic process according to the first time step and the second time step; Wherein, the first grid set includes a plurality of first grids, the second grid set includes a plurality of second grids; the first time step is greater than the second time step.

[0005] In some embodiments of the present invention, the dividing the plurality of grids into at least a first grid set and a second grid set includes: Determining a time grading index corresponding to each of the grids; Dividing the plurality of grids into at least a first grid set and a second grid set according to the time grading index corresponding to each of the grids.

[0006] In some embodiments of the present invention, the determining a time grading index corresponding to each of the grids includes: Determining the minimum time step of all the grids according to the grid water depth and the critical water depth of each of the grids; Determine the time grading index corresponding to each of the grids according to the minimum time step, the preset time grading coefficient, and the maximum time step of each of the grids.

[0007] In some embodiments of the present invention, the determining the first simulation result of the shallow water dynamic process according to the first time step and the second time step includes: Determine the first physical quantity value and the first physical flux value of the first grid set according to the first time step; Determine the second physical quantity value and the second physical flux value of the second grid set according to the second time step; Determine the first simulation result according to the first physical quantity value, the first physical flux value, the second physical quantity value, and the second physical flux value.

[0008] In some embodiments of the present invention, there is a boundary grid set between the first grid set and the second grid set, and the method further includes: Predict the third physical quantity value and the third physical flux value of the boundary grid set; Determine the fourth physical quantity value and the fourth physical flux value of the second grid set; According to the fourth physical quantity value and the fourth physical flux value, correct the third physical quantity value and the third physical flux value to obtain the fifth physical quantity value and the fifth physical flux value of the boundary grid set.

[0009] In some embodiments of the present invention, after obtaining the fifth physical quantity value and the fifth physical flux value of the boundary grid set, the method further includes: Determine the second simulation result of the shallow water dynamic process according to the first physical quantity value of the first grid set, the first physical flux value of the first grid set, the fourth physical quantity value, the fourth physical flux value, the fifth physical quantity value, and the fifth physical flux value.

[0010] In some embodiments of the present invention, the predicting the third physical quantity value and the third physical flux value of the boundary grid set includes: Predict the third physical quantity value and the third physical flux value according to the first physical quantity value and the first physical flux value of the first grid set.

[0011] In some embodiments of the present invention, the determining the fourth physical quantity value and the fourth physical flux value of the second grid set includes: Determine the boundary conditions, which are used to define the fourth physical quantity value and the fourth physical flux value; Determine the sixth physical quantity value and the sixth physical flux value at a subsequent time point of the second grid set according to the boundary conditions and the first simulation result; Determine the fourth physical quantity value and the fourth physical flux value according to the second physical quantity value of the second grid set, the second physical flux value of the second grid set, the sixth physical quantity value, and the sixth physical quantity value.

[0012] In some embodiments of the present invention, the determining the boundary conditions includes: Determine the boundary conditions according to the first physical quantity value of the first grid set.

[0013] In some embodiments of the present invention, the determining the boundary conditions according to the first physical quantity value of the first grid set includes: Expand the first physical quantity value according to the Taylor expansion formula to determine the boundary conditions.

[0014] The technical solutions provided by the embodiments of the present invention may include the following beneficial effects: Divide multiple grids into at least a first grid set and a second grid set, so as to divide the grids in different regions into different grid sets according to the required accuracy requirements; determine the first time step corresponding to the first grid set according to the first grid set, so as to determine a suitable local time step according to the accuracy requirements of the first grid set; determine the second time step corresponding to the second grid set according to the second grid set, so as to determine a suitable local time step according to the accuracy requirements of the second grid set; determine the first simulation result of the shallow water dynamic process according to the first time step and the second time step, so as to determine the simulation result according to the local time steps respectively corresponding to different grid sets. By respectively determining suitable local time steps according to the accuracy requirements of different grid sets, the problem of too long calculation time caused by a small global unified time step and the problem of low accuracy of the simulation result caused by a large global unified time step are avoided, which not only improves the efficiency of the shallow water dynamic process simulation method but also can improve the accuracy of the simulation result.

[0015] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present invention. Brief Description of the Drawings

[0016] The drawings here are incorporated into the specification and constitute a part of this specification, showing embodiments consistent with the present invention and used together with the specification to explain the principles of the present invention.

[0017] Figure 1 is a schematic flowchart of a shallow water dynamic process simulation method based on local time steps shown according to the first embodiment; Figure 2It is a schematic flowchart of a shallow water dynamic process simulation method based on local time steps shown in the second embodiment; Figure 3 It is a schematic flowchart of a shallow water dynamic process simulation method based on local time steps shown in the third embodiment; Figure 4 It is a schematic flowchart of a shallow water dynamic process simulation method based on local time steps shown in the fourth embodiment; Figure 5 It is a schematic flowchart of a shallow water dynamic process simulation method based on local time steps shown in the fifth embodiment; Figure 6 It is a schematic diagram for determining a first simulation result shown in one embodiment; Figure 7 It is a schematic diagram for predicting the third physical quantity value and the third physical flux value of a boundary grid set, and obtaining the fourth physical quantity value and the fourth physical flux value of a second grid set shown in one embodiment; Figure 8 It is a schematic diagram for determining a second simulation result shown in one embodiment; Figure 9-1 It is a schematic diagram of the grid and resolution of a target area shown in one embodiment; Figure 9-2 It is a schematic diagram of tidal verification shown in one embodiment; Figure 10 It is a schematic diagram of the grid grading situation at the initial moment shown in one embodiment; Figure 11 It is a tidal level verification diagram of a tide shown in one embodiment; Figure 12 It is a flow velocity verification diagram of a tidal current shown in one embodiment; Figure 13 It is a verification diagram of storm surge shown in one embodiment. Detailed implementation manners

[0018] Here, exemplary embodiments will be described in detail, and the examples are shown in the drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The implementation manners described in the following exemplary embodiments do not represent all implementation manners consistent with the present invention. On the contrary, they are merely examples of devices and methods consistent with some aspects of the present invention as detailed in the appended claims.

[0019] Shallow water dynamics describe the movement of water bodies at depths significantly smaller than the horizontal scale of the flow. They can predict and assess disasters such as storm surge levels, flood magnitude, and flood evolution, and are widely used in scenarios such as estuaries, coastal wetlands, storm surge floodplains, and urban flood evolution. The dynamics of shallow water flow are often influenced by a variety of factors. Hydrodynamic simulations in estuaries and coastal areas must account for tides, storm surges, and complex topography. Hydrodynamic simulations in coastal wetlands must address the interaction between water flow and wetland vegetation. Hydrodynamic simulations of storm surge floodplains involve the complex interaction of wind, waves, and tides. Urban flood evolution requires considering the influence of multiple local factors on water flow, such as buildings, roads, and underground infrastructure. All of these factors require shallow water dynamics simulation methods that can efficiently simulate large-scale hydrodynamic processes while also accurately capturing local topographic changes and flow characteristics at small scales, thereby achieving accurate forecasting and decision support.

[0020] Existing shallow water dynamic simulation methods primarily rely on unstructured grid methods to adapt to complex terrain variations and irregular underlying surfaces. However, these simulation methods typically employ a unified time step across the entire simulation area, meaning that the same time step is used for calculations throughout the entire simulation domain. While this approach ensures computational stability, it also has significant drawbacks. First, because the entire domain is divided into high-precision and low-precision regions, using a unified time step, when the time step is large, local hydrodynamic variations in the high-precision region cannot be accurately captured, affecting the accuracy of the simulation results. Smaller time steps require extensive computation and resource consumption in the low-precision region, reducing the efficiency of the shallow water dynamic simulation method. Consequently, existing shallow water dynamic process simulation methods suffer from low efficiency and poor accuracy. Furthermore, when dealing with hydrodynamic processes of varying time scales, a fixed time step cannot flexibly adapt to the spatiotemporal variations of different regions. This is particularly true in the case of sudden and volatile events such as storm surges and floods, where timely adjustments cannot be made to maintain a balance between computational efficiency and accuracy.

[0021] An exemplary embodiment of the present invention provides a method for simulating shallow water dynamic processes based on a local time step, such as Figure 1 As shown, the method includes: S100: Construct a shallow water dynamic process model to divide the target area into multiple grids, where the target area includes an ocean area and a land area adjacent to the ocean area.

[0022] S200: Divide a plurality of grids into at least a first grid set and a second grid set.

[0023] S300: Determine a first time step corresponding to the first grid set according to the first grid set.

[0024] S400. Determine a second time step corresponding to the second grid set according to the second grid set.

[0025] S500. Determine a first simulation result of the shallow water dynamic process according to the first time step and the second time step.

[0026] Among them, the first grid set includes a plurality of first grids, and the second grid set includes a plurality of second grids. The first time step is greater than the second time step.

[0027] In this embodiment, the multiple grids are at least divided into a first grid set and a second grid set, so as to divide the grids in different regions into different grid sets according to the required precision requirements; determine a first time step corresponding to the first grid set according to the first grid set, so as to determine a suitable local time step according to the precision requirements of the first grid set; determine a second time step corresponding to the second grid set according to the second grid set, so as to determine a suitable local time step according to the precision requirements of the second grid set; determine a first simulation result of the shallow water dynamic process according to the first time step and the second time step, so as to determine the simulation result according to the local time steps respectively corresponding to different grid sets. By respectively determining suitable local time steps according to the precision requirements of different grid sets, the problems of too long calculation time caused by a small globally unified time step and low precision of the simulation result caused by a large globally unified time step are avoided, which not only improves the efficiency of the shallow water dynamic process simulation method but also can improve the accuracy of the simulation result.

[0028] Exemplarily, the multiple grids can be divided into a first grid set, a second grid set, a third grid set... an Nth grid set according to requirements. The corresponding time steps can be determined respectively according to the first grid set, the second grid set, the third grid set... the Nth grid set. According to the time steps respectively corresponding to the above grid sets, a first simulation result of the shallow water dynamic process can be determined.

[0029] Exemplarily, the sizes of the multiple first grids can be the same or different, and the sizes of the multiple second grids can be the same or different. The size of the first grid set is greater than the size of the second grid set, indicating that only the overall change of the hydrodynamic force needs to be captured in the first grid set, while the change of the hydrodynamic force needs to be captured more precisely in the second grid set. That is, the first grid set belongs to the low-precision area, and the second grid set belongs to the high-precision area. Therefore, the first time step being greater than the second time step not only satisfies the capture of the hydrodynamic force change in the first grid set as a whole to improve the efficiency of the simulation method, but also can satisfy the precise capture of the hydrodynamic force change in the local area, thereby improving the accuracy of the simulation result.

[0030] Exemplarily, during the simulation process, although the first time step and the second time step are determined, the first grid set and the second grid set change with the simulation process. A grid that belonged to the first grid set in the previous step may be divided into the second grid set in the next step. A grid that belonged to the second grid set in the previous step may also be divided into the first grid set in the next step to adapt to the simulation process of storm surges, floods, etc., which are sudden and have drastic changes.

[0031] Exemplarily, the sizes of multiple first grids / second grids may be the same or different. When the time steps corresponding to all grid sets are equal, it is the global unified time step in the prior art.

[0032] Exemplarily, the size of the first grid may be larger than the size of the second grid.

[0033] It can be understood that since using a smaller time step in the high-precision area can ensure the accuracy of the first simulation result, and using a larger time step in the low-precision area can increase the efficiency of the simulation process, the problems brought by the global unified time step in the traditional shallow water dynamic process simulation method are avoided. Further, since the time steps in different precision areas are different, this embodiment can effectively handle complex terrains, non-uniform underlying surfaces, and multi-scale hydrodynamic processes, and can balance efficiency and accuracy in large-scale and small-scale areas, optimizing the reliability of cross-scale shallow water dynamic process simulation. Through the refined setting of the time step, unnecessary calculation processes are reduced. Especially in the long-term large-scale simulation process, the calculation cost is significantly reduced. For variable environments such as sudden storm surges, complex tides, and dynamic terrains, the accuracy and reliability of the first simulation result can also be improved, increasing the application scope of the shallow water dynamic process simulation method based on local time steps.

[0034] Exemplarily, before step S100, the method further includes constructing a shallow water dynamic process model. The method for constructing a shallow water dynamic process model includes: S10. Determine the simulation requirements according to the simulation target.

[0035] S11. Determine the target area and the target data of the target area according to the simulation requirements.

[0036] S12. Construct a shallow water dynamic process model according to the target data and the accuracy requirements.

[0037] In step S10, the simulation target can be determined by application scenarios, such as scenarios like estuarine coast, coastal wetland, storm surge overtopping, and urban block flood evolution. The simulation requirements are the key factors affecting the hydrodynamic simulation process in the corresponding scenarios, such as terrain, tide, wind speed, waves, etc. In step S11, according to the simulation requirements, the area covered by the simulation target can be determined as the target area, and the target data can include relevant data such as the terrain, meteorology, hydrology, flow field, and boundary conditions of the target area. In step S12, an appropriate grid resolution can be selected according to the obtained target data and accuracy requirements. High-resolution grids are selected in high-precision areas (such as shorelines, wetlands, etc.), while low-resolution grids can be used in places far from important areas to construct a suitable shallow water dynamic process model. At the same time, physical parameters in the model, such as bottom friction, wind resistance, wave propagation, and turbulence models, also need to be set.

[0038] Exemplarily, after constructing the shallow water dynamic process model, initial conditions and target boundary conditions can be set to improve the reliability of the shallow water dynamic process model. The initial conditions can include physical quantity values such as water level, flow velocity, temperature, and salinity. The target boundary conditions related to the tidal water level, flow rate, wind speed, wind direction, wave height, wave length, and wave period, etc. of the open boundary (the side of the model's boundary near the ocean) can be set based on historical tidal data, tidal forecasts, meteorological forecasts, typhoon simulation data, storm surge, and wave-related simulations.

[0039] In one embodiment, as Figure 2 shown, dividing the multiple grids into at least a first grid set and a second grid set in step S200 includes: S210. Determine the time grading index corresponding to each grid.

[0040] S220. According to the time grading index corresponding to each grid, divide the multiple grids into at least a first grid set and a second grid set.

[0041] In this embodiment, since the time grading index can characterize whether the area to which all grids in the entire region belong is a high-precision area or a low-precision area, by dividing the multiple grids into at least a first grid set and a second grid set according to the time grading index corresponding to each grid, the reliability of the first grid set and the second grid set can be improved, thereby improving the reliability of the simulation method.

[0042] Exemplarily, when the time grading index corresponding to a part of the grids is within a first preset range, this part of the grids is divided into the first grid set. When the time grading index corresponding to another part of the grids is within a second preset range, this part of the grids is divided into the second grid set.

[0043] In one embodiment, as Figure 3As shown, in step S220, according to the time grading indices corresponding to each grid, dividing the multiple grids into at least a first grid set and a second grid set includes: S221. Determine the minimum time step of all grids according to the grid water depth and the critical water depth of each grid.

[0044] S222. Determine the time grading index corresponding to each grid according to the minimum time step, the preset time grading coefficient, and the maximum time step of each grid.

[0045] In this embodiment, since the minimum time step is related to the grid water depth and the critical water depth, determining the minimum time step according to the grid water depth and the critical water depth can improve the reliability of the minimum time step. At the same time, the preset grading index can determine the number of grid sets into which the multiple grids are divided, and the maximum time step of each grid can represent the limitation of the time step of each grid. By determining the time grading index corresponding to each grid according to the minimum time step, the preset time grading coefficient, and the maximum time step of each grid, the reliability of the time grading index is improved.

[0046] Exemplarily, the maximum time step can be determined based on the Courant-Friedrichs-Lewy (CFL) criterion by the following formula: ; where is the Courant number, with a value of 0.9; is the distance from the center of the th grid to its th side; , are the flow velocities in the normal local coordinate system of the th side of the th grid; is the grid water depth;

[0047] is the critical water depth; is the acceleration due to gravity. When the water depth of the grid is less than the critical water depth, the grid is a dry grid, and the default maximum time step of the dry grid is infinite. However, considering the actual situation, its time step is set to the maximum local time step of all wet grid cells. ; Exemplarily, the minimum time step can be determined by the following formula: When the shallow water dynamic process model is a model with a unified time step for the entire region, the time grading index corresponding to each grid can be determined by the following formula: ; Exemplarily, according to the time grading index all grids can be divided into different sets to determine the local time steps and the maximum time intervals corresponding to different grid sets, which can be specifically determined by the following formula: where

[0048] is the minimum value of the edges of two adjacent grids, and is the maximum time grading index.

[0049] In one embodiment, determining the first simulation result of the shallow water dynamic process according to the first time step and the second time step in step S500 includes: S510. Determine the first physical quantity value and the first physical flux value of the first grid set according to the first time step.

[0050] S520. Determine the second physical quantity value and the second physical flux value of the second grid set according to the second time step.

[0051] S530. Determine the first simulation result according to the first physical quantity value, the first physical flux value, the second physical quantity value and the second physical flux value.

[0052] In this embodiment, when appropriate time steps are selected, the accuracies of the determined first physical quantity value, the first physical flux value, the second physical quantity value and the second physical flux value are relatively high. By respectively determining appropriate time steps and determining the corresponding physical quantity values and physical flux values according to the time steps, and then determining the first simulation result, the reliability of the first simulation result is improved.

[0053] Exemplarily, taking the first grid set and the second grid set as an example, if the current time is 50S, the first time step of the first grid set is 4S, and the second time step of the second grid set is 1S, the physical quantity value and the physical flux value of the first grid set at 54S are the first physical quantity value and the first physical flux value, and the physical quantity value and the physical flux value of the second grid set at 51S are the second physical quantity value and the second physical flux value.

[0054] Exemplarily, the amount of a physical quantity passing through a certain interface per unit time is called the physical flux value. The physical quantity value can include flow velocity, water level and wave, and the corresponding physical flux values can include momentum flux, mass flux and wave energy flux.​

[0055] In one embodiment, there is a boundary grid set between the first grid set and the second grid set. As Figure 4 shown, the method further includes: S600. Predict the third physical quantity value and the third physical flux value of the boundary grid set.

[0056] S700. Determine the fourth physical quantity value and the fourth physical flux value of the second grid set.

[0057] S800. Correct the third physical quantity value and the third physical flux value according to the fourth physical quantity value and the fourth physical flux value to obtain the fifth physical quantity value and the fifth physical flux value of the boundary grid set.

[0058] In this embodiment, since there is also a boundary grid set between the first grid set and the second grid set, by predicting and correcting the third physical quantity value and the third physical flux value of the boundary grid set to obtain the fifth physical quantity value and the fifth physical flux value of the boundary grid set, the reliability of determining the fifth physical quantity value and the fifth physical flux value of the boundary grid set is improved.

[0059] In one embodiment, after correcting the third physical quantity value and the third physical flux value according to the fourth physical quantity value and the fourth physical flux value in step S800 to obtain the fifth physical quantity value and the fifth physical flux value of the boundary grid set, the method further includes: Determine the second simulation result of the shallow water dynamic process according to the first physical quantity value of the first grid set, the first physical flux value of the first grid set, the fourth physical quantity value, the fourth physical flux value, the fifth physical quantity value and the fifth physical flux value.

[0060] In this embodiment, by determining the second simulation result of the shallow water dynamic process according to the physical quantity values and physical flux values of the first grid set, the second grid set and the boundary grid set, the reliability of the determined second simulation result is improved.

[0061] It can be understood that the physical quantity value, the physical flux value of the first grid set and the physical quantity values and physical flux values of part of the second grid set can determine the first simulation result. The specific details will be described in the following content.

[0062] Exemplarily, when there are multiple grid sets, there is a corresponding boundary grid set between two adjacent grid sets.

[0063] In one embodiment, predicting the third physical quantity value and the third physical flux value of the boundary grid set in step S600 includes: Predict the third physical quantity value and the third physical flux value according to the first physical quantity value and the first physical flux value of the first grid set.

[0064] In this embodiment, since the first grid set is adjacent to the boundary grid set, the reliability of the predicted third physical quantity value and the third physical flux value is improved by predicting the third physical quantity value and the third physical flux value according to the first grid set.

[0065] Exemplarily, the third physical quantity value and the third physical flux value can be determined according to the first grid at the junction of the first grid set and the boundary grid set. According to the third physical quantity value and the third physical flux value, the sum of the fluxes of the grids at the junction of the first grid set and the boundary grid set can be determined, that is, the total flux to be corrected.

[0066] Exemplarily, if the current time is 50S, the first time step of the first grid set is 4S, and the second time step of the second grid set is 1S. The first grid set provides the physical quantity values and physical flux values at 50S and 54S, and then expands at the boundary between the first grid set and the boundary grid set to predict the physical quantity values and physical flux values at 51S, 52S, and 53S.

[0067] In one embodiment, determining the fourth physical quantity value and the fourth physical flux value in step S700, as Figure 5 shown, includes: S710. Determine the boundary conditions, which are used to define the fourth physical quantity value and the fourth physical flux value.

[0068] S720. According to the boundary conditions and the first simulation result, determine the sixth physical quantity value and the sixth physical flux value at the subsequent time points of the second grid set.

[0069] S730. According to the second physical quantity value of the second grid set, the second physical flux value of the second grid set, the sixth physical quantity value, and the sixth physical quantity value, determine the fourth physical quantity value and the fourth physical flux value.

[0070] In this embodiment, by setting boundary conditions to define the fourth physical quantity value and the fourth physical flux value, the reliability of the fourth physical quantity value and the fourth physical flux value is improved. Moreover, since the time steps of the second grid set and the first grid set are different, one first time step may include multiple second time steps. At the initial time point, the first part of the grid set of the second grid set can determine the second physical quantity value and the second physical flux value. At subsequent time points, the second part of the grid set of the second grid set can determine the sixth physical quantity value and the sixth physical flux value. By determining the fourth physical quantity value and the fourth physical flux value according to the second physical quantity value, the second physical flux value, the sixth physical quantity value, and the sixth physical flux value, the reliability of the fourth physical quantity value and the fourth physical flux value can be improved. Moreover, since the second grid set is adjacent to the boundary grid set, the third physical quantity value and the third physical flux value are corrected according to the second grid set, improving the reliability of the correction.

[0071] Exemplarily, if the current time is 50S, the first time step of the first grid set is 4S, and the second time step of the second grid set is 1S, several subsequent time steps of the second grid set relative to the first grid set are multiple subsequent time points, such as 52S, 53S, and 54S. It can be understood that since the current time is the same, the next step of the first grid set is 54S, and the next step of the second grid set is 51S, then there are multiple subsequent time points between 51S and 54S. Exemplarily, the physical quantity value and the physical flux value of the second grid set at 51S are the second physical quantity value and the second physical flux value, and the physical quantity value and the physical flux value of the second grid set at 52S, 53S, and 54S are the sixth physical quantity value and the sixth physical flux value. The physical quantity value and the physical flux value of the second grid set at 51S, 52S, 53S, and 54S are the fourth physical quantity value and the fourth physical flux value.

[0072] It can be understood that for the boundary grid set, the physical quantity value and the physical flux value at 51S, 52S, and 53S are unknown (the first simulation result of the first grid set can provide the physical quantity value and the physical flux value of the boundary grid set at 50S and 54S), and for the second grid set, the physical quantity value and the physical flux value at 52S, 53S, and 54S are unknown. The physical quantity value and the physical flux value of the boundary grid set at 54S are corrected by the fourth physical quantity value and the fourth physical flux value of the second grid set, and then together with the physical quantity value and the physical flux value of the first grid set at 50S, and the physical quantity value and the physical flux value of the boundary grid set at 51S, 52S, and 53S, they constitute the fifth physical quantity value and the fifth physical flux value.

[0073] Exemplarily, according to the order and boundary conditions of multiple subsequent time points, the target physical quantity values and target physical flux values at multiple subsequent time points can be calculated and updated to the sixth physical quantity value and the sixth physical flux value, and the total flux (the fourth physical quantity value and the fourth physical flux value) can be determined.

[0074] In one embodiment, determining the boundary conditions in step S710 includes determining the boundary conditions according to the first physical quantity values of the first grid set.

[0075] In this embodiment, since the boundary grid set is between the first grid set and the second grid set, by using the first grid set as a limiting condition, the reliability of determining the sixth physical quantity value and the sixth physical flux value of the second grid set can be improved.

[0076] Exemplarily, the total flux can be determined through the second grid set, and the total flux to be corrected (the third physical quantity value and the third physical flux value) can be determined according to the first grid set. Since the boundary grid set is adjacent to both the first grid set and the second grid set and the flux is conserved in the boundary grid set, the total flux is used to correct the total flux to be corrected, which improves the reliability of the correction and also improves the reliability of the fifth physical quantity value and the fifth physical flux value.

[0077] Exemplarily, the boundary conditions can also be determined through the first physical quantity values and the first physical flux values of the first grid set.

[0078] In one embodiment, determining the boundary conditions according to the first physical quantity values of the first grid set in the step includes: Expanding the first physical quantity value according to the Taylor expansion formula to determine the boundary conditions.

[0079] In this embodiment, since the time states of the physical quantity values in different sets are different, the first physical quantity value is expanded through the Taylor expansion to determine the boundary conditions of the second grid set, thereby improving the reliability of the boundary conditions.

[0080] Exemplarily, the current time is seconds, and the target physical quantity values and target physical flux values at the subsequent time points of the second grid set are calculated to be ( , , ). The sum of the target physical quantities and target physical fluxes at these subsequent time points is the sixth physical quantity value and the sixth physical flux value, and the first physical quantity value is expanded through the Taylor expansion formula as the boundary condition of the second grid set at time. . The first physical quantity value

[0081] ; Therefore, the boundary conditions can be obtained : ; wherein, is the quotient of the time step of the first grid and the time step of the second grid, is any step in the advancement step of the interface grid set, such as the first step, the second step, the third step, etc., are the physical quantity value and the physical flux value.

[0082] To ensure the conservation of the physical flux value in the above process, it is necessary to recalculate and correct the fourth physical quantity value and the fourth physical flux value (total flux) of the second grid set for the third physical flux value and the third physical quantity value of the interface grid set. Based on the total flux the interface grid set is corrected, and the specific correction formula is as follows: ; wherein, is the flux.

[0083] Exemplarily, after correcting the interface grid, it is judged whether the preset cut-off time is reached. If so, the loop is aborted and the calculation result is output, and the model calculation result is output. If not, the grading index of the grid is calculated again for the loop.

[0084] Exemplarily, as Figures 6 to 8 shown, the first grid set is on the left side and the second grid set is on the right side. The third physical quantity value and the third physical flux value are predicted through the first time step (i.e., through the first physical quantity value and the first physical flux value of the first grid set) to determine the total flux to be corrected of the boundary grid set. At the same time, the boundary conditions are determined through the first physical quantity value and the first physical flux value of the first grid set, and the target physical quantity values and the target physical flux values at multiple subsequent time points are calculated and updated in sequence according to the boundary conditions and multiple subsequent time points to obtain the total flux of the second grid set. Due to the flux conservation of the boundary grid set, the total flux to be corrected is corrected through the total flux, which improves the reliability of determining the fourth physical quantity value and the fourth physical flux value of the second grid set, thereby improving the reliability of the second simulation result.

[0085] Exemplarily, as Figure 6 shown, i -2 and i -1 are multiple first grids in the first grid set, i +1, i +2 and i +3 are multiple second grids in the second grid set, i is the boundary grid set, is the current moment of the first grid, For the next moment of the first grid set, For the current moment i The physical quantity value and physical flux value of the -2 grid, For the current moment i The physical quantity value and physical flux value of the -1 grid, For the next moment i The physical quantity value and physical flux value of the -2 grid, For the next moment i The physical quantity value and physical flux value of the -1 grid. For the current moment of the second grid, For the next moment of the second grid set, For the second next moment (subsequent time point) of the second grid set, For the K th next moment (subsequent time point) of the second grid set, For the Mt th next moment (subsequent time point) of the second grid set. For the current moment i The physical quantity value and physical flux value of the +1 grid, For the next moment (subsequent time point) i The physical quantity value and physical flux value of the +1 grid, For the current moment The physical quantity value and physical flux value of the grid, For the next moment (subsequent time point) i The physical quantity value and physical flux value of the +2 grid. Among them, The moment of is equal to The moment of . For the second time step, For the first time step. Among them, according to The first physical quantity value and the first physical flux value can be determined. According to The second physical quantity value and the second physical flux value can be determined, and thus the first simulation result can be determined.

[0086] Exemplarily, as Figure 7 and Figure 8 shown, since the second time step is smaller than the first time step, the boundary grid set i is between the first grid set and the second grid set. The third physical quantity value and the third physical flux value of the boundary grid set can be predicted through the first physical quantity value and the first physical flux value , , and The subsequent time points between are 、 and , while taking the third physical quantity value and the third physical flux value as boundary conditions, based on the first simulation result (based on the second physical quantity value and the second physical flux value), it is possible to sequentially calculate and update the target physical quantity value and the target physical flux value at multiple subsequent time points ( , , , , , ). According to the multiple target physical quantity values and multiple target physical flux values (the sixth physical quantity value and the sixth physical flux value), as well as the second physical quantity value and the second physical flux value, it is possible to determine the fourth physical quantity value and the fourth physical flux value. At the same time, due to flux conservation, the of the boundary grid set is corrected according to the fourth physical quantity value and the fourth physical flux value. After correction, it is the same as the physical quantity value and the physical flux value of the first grid set at moment, as well as the partial physical quantity value and the partial physical flux value of the boundary grid set ( , ), which together constitute the fifth physical quantity value and the fifth physical flux value.

[0087] Exemplarily, as Figures 6 to 8 shown, is the physical quantity value and the physical flux value of the grid at moment i +1, is the physical quantity value and the physical flux value of the grid at moment i +1, is the physical quantity value and the physical flux value of the grid at moment i +1. is the physical quantity value and the physical flux value of the grid at moment i +2, is the physical quantity value and the physical flux value of the grid at moment i +2, is the physical quantity value and the physical flux value of the grid at moment i +2.

[0088] Example: S21. Define the simulation target and determine the simulation requirements.

[0089] To demonstrate that the present invention can significantly improve the computational efficiency in calculating shallow water hydrodynamic processes, in this embodiment, taking the simulation of typical storm surges in the coastal areas of China as an example, the super typhoon 'Lekima' (No. 1909) in the 9th of 2019 and the super typhoon 'In-Fa' (No. 2106) in the 6th of 2021 are selected as the storm events to be simulated. The simulation time is from August 1st to 15th, 2019 and from July 18th to 28th, 2021.

[0090] S22. Determine the target area and obtain the relevant data required for constructing the hydrodynamic model.

[0091] The regional scope of the storm surge model covers seas such as the Bohai Sea, the Yellow Sea, the East China Sea, and the Northwest Pacific Ocean, as well as parts of the basins of major rivers such as the Yangtze River and the Qiantang River. The ocean open boundary of the model (the side of the model's boundary close to the ocean) is set according to the typhoon 48-hour warning line set by the Chinese government to ensure that the impact of the storm surge on the coastal areas of China can be accurately reflected.

[0092] In this embodiment, ocean data is obtained from multiple sources, mainly including the latest nautical chart data of the Chinese coast, global shoreline remote sensing data, and bathymetric data. The bathymetric data used in the model is mainly extracted from the latest nautical charts of the Chinese coast and the global bathymetry and topography data (SRTM15+) with a resolution of 15 arc seconds. The obtained bathymetric data is converted to a unified coordinate system and a vertical reference plane of the mean sea level. In addition, the runoff data of the rivers comes from the hydrological stations near the river mouths to ensure the timeliness and regional representativeness of the input data.

[0093] Through a Python script, the fifth-generation global atmospheric reanalysis dataset (ECMWF Reanalysis v5, ERA5) is batch retrieved to obtain the wind field data of the region during the storm event. These data include meteorological parameters such as the wind speed at a height of 10 meters, the air temperature at a height of 2 meters, and the surface pressure. Using the bilinear interpolation method, these meteorological data are interpolated to all grid points of the model as the driving input of the model.

[0094] S23. Divide the grid, specify the model parameters, and construct the hydrodynamic model.

[0095] The whole model consists of 50,171 unstructured triangular grids, and the total number of grid nodes reaches 26,455. The side length span of the grid is relatively large, with the minimum side length being about 200 meters and the maximum side length reaching 40,000 meters. Considering the complexity of the hydrodynamic changes in the Hangzhou Bay and the Yangtze River Delta regions, in this embodiment, the grids in this region are particularly refined to accurately capture the hydrodynamic characteristics of this region. The grid and resolution are shown by Figure 9-1 as follows.

[0096] The production of the model input file involves the setting of multiple key parameters, including roughness coefficient, bottom drag coefficient, sidewall coefficient, wind stress coefficient, etc. The roughness coefficient is controlled by the Manning coefficient, and the choice of the Manning coefficient has a significant impact on the model calculation results, especially when simulating complex hydrodynamic processes. Given that this model spans most of the waters in China, to ensure the accuracy of the calculation results, in this implementation case, through a method combining numerical experiments and field observations, the corresponding model setting parameters are determined for different regions. Through the analysis of the hydrological and hydrodynamic characteristics of different sea areas and river basins, the Manning coefficient and other control parameters suitable for each region are accurately selected to reflect the responses of storm surges to different topographies, bottom sediments, and flow velocities.

[0097] Assign attribute information to unstructured grids, specifically: the ocean bathymetry data obtained from multi-source datasets is distributed to each grid node and element through high-order interpolation; the number of vertical layers of the three-dimensional grid is determined through a predefined vertical stratification strategy; based on topographic features and numerical experiments, the roughness coefficient is assigned to each grid element in the unstructured grid.

[0098] S24. Set boundary conditions and initial conditions.

[0099] This model has a total of two open boundary conditions: including the ocean boundary driven by tidal levels and the river boundaries driven by flow rates (mainly river boundaries such as the Yangtze River and Qiantang River). The data of the ocean boundary driven by tidal levels is sourced from the TPXO9 dataset developed by George H. H. H. and his team at the Massachusetts Institute of Technology (MIT) in the United States, covering 15 main tidal components such as 2N2, K1, K2, M2, M4, MF, MM, MN4, MS4, N2, O1, P1, Q1, S1, S2. After astronomical correction, the dataset is interpolated and finally input into the model calculation grid. The data of the river boundaries driven by flow rates is sourced from the average annual runoff provided by hydrological stations to ensure that the simulation results reflect the actual river input conditions.

[0100] To ensure the correctness of the model simulation results, all simulations start before the typhoon occurs, thus minimizing the impact of initial conditions.

[0101] S25. Calculate the grading index of all grids, partition the grid sets, and determine the time step of each grid set.

[0102] Based on the attribute information assigned to the unstructured grid and the physical quantity values of the cells calculated by the model (the first calculation is given by the initial value conditions of the model), obtain the size of the grid cells, the grid water depth, and the boundary flow velocity of the grid. Based on the CFL criterion, calculate the maximum time step required for each grid. .

[0103]

[0104] Figure 10 Show the grid grading at T = 0 h (initial time). Figure 10 All the grid sets in are divided into 7 colors. Each color of grids represents a grid set, and there are a total of 7 grid sets.

[0105] S26. Start calculating the first simulation result, and calculate the physical flux values and corresponding physical quantity values of each grid set at the corresponding time step.

[0106] Calculate the next time step corresponding to each grid set ( , , …) of the physical flux values and physical quantity values.

[0107] S27. Use the Taylor expansion values of the first physical quantity value and the first physical flux value calculated for the first grid set as the boundary conditions for the second grid set at subsequent time points , and start calculating the second simulation result, advancing the calculation and updating to obtain the fourth physical flux value and the fourth physical quantity value of the second grid set.

[0108] At this time, the times of the grid physical quantity values of different sets are different. For example, when the time grading index is , the time scale at which this grid set is located is , while when the time grading index is , the time scale at which this grid set is located is . To ensure the continuity of the model calculation, the first physical quantity value and the first physical flux value of the interface grid set are now expanded to the intermediate time through Taylor expansion and used as the initial boundary conditions for the second grid set at time and calculate the sixth physical flux value and the sixth physical quantity value of the second grid set at subsequent time points ( , , ).

[0109]

[0110] ; S28. Based on the total flux calculated for the second grid set correct and update the physical flux values and physical quantity values of the interface grid set.

[0111] In the calculation of the above process, the total flux of the second grid set is obtained by calculating the boundary conditions predicted by the Taylor expansion of the first physical quantity value and the first physical flux value of the first grid set. Since there is a prediction step in this process, there is a certain error between the flux to be corrected of the interface layer grid set predicted according to the first grid set and the total flux of the interface layer grid predicted according to the second grid set. If not corrected, the error will accumulate step by step, having a huge impact on the accuracy of the model calculation results. Therefore, in order to ensure the flux conservation of the total flux to be corrected and the total flux, correction is required. Based on the total flux of the second grid set Correct the total flux to be corrected. The specific correction method is as follows:

[0112] S29. Judge whether the total time has accumulated to the total time set by the model. If so, end the loop, output the model calculation result, and verify the model accuracy; if not, return to execute S25.

[0113] The above process is a complete calculation loop. S21 is the entry of the loop. At this time, judge whether the cut-off time set by the model is reached. If so, the loop can be aborted and the calculation result can be output; if not, return to S21 to enter the next new loop until all calculations are completed.

[0114] According to one aspect of the present application, step S29 is further as follows: S291. Judge whether the loop terminates.

[0115] In this embodiment, the cut-off time of the model is August 15, 2019 and July 28, 2021. If the cut-off time set by the model is reached, the loop terminates and the model calculation result is output. If not terminated, return to S25 to enter the next loop.

[0116] S292. Based on the calculation result, verify the astronomical tide.

[0117] In this experimental example, we verified the tides from May 20, 2019 to June 21, 2019 and from July 15, 2019 to July 31, 2019, named tide verification 1 and tide verification 2 respectively, including a spring-neap tide cycle, named spring tide A, spring tide B, neap tide A, and neap tide B respectively; a total of 5 tide gauge stations and 2 current stations were verified, which are located near the Hangzhou Bay, the Yangtze River Estuary, and the Zhoushan Islands. Attached Figure 9-2 shows the schematic diagrams of tide verification, current verification, and storm surge.

[0118] In Figure 11 and Figure 12In it, two working conditions are given. and Water level and flow velocity verification under two conditions can be obtained. It can be known that the simulated tidal levels match the observed data well in terms of tidal range and phase, and for the global unified time step model scheme ( ) and the local time step scheme ( ), the results of the two also have good consistency, which reflects the accuracy of the local time step. To further quantify the ability of the model to reproduce tidal hydrodynamics, the root mean square error (RMSE) between the model results and the observed values was calculated. Based on the data in Figure 11 , the astronomical tide RMSEs are all no greater than 0.25 m. For the tidal current verification, the RMSE of the flow velocity is between 0.1 - 0.35 m / s, and the RMSE of the flow direction is between 20 - 40°. In addition, it can also be seen that the calculation results of the global unified time step model scheme and the local time step scheme show significant consistency, and the RMSE can reach the centimeter level.

[0119] S293. Based on the calculation results, the storm surge is verified.

[0120] In this experimental example, Figure 13 the storm surge data of four monitoring stations are verified. By comparison, it can be seen that the phase and amplitude of the model calculated values are basically consistent with the observed data, and the storm surge process under the influence of typhoon can be clearly observed. The maximum storm surges at the four stations of Niupi Reef, Nancao East, Luchaogang, and Zhenhai are 0.8403 m, 0.5798 m, 1.1956 m, and 1.2631 m respectively. Table 1 shows the improvement effect of the local time step on the calculation efficiency.

[0121] Table 1

[0122] In an exemplary embodiment, a computer device is provided, including a processor and a memory. The memory stores a computer program, and when the processor executes the computer program, the steps of any one of the above-mentioned shallow water dynamic process simulation methods based on the local time step are implemented.

[0123] In an exemplary embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps of any one of the above-mentioned shallow water dynamic process simulation methods based on the local time step are implemented. The computer-readable storage medium can be a read-only memory (ROM), a random access memory (RAM), a CD-ROM, a magnetic tape, a floppy disk, an optical data storage device, etc.

[0124] In an exemplary embodiment, a computer program product is provided, including a computer program which, when executed by a processor, implements the steps of any one of the above-mentioned shallow water dynamic process simulation methods based on local time steps.

[0125] Those skilled in the art will readily conceive of other embodiments of the present invention after considering the specification and practicing the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present invention, which follow the general principles of the present invention and include known common knowledge or conventional technical means in the technical field not disclosed by the present invention.

Claims

1. A shallow water dynamic process simulation method based on local time steps, characterized in that, The method includes: Constructing a shallow water dynamic process model to divide a target area into a plurality of grids, where the target area includes an ocean area and a land area adjacent to the ocean area; Dividing the plurality of grids into at least a first grid set and a second grid set; Determining a first time step corresponding to the first grid set according to the first grid set; Determining a second time step corresponding to the second grid set according to the second grid set; Determining a first simulation result of the shallow water dynamic process according to the first time step and the second time step; Wherein, the first grid set includes a plurality of first grids, and the second grid set includes a plurality of second grids; the first time step is greater than the second time step.

2. The method for simulating shallow water dynamic processes based on local time steps according to claim 1, characterized in that The dividing the plurality of grids into at least a first grid set and a second grid set includes: Determining a time grading index corresponding to each of the grids; Dividing the plurality of grids into at least a first grid set and a second grid set according to the time grading index corresponding to each of the grids.

3. The shallow water dynamic process simulation method based on local time steps according to claim 2, wherein The determining a time grading index corresponding to each of the grids includes: Determining the minimum time step of all the grids according to the grid water depth and the critical water depth of each of the grids; Determining the time grading index corresponding to each of the grids according to the minimum time step, a preset time grading coefficient, and the maximum time step of each of the grids.

4. The shallow water dynamic process simulation method based on local time steps according to claim 1, characterized in that The determining a first simulation result of the shallow water dynamic process according to the first time step and the second time step includes: Determining a first physical quantity value and a first physical flux value of the first grid set according to the first time step; Determining a second physical quantity value and a second physical flux value of the second grid set according to the second time step; Determining the first simulation result according to the first physical quantity value, the first physical flux value, the second physical quantity value, and the second physical flux value.

5. The method for simulating shallow water dynamic processes based on local time steps according to any one of claims 1 to 4, characterized in that There is a boundary grid set between the first grid set and the second grid set, and the method further includes: Predicting a third physical quantity value and a third physical flux value of the boundary grid set; Determining a fourth physical quantity value and a fourth physical flux value of the second grid set; Correcting the third physical quantity value and the third physical flux value according to the fourth physical quantity value and the fourth physical flux value to obtain a fifth physical quantity value and a fifth physical flux value of the boundary grid set.

6. The method for simulating shallow water dynamic processes based on local time steps according to claim 5, wherein After obtaining the fifth physical quantity value and the fifth physical flux value of the boundary grid set, the method further includes: Determining a second simulation result of the shallow water dynamic process according to the first physical quantity value of the first grid set, the first physical flux value of the first grid set, the fourth physical quantity value, the fourth physical flux value, the fifth physical quantity value, and the fifth physical flux value.

7. The shallow water dynamic process simulation method based on local time steps according to claim 5, characterized in that The predicting a third physical quantity value and a third physical flux value of the boundary grid set includes: Predicting the third physical quantity value and the third physical flux value according to the first physical quantity value and the first physical flux value of the first grid set.

8. The method for simulating shallow water dynamic processes based on local time steps according to claim 5, wherein The determining a fourth physical quantity value and the fourth physical flux value of the second grid set includes: Determine boundary conditions for defining the value of the fourth physical quantity and the value of the fourth physical flux; Based on the boundary conditions and the first simulation result, determine the value of the sixth physical quantity and the value of the sixth physical flux at a subsequent time point for the second grid set; Based on the value of the second physical quantity of the second grid set, the value of the second physical flux of the second grid set, the value of the sixth physical quantity, and the value of the sixth physical quantity, determine the value of the fourth physical quantity and the value of the fourth physical flux.

9. The shallow water dynamic process simulation method based on local time steps according to claim 8, characterized in that, The determining of the boundary conditions includes: Based on the value of the first physical quantity of the first grid set, determine the boundary conditions.

10. The shallow water dynamic process simulation method based on local time steps according to claim 9, characterized in that, The determining of the boundary conditions based on the value of the first physical quantity of the first grid set includes: Expand the value of the first physical quantity according to the Taylor expansion formula to determine the boundary conditions.

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