A method for simulating shallow water dynamic processes based on local time steps

Abstract

The present invention relates to a method for simulating shallow water dynamic processes based on local time steps. The method comprises: dividing a target area into multiple grids based on a shallow water dynamic process model, the target area including an ocean area and a land area adjacent to the ocean area; dividing the multiple grids into at least a first grid set and a second grid set; determining a first time step corresponding to the first grid set based on the first grid set; determining a second time step corresponding to the second grid set based on the second grid set; and determining a first simulation result of the shallow water dynamic process based on the first time step and the second time step; wherein the first grid set includes multiple first grids and the second grid set includes multiple second grids; and the first time step is greater than the second time step. By determining appropriate local time steps based on the accuracy requirements of different grid sets, the efficiency of the shallow water dynamic process simulation method is improved.

Description

Technical Field

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

[0002] Shallow water dynamics describe water movement at depths significantly smaller than the horizontal scale of the flow. They can predict and assess disasters such as storm surge levels, flood surges, and flood evolution, and are widely used in scenarios such as estuaries, coasts, and coastal wetlands. However, because shallow water dynamics often have a uniform time step across the entire region, simulations of these processes can be inaccurate. Summary of the Invention

[0003] In order to overcome the problems existing in the related art, the present invention provides a method for simulating shallow water dynamic processes based on a local time step.

[0004] According to an embodiment of the present invention, a method for simulating shallow water dynamic processes based on a local time step is provided, the method comprising:

[0005] Constructing a shallow water dynamic process model to divide a target area into a plurality of grids, wherein the target area includes an ocean area and a land area adjacent to the ocean area;

[0006] dividing the plurality of grids into at least a first grid set and a second grid set;

[0007] Determining a first time step corresponding to the first grid set according to the first grid set;

[0008] determining, according to the second grid set, a second time step corresponding to the second grid set;

[0009] determining a first simulation result of a shallow water dynamic process according to the first time step and the second time step;

[0010] The first grid set includes a plurality of first grids, the second grid set includes a plurality of second grids, and the first time step is greater than the second time step.

[0011] In some embodiments of the present invention, dividing the plurality of grids into at least a first grid set and a second grid set comprises:

[0012] Determining a time classification index corresponding to each of the grids;

[0013] The plurality of grids are divided into at least a first grid set and a second grid set according to the time classification index corresponding to each grid.

[0014] In some embodiments of the present invention, determining the time grading index corresponding to each grid includes:

[0015] Determining the minimum time step of all the grids according to the grid water depth and critical water depth of each grid;

[0016] The time classification index corresponding to each of the grids is determined according to the minimum time step, the preset time classification coefficient and the maximum time step of each of the grids.

[0017] In some embodiments of the present invention, determining a first simulation result of a shallow water dynamic process according to the first time step and the second time step includes:

[0018] Determining a first physical quantity value and a first physical flux value of the first grid set according to the first time step;

[0019] determining a second physical quantity value and a second physical flux value of the second grid set according to the second time step;

[0020] The first simulation result is determined according to the first physical quantity value, the first physical flux value, the second physical quantity value, and the second physical flux value.

[0021] In some embodiments of the present invention, a boundary grid set exists between the first grid set and the second grid set, and the method further includes:

[0022] predicting a third physical quantity value and a third physical flux value of the boundary grid set;

[0023] determining a fourth physical quantity value and a fourth physical flux value of the second grid set;

[0024] The third physical quantity value and the third physical flux value are corrected 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.

[0025] 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:

[0026] A second simulation result of the shallow water dynamic process is determined based on 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.

[0027] In some embodiments of the present invention, predicting the third physical quantity value and the third physical flux value of the boundary grid set includes:

[0028] The third physical quantity value and the third physical flux value are predicted according to the first physical quantity value and the first physical flux value of the first grid set.

[0029] In some embodiments of the present invention, determining the fourth physical quantity value and the fourth physical flux value of the second grid set includes:

[0030] determining boundary conditions, wherein the boundary conditions are used to limit the fourth physical quantity value and the fourth physical flux value;

[0031] determining a sixth physical quantity value and a sixth physical flux value of the second grid set at a subsequent time point according to the boundary condition and the first simulation result;

[0032] The fourth physical quantity value and the fourth physical flux value are determined 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 flux value.

[0033] In some embodiments of the present invention, determining the boundary conditions includes:

[0034] The boundary condition is determined according to a first physical quantity value of the first grid set.

[0035] In some embodiments of the present invention, determining the boundary condition according to the first physical quantity value of the first grid set includes:

[0036] The first physical quantity value is expanded according to a Taylor expansion to determine the boundary condition.

[0037] The technical solutions provided by the embodiments of the present invention may have the following beneficial effects:

[0038] The plurality of grids are divided into at least a first grid set and a second grid set, so that the grids in different areas are divided into different grid sets according to the required accuracy requirements; based on the first grid set, a first time step corresponding to the first grid set is determined, so as to determine a suitable local time step according to the accuracy requirements of the first grid set; based on the second grid set, a second time step corresponding to the second grid set is determined, so as to determine a suitable local time step according to the accuracy requirements of the second grid set; based on the first time step and the second time step, a first simulation result of the shallow water dynamic process is determined, so as to determine the simulation result according to the local time steps corresponding to the different grid sets. By determining the appropriate local time step according to the accuracy requirements of different grid sets, the problem of excessive calculation time caused by a small global unified time step and the problem of low simulation result accuracy 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 improves the accuracy of the simulation results.

[0039] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0041] Figure 1 is a flow chart of a shallow water dynamic process simulation method based on a local time step according to the first embodiment;

[0042] Figure 2 is a flow chart of a shallow water dynamic process simulation method based on a local time step according to a second embodiment;

[0043] Figure 3 is a flow chart of a method for simulating shallow water dynamic processes based on a local time step according to a third embodiment;

[0044] Figure 4 is a flow chart of a shallow water dynamic process simulation method based on a local time step according to a fourth embodiment;

[0045] Figure 5 is a flow chart of a method for simulating shallow water dynamic processes based on a local time step according to a fifth embodiment;

[0046] Figure 6 is a schematic diagram illustrating determining a first simulation result according to an embodiment;

[0047] Figure 7 is a schematic diagram illustrating a method of predicting a third physical quantity value and a third physical flux value of a boundary grid set, and obtaining a fourth physical quantity value and a fourth physical flux value of a second grid set according to an embodiment;

[0048] Figure 8 is a schematic diagram illustrating determining a second simulation result according to an embodiment;

[0049] Figure 9-1 is a schematic diagram showing a grid and resolution of a target area according to an embodiment;

[0050] Figure 9-2 is a schematic diagram showing tide verification according to an embodiment;

[0051] Figure 10 is a schematic diagram showing a grid classification situation at an initial moment according to an embodiment;

[0052] Figure 111 is a tide level verification diagram according to an embodiment;

[0053] Figure 12 is a flow velocity verification diagram of a tidal current according to an embodiment;

[0054] Figure 13 FIG. 4 is a verification diagram of storm surge according to an embodiment. DETAILED DESCRIPTION

[0055] Exemplary embodiments will be described in detail herein, examples of which are illustrated in the accompanying drawings. In the following description, when referring to the drawings, like numbers in different figures represent like or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments are not intended to represent all possible embodiments consistent with the present invention. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the present invention, as detailed in the appended claims.

[0056] 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.

[0057] 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.

[0058] 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:

[0059] 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.

[0060] S200: Divide a plurality of grids into at least a first grid set and a second grid set.

[0061] S300: Determine a first time step corresponding to the first grid set according to the first grid set.

[0062] S400: Determine a second time step corresponding to the second grid set according to the second grid set.

[0063] S500: Determine a first simulation result of a shallow water dynamic process according to the first time step and the second time step.

[0064] The first grid set includes a plurality of first grids, the second grid set includes a plurality of second grids, and the first time step is greater than the second time step.

[0065] In this embodiment, multiple grids are divided into at least a first grid set and a second grid set, so that grids in different areas are divided into different grid sets according to the required accuracy requirements; based on the first grid set, a first time step corresponding to the first grid set is determined, so as to determine a suitable local time step according to the accuracy requirements of the first grid set; based on the second grid set, a second time step corresponding to the second grid set is determined, so as to determine a suitable local time step according to the accuracy requirements of the second grid set; based on the first time step and the second time step, a first simulation result of the shallow water dynamic process is determined, so as to determine the simulation result according to the local time steps corresponding to different grid sets. By determining suitable local time steps according to the accuracy requirements of different grid sets, the problem of excessive calculation time caused by a small global unified time step and the problem of low simulation result accuracy 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 improves the accuracy of the simulation results.

[0066] Exemplarily, multiple grids can be divided into a first grid set, a second grid set, a third grid set...an Nth grid set according to needs. The corresponding time steps can be determined respectively according to the first grid set, the second grid set, the third grid set...an Nth grid set. According to the time steps corresponding to the above grid sets, the first simulation result of the shallow water dynamic process can be determined.

[0067] For example, 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 larger than the size of the second grid set, indicating that in the first grid set, only the changes in hydrodynamics need to be captured from the overall perspective, while in the second grid set, the changes in hydrodynamics need to be captured more accurately. 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 larger than the second time step not only satisfies the need to capture the hydrodynamic changes of the first grid set as a whole to improve the efficiency of the simulation method, but also satisfies the need to accurately capture the changes in hydrodynamics in the local area, thereby improving the accuracy of the simulation results.

[0068] For example, during a simulation, although the first and second time steps are fixed, the first and second grid sets may change as the simulation progresses. A grid that belonged to the first grid set in the previous step may be assigned to the second grid set in the next step. A grid that belonged to the second grid set in the previous step may also be assigned to the first grid set in the next step. This allows for the simulation of sudden and volatile events such as storm surges and floods.

[0069] For example, the sizes of the plurality of 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.

[0070] Exemplarily, the size of the first grid may be larger than the size of the second grid.

[0071] It is understandable that, since using a smaller time step in a high-precision area can ensure the accuracy of the first simulation result, using a larger time step in a low-precision area can increase the efficiency of the simulation process, thus avoiding the problems caused by the unified time step in the entire area in the traditional shallow water dynamic process simulation method. Furthermore, since the time steps in different precision areas are different, this embodiment can effectively handle complex terrain, non-uniform underlying surface and multi-scale hydrodynamic processes, and can take into account both efficiency and accuracy in large-scale and small-scale areas, thereby optimizing the reliability of cross-scale shallow water dynamic process simulation. By setting a refined time step, unnecessary calculation processes are reduced, especially in long-term and large-scale simulation processes, the calculation cost is significantly reduced. For variable environments such as sudden storm surges, complex tides and dynamic terrain, the accuracy and reliability of the first simulation result can also be improved, increasing the scope of application of the shallow water dynamic process simulation method based on local time steps.

[0072] Exemplarily, before step S100, the method further includes constructing a shallow water dynamic process model. The method for constructing the shallow water dynamic process model includes:

[0073] S10. Determine simulation requirements based on simulation objectives.

[0074] S11. Determine the target area and target data of the target area according to simulation requirements.

[0075] S12. Construct a shallow water dynamic process model based on target data and accuracy requirements.

[0076] In step S10, the simulation target can be determined by the application scenario, such as estuaries, coastal wetlands, storm surge floodplains, and urban neighborhood flood evolution. The simulation requirements are the key factors that influence the hydrodynamic simulation process in the corresponding scenario, such as topography, tides, wind speed, and waves. In step S11, based on the simulation requirements, the area covered by the simulation target can be determined as the target area. The target data can include relevant data such as the target area's topography, meteorology, hydrology, flow field, and boundary conditions. In step S12, an appropriate grid resolution can be selected based on the obtained target data and accuracy requirements. High-resolution grids are selected in high-precision areas (such as coastlines and wetlands), while low-resolution grids can be used in areas away from important areas to construct a suitable shallow water dynamic process model. At the same time, physical parameters in the model need to be set, such as bottom friction, wind resistance, wave propagation, and turbulence model.

[0077] For example, after constructing a shallow water dynamic process model, initial conditions and target boundary conditions can be set to improve the model's reliability. Initial conditions can include physical quantities such as water level, flow rate, temperature, and salinity. Target boundary conditions related to tidal water level, flow rate, wind speed, wind direction, wave height, wavelength, and wave period at the open boundary (the ocean side of the model) can be set based on historical tidal data, tidal forecasts, weather forecasts, typhoon simulation data, storm surge, and wave-related simulations.

[0078] In one embodiment, if Figure 2 As shown, the step S200 of dividing the plurality of grids into at least a first grid set and a second grid set includes:

[0079] S210: Determine the time classification index corresponding to each grid.

[0080] S220 , dividing the plurality of grids into at least a first grid set and a second grid set according to a time classification index corresponding to each grid.

[0081] In this embodiment, since the time grading index can characterize whether the area to which all grids in the entire area belong is a high-precision area or a low-precision area, by dividing 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.

[0082] For example, when the time grading index corresponding to a portion of grids is within a first preset range, the portion of grids is divided into a first grid set. When the time grading index corresponding to another portion of grids is within a second preset range, the portion of grids is divided into a second grid set.

[0083] In one embodiment, if Figure 3As shown, in step S220, the multiple grids are divided into at least a first grid set and a second grid set according to the time classification index corresponding to each grid, including:

[0084] S221. Determine the minimum time step of all grids based on the grid water depth and critical water depth of each grid.

[0085] S222: Determine the time classification index corresponding to each grid according to the minimum time step, the preset time classification coefficient and the maximum time step of each grid.

[0086] In this embodiment, since the minimum time step is related to the grid water depth and critical water depth, determining the minimum time step based on the grid water depth and critical water depth can improve the reliability of the minimum time step. Furthermore, the preset grading index can determine the number of grid sets into which multiple grids can be divided, and the maximum time step of each grid can represent the time step limit of each grid. By determining the time grading index corresponding to each grid based on 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.

[0087] For example, the maximum time step It can be determined based on the Courant-Friedrichs-Lewy (CFL) criterion using the following formula:

[0088] ;

[0089] in, is the Courant number, which is 0.9; For the The center of the grid to its The distance between the edges; 、 is the flow velocity in the local coordinate system normal to the jth edge of the i-th grid; is the grid water depth; 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. The default maximum time step of the dry grid is infinite, but considering the actual situation, its time step is set to the maximum local time step of all wet grid cells.

[0090] For example, the minimum time step It can be determined by the following formula:

[0091] ;

[0092] For example, the preset time classification coefficient Can be a specified grading coefficient, which can be any integer and is used to limit the time grading index. The shallow water dynamic process model is a model with a unified time step for the entire region, and the time classification index corresponding to each grid is It can be determined by the following formula:

[0093] ;

[0094] For example, according to the time-classified index Ability to divide all grids into different sets to determine the local time steps corresponding to different grid sets and maximum time interval , which can be determined by the following formula:

[0095]

[0096] in, is the minimum value of the edge of two adjacent grids, is the maximum time classification index.

[0097] In one embodiment, determining a first simulation result of a shallow water dynamic process according to the first time step and the second time step in step S500 includes:

[0098] S510 : Determine a first physical quantity value and a first physical flux value of a first grid set according to a first time step.

[0099] S520 : Determine a second physical quantity value and a second physical flux value of the second grid set according to the second time step.

[0100] S530: Determine a 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.

[0101] In this embodiment, when a suitable time step is selected, the accuracy of the determined first physical quantity value, first physical flux value, second physical quantity value, and second physical flux value is high. By respectively determining a suitable time step and determining the corresponding physical quantity value and physical flux value according to the time step, and then determining the first simulation result, the reliability of the first simulation result is improved.

[0102] For example, 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 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 physical flux value of the second grid set at 51S are the second physical quantity value and the second physical flux value.

[0103] For example, the amount of a physical quantity passing through a certain interface per unit time is called a physical flux value. Physical quantity values ​​can include flow velocity, water level, and waves, and the corresponding physical flux values ​​can include momentum flux, mass flux, and wave energy flux.

[0104] In one embodiment, there is a boundary grid set between the first grid set and the second grid set, such as Figure 4 As shown, the method further includes:

[0105] S600: Predict a third physical quantity value and a third physical flux value of the boundary grid set.

[0106] S700: Determine a fourth physical quantity value and a fourth physical flux value of the second grid set.

[0107] 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 a fifth physical quantity value and a fifth physical flux value of the boundary grid set.

[0108] In this embodiment, since there is a boundary grid set 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 are predicted and corrected to obtain the fifth physical quantity value and the fifth physical flux value of the boundary grid set, thereby improving the reliability of determining the fifth physical quantity value and the fifth physical flux value of the boundary grid set.

[0109] 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:

[0110] A second simulation result of the shallow water dynamic process is determined based on 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.

[0111] In this embodiment, by determining the second simulation result of the shallow water dynamic process based on 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.

[0112] It is understandable that the physical quantity values ​​and physical flux values ​​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, which will be described in detail later.

[0113] Exemplarily, when there are multiple grid sets, there is a corresponding boundary grid set between each two adjacent grid sets.

[0114] In one embodiment, the third physical quantity value and the third physical flux value of the predicted boundary grid set in step S600 include:

[0115] A third physical quantity value and a third physical flux value are predicted based on the first physical quantity value and the first physical flux value of the first grid set.

[0116] 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 third physical flux value is improved by predicting the third physical quantity value and third physical flux value based on the first grid set.

[0117] Exemplarily, the third physical quantity value and the third physical flux value can be determined based on the first grid at the junction of the first grid set and the boundary grid set. Based on 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, that is, the total flux to be corrected, can be determined.

[0118] For example, if the current time is 50 seconds, the first time step of the first grid set is 4 seconds, and the second time step of the second grid set is 1 second. The first grid set provides physical quantity values ​​and physical flux values ​​at 50 seconds and 54 seconds, and then expands at the boundary between the first grid set and the boundary grid set to predict physical quantity values ​​and physical flux values ​​at 51 seconds, 52 seconds, and 53 seconds.

[0119] In one embodiment, the fourth physical quantity value and the fourth physical flux value of the second grid set are determined in step S700, such as Figure 5 Shown, including:

[0120] S710: Determine boundary conditions, where the boundary conditions are used to limit a fourth physical quantity value and a fourth physical flux value.

[0121] S720 : Determine a sixth physical quantity value and a sixth physical flux value at a subsequent time point of the second grid set according to the boundary condition and the first simulation result.

[0122] S730 : Determine a fourth physical quantity value and a 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 flux value.

[0123] In this embodiment, boundary conditions are set to limit the fourth physical quantity value and the fourth physical flux value, thereby improving the reliability of the fourth physical quantity value and the fourth physical flux value. Moreover, because the time steps of the second grid set and the first grid set are different, a first time step may include multiple second time steps. At an initial time point, the first portion of the grid sets of the second grid set can determine the second physical quantity value and the second physical flux value. At a subsequent time point, the second portion of the grid sets 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 based on 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, because the second grid set is adjacent to the boundary grid set, the third physical quantity value and the third physical flux value are corrected based on the second grid set, thereby improving the reliability of the correction.

[0124] For example, if the current moment is 50 seconds, the first time step of the first grid set is 4 seconds, and the second time step of the second grid set is 1 second, then the next several time steps of the second grid set relative to the first grid set are multiple subsequent time points, such as 52 seconds, 53 seconds, and 54 seconds. It can be understood that since the current moment is the same, the next step of the first grid set is 54 seconds, and the next step of the second grid set is 51 seconds, then there are multiple subsequent time points between 51 seconds and 54 seconds. For example, the physical quantity value and physical flux value of the second grid set at 51 seconds are the second physical quantity value and the second physical flux value, and the physical quantity value and physical flux value of the second grid set at 52 seconds, 53 seconds, and 54 seconds are the sixth physical quantity value and the sixth physical flux value. The physical quantity value and physical flux value of the second grid set at 51 seconds, 52 seconds, 53 seconds, and 54 seconds are the fourth physical quantity value and the fourth physical flux value.

[0125] It is understood that for the boundary mesh set 51S, 52S, and 53S, the physical quantity values ​​and physical flux values ​​are unknown (the first simulation results for the first mesh set can provide the physical quantity values ​​and physical flux values ​​for the boundary mesh sets 50S and 54S). For the second mesh set, the physical quantity values ​​and physical flux values ​​for 52S, 53S, and 54S are unknown. The physical quantity values ​​and physical flux values ​​of the boundary mesh set 54S are corrected using the fourth physical quantity value and fourth physical flux value of the second mesh set. These values, together with the physical quantity value and physical flux value of the first mesh set 50S and the physical quantity value and physical flux value of the boundary mesh sets 51S, 52S, and 53S, form the fifth physical quantity value and fifth physical flux value.

[0126] Exemplarily, according to the order and boundary conditions of the multiple subsequent time points, the target physical quantity values ​​and target physical flux values ​​of the multiple subsequent time points can be calculated and updated in sequence with 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.

[0127] In one embodiment, determining the boundary condition in step S710 includes determining the boundary condition according to a first physical quantity value of the first grid set.

[0128] In this embodiment, since the boundary grid set is between the first grid set and the second grid set, the reliability of determining the sixth physical quantity value and the sixth physical flux value of the second grid set can be improved by using the first grid set as a restriction condition.

[0129] 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 based on the first grid set. Since the boundary grid set is adjacent to both the first grid set and the second grid set, the flux is conserved in the boundary grid set. The total flux to be corrected is corrected by the total flux, which improves the reliability of the correction and also improves the reliability of the fifth physical quantity value and the fifth physical flux value.

[0130] Exemplarily, the boundary condition may also be determined by the first physical quantity value and the first physical flux value of the first grid set.

[0131] In one embodiment, the step of determining the boundary condition according to the first physical quantity value of the first grid set includes:

[0132] The first physical quantity value is expanded according to Taylor expansion to determine the boundary conditions.

[0133] In this embodiment, since the time states of physical quantity values ​​of different sets are different, the first physical quantity value is expanded through Taylor expansion to determine the boundary conditions of the second grid set, thereby improving the reliability of the boundary conditions.

[0134] For example, the current time is seconds, and the subsequent time points of the second grid set are calculated as ( , , ) of the target physical quantity value and the target physical flux value (the sum of the target physical quantity and the target physical flux 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 by Taylor expansion as the second grid set in Boundary conditions at time The first physical quantity value

[0135] ;

[0136] So we can get the boundary conditions :

[0137] ;

[0138] in, 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 of the interface mesh set, such as the first step, the second step, the third step, etc. are physical quantity values ​​and physical flux values.

[0139] In order to ensure the conservation of the physical flux value in the above process, the fourth physical quantity value and the fourth physical flux value (total flux) of the second grid set are required to recalculate and correct the third physical flux value and the third physical quantity value of the interface grid set. Correct the interface grid set. The specific correction formula is as follows:

[0140] ;

[0141] in, is the flux.

[0142] For example, after modifying the interface grid, determine Whether the preset deadline is reached, if so, the loop is terminated to output the calculation results and the model calculation results, if not, the grid grading index is calculated again to cycle.

[0143] For example, Figures 6 to 8 As shown, the left side shows the first grid set, and the right side shows the second grid set. The third physical quantity value and the third physical flux value are predicted using the first time step (i.e., using the first physical quantity value and the first physical flux value of the first grid set) to determine the total flux to be corrected for the boundary grid set. Simultaneously, the boundary conditions are determined using the first physical quantity value and the first physical flux value of the first grid set. Based on the boundary conditions and multiple subsequent time points, the target physical quantity values ​​and the target physical flux values ​​are sequentially calculated and updated to obtain the total flux for the second grid set. Due to the flux conservation of the boundary grid set, the total flux to be corrected is corrected using the total flux, improving the reliability of determining the fourth physical quantity value and the fourth physical flux value for the second grid set, thereby improving the reliability of the second simulation result.

[0144] For example, Figure 6 As shown, i -2 and i -1 is a number of first grids in the first grid set, i +1, i +2 andi +3 is a plurality of second grids in the second grid set, i is the boundary grid set, is the current time of the first grid, is the next moment of the first grid set, For the current moment i -2 physical quantity values ​​and physical flux values ​​of the grid, For the current moment i -1 physical quantity values ​​and physical flux values ​​of the grid, For the next moment i -2 physical quantity values ​​and physical flux values ​​of the grid, For the next moment i -1 The physical quantity values ​​and physical flux values ​​of the grid. is the current time of the second grid, is the next moment of the second grid set, is the second next moment (subsequent time point) of the second grid set, The second grid set K The next moment (subsequent time point), The second grid set Mt The next moment (subsequent time point). For the current moment i +1 grid physical quantity values ​​and physical flux values, For the next moment (subsequent time point) i +1 grid physical quantity values ​​and physical flux values, For the current moment Physical quantity values ​​and physical flux values ​​of the grid, For the next moment (subsequent time point) i +2 grid physical quantity values ​​and physical flux values. Among them, The moment is equal to , The moment is equal to . is the second time step, is the first time step. A first physical quantity value and a first physical flux value can be determined according to If the second physical quantity value and the second physical flux value can be determined, then the first simulation result can also be determined.

[0145] For example, Figure 7 and Figure 8 As shown, since the second time step is smaller than the first time step, the boundary grid set iThe first physical quantity value and the first physical flux value can be used to predict the third physical quantity value and the third physical flux value of the boundary grid set. 、 、 and The subsequent time points between 、 and , while taking the third physical quantity value and the third physical flux value as boundary conditions, on the basis of the first simulation result (on the basis of the second physical quantity value and the second physical flux value), the target physical quantity value and the target physical flux value at multiple subsequent time points can be calculated and updated in sequence ( 、 、 、 、 、 ). According to the plurality of target physical quantity values ​​and the plurality of target physical flux values ​​(the sixth physical quantity value and the sixth physical flux value) and the second physical quantity value and the second physical flux value, the fourth physical quantity value and the fourth physical flux value can be determined. At the same time, due to the conservation of flux, the boundary grid set is corrected according to the fourth physical quantity value and the fourth physical flux value. , after correction, the first grid set The physical quantity values ​​and physical flux values ​​at the moment, as well as the partial physical quantity values ​​and partial physical flux values ​​of the boundary grid set ( 、 ) together constitute the fifth physical quantity value and the fifth physical flux value.

[0146] For example, Figures 6 to 8 As shown, for time i +1 grid physical quantity values ​​and physical flux values, for time i +1 grid physical quantity values ​​and physical flux values, for time i +1 grid's physical quantity values ​​and physical flux values. for time i +2 grid physical quantity values ​​and physical flux values, for time i +2 grid physical quantity values ​​and physical flux values, for time i +2 Grid physical quantity values ​​and physical flux values.

[0147] Example:

[0148] S21. Clarify the simulation objectives and determine the simulation requirements.

[0149] To demonstrate the significant improvement in computational efficiency achieved by the present invention in shallow water dynamics calculations, this example uses a typical storm surge simulation near the coast of China as an example. Super Typhoon Lekima (number 1909) of 2019 and Super Typhoon Fireworks (number 2106) of 2021 were selected as the simulated storm events. The simulation period was August 1–15, 2019, and July 18–28, 2021.

[0150] S22. Determine the target area and obtain relevant data required to build a hydrodynamic model.

[0151] The storm surge model covers the Bohai Sea, Yellow Sea, East China Sea, and Northwest Pacific Ocean, as well as parts of the Yangtze River and Qiantang River basins. The model's ocean boundary (the ocean side of the model) is set according to the 48-hour typhoon warning line established by the Chinese government to ensure accurate reflection of the impacts of storm surges on China's coastal areas.

[0152] In this example, ocean data is obtained from multiple sources, primarily including the latest nautical charts of the Chinese coast, global coastline remote sensing data, and seafloor topography data. The topographic data used in the model is primarily extracted from the latest nautical charts of the Chinese coast and the 15-arc-second resolution global bathymetry and topography database (SRTM15+). The acquired topographic data is converted to a unified coordinate system and a vertical datum based on mean sea level. Furthermore, river runoff data is obtained from local hydrological stations near the estuary, ensuring the timeliness and regional representativeness of the input data.

[0153] A Python script batch-retrieves the fifth-generation ECMWF Reanalysis v5 (ERA5) reanalysis dataset to obtain regional wind data during the storm event. This data includes meteorological parameters such as wind speed at 10 meters, air temperature at 2 meters, and surface pressure. Using bilinear interpolation, this meteorological data is interpolated to all model grid points and serves as the driving input for the model.

[0154] S23. Divide the grid, give model parameters, and build a hydrodynamic model.

[0155] The entire model consists of 50,171 unstructured triangular grids, with a total of 26,455 grid nodes. The side length of the grid spans a large range, with a minimum side length of about 200 meters and a maximum side length of up to 40,000 meters. Considering the complexity of the hydrodynamic changes in the Hangzhou Bay and Yangtze River Delta regions, this embodiment has made a detailed processing of the grid in this area in order to accurately capture the hydrodynamic characteristics of the region. The grid and resolution are determined by Figure 9-1 shown.

[0156] The preparation of the model input file involves the setting of multiple key parameters, including roughness, bottom drag coefficient, wall coefficient, wind stress coefficient, etc. The roughness 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 China's sea areas, in order to ensure the accuracy of the calculation results, this implementation case determines the corresponding model setting parameters for different regions through a combination of numerical experiments and field observations. 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 response of different terrain, bottom sediments and flow velocity conditions to storm surges.

[0157] Attribute information is assigned to unstructured grids. Specifically, ocean bathymetric data obtained from multi-source datasets are assigned to each grid node and cell through high-order interpolation. The number of vertical stratification layers for the three-dimensional grid is determined through a predefined vertical stratification strategy. Roughness is assigned to each grid cell in the unstructured grid based on terrain characteristics and numerical experiments.

[0158] S24. Set boundary conditions and initial conditions.

[0159] The model has two open boundary conditions: an ocean boundary driven by tide level and a river boundary driven by flow rate (primarily for rivers like the Yangtze and Qiantang Rivers). The tide-driven ocean boundary data are derived from the TPXO9 dataset developed by George HHH and his team at the Massachusetts Institute of Technology (MIT). It covers 15 major tidal components: 2N2, K1, K2, M2, M4, MF, MM, MN4, MS4, N2, O1, P1, Q1, S1, and S2. After astronomical corrections, the dataset is interpolated and ultimately input into the model's computational grid. The flow-driven river boundary data are derived from the average annual runoff provided by hydrological stations to ensure that the simulation results reflect actual river input conditions.

[0160] To ensure the correctness of the model simulation results, all simulations were started before the typhoon took effect, thereby minimizing the impact of initial conditions.

[0161] S25. Calculate all grid classification indices, divide the grids into sets, and determine the time step of each grid set.

[0162] Based on the unstructured grid allocation attribute information and the unit physical quantity values ​​calculated by the model (the first calculation is given by the model initial value conditions), the grid unit size, grid water depth, and grid boundary velocity are obtained. Based on the CFL criterion, the maximum time step required for each grid is calculated. .

[0163]

[0164] Figure 10 Shows the grid classification at T=0h (initial time). Figure 10 All grid sets in are divided into 7 colors. Each color of grid represents a grid set, and there are 7 grid sets in total.

[0165] S26 , starting to calculate the first simulation result, calculating the physical flux value and the corresponding physical quantity value of each grid set at the corresponding time step.

[0166] Calculate the next time step corresponding to each grid set ( 、 、 …).

[0167] S27, using the Taylor expansion value of the first physical quantity value and the first physical flux value calculated by the first grid set as the boundary condition of the second grid set at a subsequent time point , start calculating the second simulation result, advance the calculation and update to obtain the fourth physical flux value and the fourth physical quantity value of the second grid set.

[0168] At this time, the time of the grid physical quantity values ​​of different sets is different. For example, the time classification index is When , the grid set is located at the time scale of , and the time-grading index is When , the grid set is located at the time scale of In order to ensure the continuity of model calculation, the first physical quantity value and the first physical flux value of the interface grid set are expanded to the intermediate moment by Taylor expansion, and used as the second grid set in Initial boundary conditions at time And calculate the subsequent time points of the second grid set ( , , )'s sixth physical flux value and sixth physical quantity value.

[0169]

[0170] ;

[0171] S28, total flux calculated based on the second grid set Corrected updating of physical flux values ​​and physical quantity values ​​for interface mesh collections.

[0172] In the calculation of the above process, the total flux of the second grid set is calculated by using the boundary conditions predicted by the first physical quantity value and the first physical flux value of the first grid set using Taylor expansion. Since there is a prediction step in this process, this leads to a certain error in the flux to be corrected of the interface layer grid set predicted by the first grid set and the total flux of the interface layer grid predicted by the second grid set. If not corrected, the error will accumulate step by step, which will have a huge impact on the accuracy of the calculation results of the model. Therefore, in order to ensure the conservation of the flux of the total flux to be corrected and the total flux, correction is required. Total flux based on the second grid set Correct the total flux to be corrected. The specific correction method is:

[0173]

[0174] S29. Determine whether the total accumulated time reaches the total time set by the model. If so, end the loop and output the model calculation results to verify the accuracy of the model; if not, return to execute S25.

[0175] The above process is a completed calculation cycle, S21 is the entrance of the cycle, and the judgment Whether the deadline set by the model is reached, if so, the loop can be terminated to output the calculation results; if not, return to S21 and enter the next new loop until all calculations are completed.

[0176] According to one aspect of the present application, step S29 is further as follows:

[0177] S291. Determine whether the loop is terminated.

[0178] The deadlines for the models in this implementation example are August 15, 2019 and July 28, 2021. If the deadline set by the model is reached, the loop is terminated and the model calculation results are output; if not, the loop returns to S25 and enters the next loop.

[0179] S292. Verify the astronomical tide based on the calculation results.

[0180] In this experimental example, we conducted model validation on the tides from May 20, 2019 to June 21, 2019, and from July 15, 2019 to July 31, 2019, respectively named Tidal Validation 1 and Tidal Validation 2, including a spring tide-neap tide cycle, respectively named Spring Tide A, Spring Tide B, Neap Tide A, and Neap Tide B; a total of 5 tide stations and 2 tidal stations were validated, located in Hangzhou Bay, the Yangtze River Estuary, and near the Zhoushan Islands. Figure 9-2 Schematic diagrams showing tide verification, tidal current verification, and storm surge.

[0181] exist Figure 11 and Figure 12 In the paper, two working conditions are given. and The water level and flow velocity under the two conditions are verified. It can be seen that the simulated tide level is very consistent with the observation data in terms of tidal range and phase, and the global unified time step model scheme ( ) and local time stepping schemes ( ), and the results of the two are also in good agreement. This reflects the accuracy of the local time step. In order to further quantify the ability of the model to reproduce tidal fluid dynamics, the root mean square error (RMSE) between the model results and the observations was calculated. Figure 11 The data show that the RMSEs for astronomical tides are all less than 0.25 m. For tidal current verification, the RMSE for velocity ranges from 0.1 to 0.35 m / s, and the RMSE for flow direction ranges from 20° to 40°. Furthermore, it can be seen that the results of the global unified time step model scheme and the local time step scheme show remarkable consistency, with RMSEs reaching the centimeter level.

[0182] S293. Verify the storm surge based on the calculation results.

[0183] In this experimental example, Figure 13 The storm surge data from four monitoring stations were verified. Comparison showed that the phase and amplitude of the model calculations were essentially consistent with the observed data, clearly demonstrating the presence of the storm surge under the influence of the typhoon. The maximum storm surges at Niupijiao, Nancaodong, Luchaogang, and Zhenhai stations were 0.8403 m, 0.5798 m, 1.1956 m, and 1.2631 m, respectively. Table 1 demonstrates the effect of increasing the local time step on computational efficiency.

[0184] Table 1

[0185]

[0186] In an exemplary embodiment, a computer device is provided, including a processor and a memory, wherein 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 local time steps are implemented.

[0187] In one exemplary embodiment, a computer-readable storage medium is provided, storing a computer program. When executed by a processor, the computer program implements any of the steps of the aforementioned method for simulating shallow water dynamic processes based on a local time step. The computer-readable storage medium may 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, or the like.

[0188] In an exemplary embodiment, a computer program product is provided, comprising 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.

[0189] Those skilled in the art will readily appreciate 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 that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein.

Claims

1. A method for simulating shallow water dynamic processes based on local time steps, characterized in that: The method comprises: Constructing a shallow water dynamic process model to divide a target area into a plurality of grids, wherein the target area includes an ocean area and a land area adjacent to the ocean area; Divide the plurality of grids into at least a first grid set and a second grid set, wherein a boundary grid set is provided between the first grid set and the second grid set; determining, according to the first grid set, a first time step corresponding to the first grid set, where the first grid set includes a plurality of first grids; determining, based on the second grid set, a second time step corresponding to the second grid set, where the second grid set includes a plurality of second grids, the first time step being greater than the second time step, and determining a first simulation result of a shallow water dynamic process based on the first time step and the second time step; Predicting a third physical quantity value and a third physical flux value of the boundary grid set based on the first physical quantity value and the first physical flux value of the first grid set, so as to determine the sum of fluxes of grids at the intersection of the first grid set and the boundary grid set as the total flux to be corrected; determining a boundary condition based on the first physical quantity value of the first grid set, wherein the boundary condition is used to limit a fourth physical quantity value and a fourth physical flux value of the second grid set; determining a sixth physical quantity value and a sixth physical flux value of the second grid set at a subsequent time point according to the boundary condition and the first simulation result; determining the fourth physical quantity value and the fourth physical flux value based on 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 flux value; 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; determining a second simulation result of the shallow water dynamic process based on 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; Among them, physical fluxes include flow velocity, water level and waves, and the corresponding physical flux values ​​include momentum flux, mass flux and wave energy flux.

2. The shallow water dynamic process simulation method based on local time step according to claim 1 is characterized in that: The dividing the plurality of grids into at least a first grid set and a second grid set comprises: Determining a time classification index corresponding to each of the grids; The plurality of grids are divided into at least a first grid set and a second grid set according to the time classification index corresponding to each grid.

3. The shallow water dynamic process simulation method based on local time step according to claim 2 is characterized in that: Determining the time classification index corresponding to each grid includes: Determining the minimum time step of all the grids according to the grid water depth and critical water depth of each grid; The time classification index corresponding to each of the grids is determined according to the minimum time step, the preset time classification coefficient and the maximum time step of each of the grids.

4. The shallow water dynamic process simulation method based on local time step according to claim 1 is characterized in that: Determining a first simulation result of a 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; The first simulation result is determined 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 shallow water dynamic process simulation method based on local time step according to claim 1 is characterized in that: The determining of the boundary condition according to the first physical quantity value of the first grid set includes: The first physical quantity value is expanded according to a Taylor expansion to determine the boundary condition.

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