Water level implicit calculation method and system suitable for bidirectional local nested ocean mode

Abstract

The invention provides a water level implicit calculation method and system for a bidirectional local nested estuary offshore numerical pattern. The method comprises the steps that an input file is read, and pattern initialization is carried out; judging whether the current mode time is greater than the ending time or not, and if yes, ending the process; if not, the mode boundary condition is read according to the current mode time, the momentum equation is solved in three steps through an operator splitting method, the positive pressure item in the third step is substituted into the continuous equation, and the water level value is solved through an implicit expression; substituting the water level value into an MY2.5-order turbulent flow closed model to calculate a vertical turbulent flow viscosity coefficient and a vertical turbulent flow diffusion coefficient, and solving a substance transport equation in two steps by using an operator splitting method; required physical information is transmitted to the virtual coarse grid, the mode time is updated, and loop iterative calculation is carried out until the end time is reached. According to the method, the calculation area of the mode can be amplified, the influence of far-field wind, water level and ocean current on the research area can be reflected, the research area can be fully and locally encrypted, and the calculation precision and efficiency are improved.

Description

Technical Field

[0001] The present invention relates to the technical field, in particular to a method and system for implicitly calculating water level in a bidirectionally nested local ocean model, and in particular to an implicit solution scheme for calculating water level in a bidirectionally nested local encrypted grid estuary near-shore numerical model. Background Art The numerical models of estuaries and offshore areas at home and abroad generally use structured quadrilateral grids and unstructured triangular grids. The advantage of structured quadrilateral grids is that they use finite difference formats, which are easy to program. More importantly, they can use high-order difference formats to improve calculation accuracy. The disadvantage is that it is difficult to fully encrypt the research area of ​​interest under the complex terrain of estuaries and offshore areas. Even if non-orthogonal curve grids are used, they can only be partially encrypted locally, and redundant grids are generated in both directions of the grid, which increases the amount of calculation and affects the stability of the model. The advantage of unstructured triangular grids is that they can fully encrypt and fully fit the coastline locally, and can cope with complex coastline and terrain changes. The disadvantage is that the finite volume method is used, and the calculation of the flux of each side of the triangle and polygon uses a large number of interpolations, which makes it difficult to use high-order calculation formats. In the offshore areas of estuaries, how to use high-order calculation formats and fully encrypt locally to improve the calculation accuracy and efficiency of the model is a key calculation problem that needs to be solved in the numerical models of estuaries and offshore areas.

[0002] A bidirectionally encrypted nested unstructured quadrilateral grid finite difference estuary offshore three-dimensional numerical model can achieve local full encryption without generating redundant grids in the two directions of the quadrilateral grid lines, while retaining the advantages of the quadrilateral grid that can easily adopt finite differences and high-order calculation formats. However, a major problem is how to give a difference format on the inner boundary of the quadrilateral nested grid, because the finite difference format needs to give values ​​at the left and right and upper and lower grid points, that is, how to give values ​​for virtual points in the coarse grid. The construction of the finite difference format, implicit solution to increase the time step, and conservation of mass and energy transport and propagation at the inner boundary are all technical problems that need to be solved.

[0003] Therefore, there is a need in the market for an implicit water level calculation method and system suitable for a locally encrypted bidirectional nested ocean model that can improve computational efficiency and model accuracy. Summary of the invention

[0004] In view of the defects in the prior art, the object of the present invention is to provide a water level implicit calculation method and system for a bidirectional local nested ocean model.

[0005] According to the present invention, a water level implicit calculation method for a bidirectional local nested ocean model includes: Step S1: read the input file and initialize the mode; Step S2: determine whether the current mode time is greater than the preset end time, if so, end the calculation process; if not, execute step S3; Step S3: reading the mode boundary conditions according to the current mode time, and solving the momentum equation in three steps using the operator splitting method, bringing the positive pressure term in the third step into the continuity equation to solve the water level value implicitly; Step S4: Substituting the water level value into the Mellor-Yamada 2.5-order turbulence closed model to calculate the vertical turbulent viscosity coefficient and the vertical turbulent diffusion coefficient; Step S5: using the vertical turbulent viscosity coefficient and the vertical turbulent diffusion coefficient, and using the operator splitting method to solve the material transport equation in two steps to obtain corresponding physical information; Step S6: transfer the required physical information to the virtual coarse grid and update the model time and model boundary conditions, and return to step S2.

[0006] Preferably, the pattern boundary condition refers to physical information at the pattern grid boundary; The physical information includes tidal current, tidal level, salinity and temperature, and the values ​​corresponding to the boundary points are different at different times.

[0007] Preferably, the time variation term in the momentum equation is as follows:

[0008] in, and represents the horizontal flow velocity in the curvilinear coordinate system, n represents the time step, a represents one-third of the time step, b represents two-thirds of the time step, represents the time step, D represents the total water depth, and J represents the Jacobian function; The material transport equation includes the salinity transport equation and the temperature transport equation: The salinity transport equation is:

[0009] The temperature transport equation is:

[0010] Where S represents salinity, and Indicates that the definition is and The velocity in the normal direction, Indicated in The vertical velocity in the coordinate system is: represents the vertical turbulent diffusion coefficient, Indicates time, and Represents the two directions of the grid, Indicates the vertical direction.

[0011] Preferably, step S3 comprises: Step S3.1: The time variation term is calculated using the time forward difference format, the advection term is calculated using the high-precision HSIMT format, and the baroclinic term, curvature term, Coriolis force term and horizontal diffusion term are calculated using the spatial central difference explicit processing to obtain the velocity information of the actual grid and the virtual fine grid. and ; Step S3.2: Implicit processing of the vertical diffusion term to calculate the velocity information of the actual grid and the virtual fine grid and , and then replace the velocity information of the virtual coarse grid according to the flux conservation and ; Step S3.3: Only the positive pressure term generated by the external gravity wave is considered, and the positive pressure term is substituted into the continuity equation and the water level is solved using the implicit format to obtain the n+1th step water level value of the actual grid and the virtual fine grid. ; Step S3.4: Replace the water level value of the virtual coarse grid according to flux conservation , and then the water level value The velocity information of the virtual coarse grid is obtained by back-transfer , replace the velocity information of the virtual coarse grid according to the flux conservation ; Step S3.5: Obtain the actual grid velocity information through the continuity equation update ,in Indicates the flow velocity information in the vertical direction.

[0012] Preferably, the step S5 of solving the material transport equation in two steps using the operator splitting method comprises: In the first step, the advection term and horizontal diffusion term are processed using the HSIMT format and the Euler format, respectively; The second step is to perform implicit processing on the vertical diffusion term according to the vertical turbulent viscosity coefficient and the vertical turbulent diffusion coefficient.

[0013] A water level implicit calculation system for a bidirectional local nested ocean model provided by the present invention comprises: Module M1: reads input file and initializes the mode; Module M2: Determine whether the current mode time is greater than the preset end time. If so, end the calculation process; if not, execute module M3; Module M3: Reading the mode boundary conditions according to the current mode time, and solving the momentum equation in three steps using the operator splitting method, bringing the positive pressure term in the third step into the continuity equation to solve the water level value implicitly; Module M4: Substitute the water level value into the Mellor-Yamada 2.5-order turbulence closed model to calculate the vertical turbulent viscosity coefficient and the vertical turbulent diffusion coefficient; Module M5: by using the vertical turbulent viscosity coefficient and the vertical turbulent diffusion coefficient, the material transport equation is solved in two steps using the operator splitting method to obtain corresponding physical information; Module M6: Transfers the required physical information to the virtual coarse grid and updates the model time and model boundary conditions, and returns to module M2.

[0014] Preferably, the pattern boundary condition refers to physical information at the pattern grid boundary; The physical information includes tidal current, tidal level, salinity and temperature, and the values ​​corresponding to the boundary points are different at different times.

[0015] Preferably, the time variation term formula in the momentum equation includes the following:

[0016] in, and represents the horizontal flow velocity in the curvilinear coordinate system, n represents the time step, a represents one-third of the time step, b represents two-thirds of the time step, represents the time step, D represents the total water depth, and J represents the Jacobian function; The material transport equation includes the salinity transport equation and the temperature transport equation: The salinity transport equation is:

[0017] The temperature transport equation is:

[0018] Where S represents salinity, and Indicates that the definition is and The velocity in the normal direction, Indicated in The vertical velocity in the coordinate system is: represents the vertical turbulent diffusion coefficient, Indicates time, and Represents the two directions of the grid, Indicates the vertical direction.

[0019] Preferably, the module M3 comprises: Module M3.1: The time variation term uses the time difference format, the advection term uses the high-precision HSIMT format, the baroclinic term, curvature term, Coriolis force term and horizontal diffusion term use the spatial central difference explicit processing, and the velocity information of the actual grid and virtual fine grid is calculated. and ; Module M3.2: Implicit treatment of vertical diffusion terms, calculating the velocity information of the actual grid and virtual fine grid and , and then replace the velocity information of the virtual coarse grid according to the flux conservation and ; Module M3.3: Only the positive pressure term generated by external gravity waves is considered. The positive pressure term is substituted into the continuity equation and the water level is solved using the implicit format to obtain the n+1-step water level value of the actual grid and the virtual fine grid. ; Module M3.4: Replace the water level value of the virtual coarse grid according to flux conservation , and then the water level value The velocity information of the virtual coarse grid is obtained by back-transfer , replace the velocity information of the virtual coarse grid according to the flux conservation ; Module M3.5: Obtaining flow velocity information of the actual grid through continuity equation update ,in Indicates the flow velocity information in the vertical direction.

[0020] Preferably, the method of solving the material transport equation in two steps by using the operator splitting method in the module M5 comprises: In the first step, the advection term and horizontal diffusion term are processed using the HSIMT format and the Euler format, respectively; The second step is to perform implicit processing on the vertical diffusion term according to the vertical turbulent viscosity coefficient and the vertical turbulent diffusion coefficient.

[0021] Compared with the prior art, the present invention has the following beneficial effects: 1. The present invention proposes a two-way local nested grid water level implicit solution based on material conservation, which can not only enlarge the calculation area of ​​the model, reflect the influence of distant wind, water level and ocean current on the study area, but also fully encrypt the study area locally, thereby improving the calculation accuracy and efficiency.

[0022] 2. Based on the assumption of flux conservation, the present invention solves the problem of model instability and significant errors generated at nested boundaries, and further improves model stability and calculation accuracy by assuming that the flux at the boundary of the low-resolution grid is equal to the sum of the corresponding boundary fluxes of the high-resolution grid.

[0023] 3. The present invention can effectively relax the restrictions of the numerical format stability criterion CFL (Courant-Friedrichs-Lewy) based on time and space steps by adopting an implicit solution for water level, thereby improving the computational efficiency of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings: Figure 1 It is a schematic diagram of the numerical model calculation process of the present invention; Figure 2 It is a schematic diagram of the momentum equation calculation process in the present invention; Figure 3 It is the effect diagram of the actual coarse grid ACG, the virtual coarse grid VCG, the actual fine grid AFG and the virtual fine grid VFG in the present invention; Figure 4 This is a schematic diagram of grid variable configuration in the present invention; Figure 5 Schematic diagram of the nested upper boundary VFG local area and the nested upper boundary AFG local area in the present invention.

[0025] in, Figure 3 Here, 1 represents the actual coarse grid ACG, 2 represents the virtual coarse grid VCG, 3 represents the actual fine grid AFG, and 4 represents the virtual fine grid VFG; Figure 5 6 in the figure represents the nested upper boundary VFG local part, and 7 represents the nested upper boundary AFG local part. DETAILED DESCRIPTION

[0026] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0027] In the actual application of ocean numerical models, there are mainly two usage scenarios. One is to use the model to replay the phenomena that have occurred, and simulate the process of the occurrence of ocean phenomena according to different input conditions of the model; the other is to forecast the phenomena that have not yet occurred, using given input conditions, such as the wind field and runoff boundary in the calculation area in a certain time period in the future, to forecast the upcoming phenomena in advance, and submit the results to the relevant departments for practical response measures. Regardless of any of the above usage scenarios, there are extremely high requirements for the computational efficiency and accuracy of the model. If the model is used for replay, the calculation time of the model should not be too long, because multiple groups of comparative tests are required to explore the impact of different factors on the model results. If the step size is too short, it will take a long time to calculate the results. In addition, the model replay results also need to be compared with the actual observation results. If the error between the two is too large, the model parameters need to be recalibrated and verified. If the model is used for forecasting, the time requirement is more stringent. Assuming that the model needs to forecast the phenomenon that will occur three days later, the model needs to complete the numerical forecast within a few hours and draw the results, which is very particular about the timeliness and accuracy of the model calculation. Therefore, improving the computational efficiency and accuracy of ocean numerical models has always been the direction explored by model developers.

[0028] The technology involved in the present invention is explained as follows: CFL (Courant-Friedrichs-Lewy) criterion: A criterion for judging the stability and convergence of a format when solving partial differential equations using the finite difference method.

[0029] IGNES: Implicit,Grid-Nesting Elevation Solution, implicit solution of nested grid water level.

[0030] Time step: The time span of each iteration when calculating the model. Generally speaking, the larger the step, the faster the model runs, but the more likely it is to be unstable.

[0031] Explicit solution: In the process of numerical solution of differential equations, time and space are differentiated from n-1 steps or n steps to n+1 steps. The spatial differential term uses the known value at time n, and the physical quantity at time n+1 is directly obtained by multiplying the time step Δt by the rate of change of the physical quantity at time n.

[0032] Implicit solution: In the process of numerical solution of differential equations, time and space are differentiated from n-1 steps or n steps to n+1 steps. The spatial differential terms use the known values ​​at time n+1, and the physical quantities at time n+1 need to be given by solving the equation iteratively.

[0033] Embodiment 1 According to a water level implicit calculation method of a bidirectional local nested ocean model provided by the present invention, Figure 1 As shown, including: Step S1: Read the input file and perform mode initialization.

[0034] Step S2: Determine whether the current mode time is greater than the preset end time. If so, end the calculation process; if not, execute step S3.

[0035] Step S3: Read the model boundary conditions according to the current model time, and use the operator splitting method to solve the momentum equation in three steps, and bring the positive pressure term in the third step into the continuity equation to solve the water level value implicitly. The model boundary conditions refer to the physical information at the boundary of the model grid, and the physical information includes tidal current, tide level, salinity and temperature. The values ​​of the corresponding boundary points at different times are different. The momentum equation formula and The directions are: ； .

[0036] In the formula, is the Coriolis force coefficient, is the acceleration due to gravity. ), advection term: ; Coriolis force term + curvature term: ; Positive pressure term: ; Baroclinic term: ; Vertical diffusion term: ; Horizontal diffusion term: .

[0037] The time variation term formula in the momentum equation includes the following:

[0038] in, and represents the horizontal flow velocity in the curvilinear coordinate system, n represents the time step, a represents one-third of the time step, b represents two-thirds of the time step, represents the time step, D represents the total water depth, i.e. the water depth plus the water level, and J represents the Jacobian function. Specifically, is the time-varying term in the momentum equation, This is the first step in solving the momentum equation, which is used to calculate the advection term, baroclinic term, curvature term, Coriolis force term, and horizontal diffusion term. To solve the second step of the momentum equation, used to calculate the vertical diffusion term, The third step in solving the momentum equation is used to calculate the positive pressure term.

[0039] The material transport equation includes the salinity transport equation and the temperature transport equation: The salinity transport equation is:

[0040] The temperature transport equation is:

[0041] Where S represents salinity, and Indicates that the definition is and The velocity in the normal direction, Indicated in The vertical velocity in the coordinate system is represents the vertical turbulent diffusion coefficient, Indicates time, and Represents the two directions of the grid, Indicates the vertical direction.

[0042] The step S3 comprises: Step S3.1: The time variation term is calculated using the time forward difference format, the advection term is calculated using the high-precision HSIMT format, and the baroclinic term, curvature term, Coriolis force term and horizontal diffusion term are calculated using the spatial central difference explicit processing to obtain the velocity information of the actual grid and the virtual fine grid. and Among them, the full name of the HSIMT format is High-order Spatial Interpolation at the Middle Temporal level.

[0043] Step S3.2: Implicit processing of the vertical diffusion term to calculate the velocity information of the actual grid and the virtual fine grid and , and then replace the velocity information of the virtual coarse grid according to the flux conservation and That is to say, the velocity information in the u and v directions of the actual grid and the virtual fine grid is used to replace the velocity information on the virtual coarse grid according to the flux conservation. In the next cycle, the vertical turbulent viscosity coefficient obtained in the previous cycle is used for calculation.

[0044] Step S3.3: Only the positive pressure term generated by the external gravity wave is considered, and the positive pressure term is substituted into the continuity equation and the water level is solved using the implicit format to obtain the n+1th step water level value of the actual grid and the virtual fine grid. ,in represents the water level value, and n represents the time step. That is, the flow rate of step n+1 is substituted into the continuity equation and the water level value is solved using the implicit format.

[0045] Step S3.4: Replace the water level value of the virtual coarse grid according to flux conservation , and then the water level value The velocity information of the virtual coarse grid is obtained by back-tracking , replace the velocity information of the virtual coarse grid according to the flux conservation .

[0046] Step S3.5: Obtain the actual grid velocity information through the continuity equation update ,in Indicates the flow velocity information in the vertical direction.

[0047] Step S4: Substituting the water level value into the Mellor-Yamada 2.5-order turbulence closed model to calculate the vertical turbulent viscosity coefficient and the vertical turbulent diffusion coefficient.

[0048] Step S5: using the operator splitting method to solve the material transport equation in two steps, in the first step, the advection term and the horizontal diffusion term are processed using the HSIMT format and the Euler format respectively; in the second step, the vertical diffusion term is implicitly processed according to the vertical turbulent viscosity coefficient and the vertical turbulent diffusion coefficient.

[0049] Step S6: transfer the required physical information to the virtual coarse grid and update the model time and model boundary conditions, and return to step S2.

[0050] Furthermore, combined with Figures 2 to 5 The water level implicit calculation method of the bidirectional local nested ocean model of the present invention is specifically described as follows: The estuarine ocean numerical model is mainly based on the Reynolds time-averaged Navier-Stokes equations of the hydrostatic approximation (assuming that the vertical acceleration is negligible) and the Boussinesq approximation. Grid, vertical Grid. In order to construct the finite difference format, the local nested encryption model often introduces a virtual grid. The present invention distinguishes between the actual grid and the virtual grid according to whether the physical quantity of the grid is output as effective information. Figure 3As shown in the figure, the high-resolution grid is called the actual fine grid (AFG), while the low-resolution grid is called the actual coarse grid (ACG). The six-layer grid extending inward from the ACG at the nesting boundary (taking triple refinement as an example, the same throughout the text) is called the virtual coarse grid (VCG). The six-layer grid extending outward from the AFG at the nesting boundary is called the virtual fine grid (VFG). After the introduction of the virtual grid, the grid can be relatively divided into two groups of smooth resolution grids, one group is the low-resolution ACG and VCG, and the other group is the high-resolution AFG and VFG.

[0051] The control equations are discretized using the finite difference method on the Arakawa C grid. Taking triple encryption as an example, a low-resolution grid can be divided into nine high-resolution grids. The schematic diagram of the grid variable configuration is shown in Figure 4 As shown in the figure, the solid upper triangle represents the flow velocity u of the high-resolution grid, the hollow upper triangle represents the flow velocity u of the low-resolution grid, the solid lower triangle represents the flow velocity v of the high-resolution grid, the hollow lower triangle represents the flow velocity v of the low-resolution grid, the solid circle represents the variables defined at the center of the high-resolution grid, such as water level, salinity and temperature, which are defined at the center of the grid, the hollow circle represents the variables defined at the center of the low-resolution grid, the thick line represents the grid line of the low-resolution grid, and the thin line represents the grid line of the high-resolution grid. It should be noted that although some variables of the high-resolution grid and the low-resolution grid overlap in position, such as the center of the coarse grid and the midpoint of each edge, they need to be calculated and stored separately during the iteration process.

[0052] The present invention calculates the variables of VCG and VFG through control equations and flux balance, respectively.

[0053] The barotropic term in the Navier-Stokes equations due to external gravity waves is implicitly treated by substituting it into the continuity equation. Solving the water level using an implicit format allows the CFL criterion to be relaxed. and The directional water level gradient term equation, water level equation and continuity equation are: (1) (2) (3) Solving the water level with the continuity equation is an extremely important step in momentum simulation. The explicit processing of the positive pressure gradient force term and the limitation of the CFL criterion greatly limit the model time step. In order to improve the calculation efficiency of the model, this paper develops an implicit solution scheme for water level in nested grids, IGNES.

[0054] Although a closed system of equations can be constructed by considering AG alone, the system of equations is unstable during the solution process, and there are significant errors at the nesting boundaries in the test. Therefore, the present invention considers AG and VFG grids when constructing the system of equations. Among them, ACG is a set of smooth low-resolution grids, while AFG and VFG can be regarded as a set of smooth high-resolution grids. It is worth noting that these two sets of grids have an overlapping area VFG. Except for the outermost VFG and the ACG near the nesting boundary, the difference equations of equations (1) to (3) can be written as: (4) (5) (6) Because local encryption destroys the two-dimensional structure of the structural grid numbering, one-dimensional numbering is required. Here, the subscript i represents the variable defined at the center of the i grid; the subscript , , and Represent the variables defined at the left midpoint, right midpoint, bottom midpoint, and top midpoint of the i grid respectively; subscript , , and Respectively represent the grids defined on the left, right, bottom and top of grid i. , , that is, the left midpoint variable of the right grid of grid i is also the right variable of grid i. The separate definitions are for easier description and understanding. The same number is used for the same variable in coding. Substituting equations (4) and (5) into equation (6), we get: (7) in: (8) (9) remember 、 、 、 。

[0055] Since VCG is not considered at this time, the ACG at the nested boundary loses its adjacent grids, making the differential equations (4) to (7) no longer valid. The outermost VFG faces the same situation. The grid boundaries of the VCG grid and the VFG grid coincide with the grid boundaries of the ACG and AFG, respectively. Based on the flux conservation, the flux at the boundary of the low-resolution grid should be equal to the sum of the corresponding boundary fluxes of the high-resolution grid. Therefore, the boundary flux of the VCG grid and the VFG grid can be replaced by the boundary flux of other grids. Taking the north side as an example, Figure 5 As shown in the figure, the thick solid lines represent the grid lines of the low-resolution grid, the thin solid lines represent the grid lines of the high-resolution grid, the thick dashed lines represent the virtual coarse grid lines, and the thin dashed lines represent the virtual fine grid lines. , then in VFG1, VFG2 and VFG3: (10) (11) (12) in , and is the coefficient, and Assume that the water level and flow velocity are continuous and parabolically distributed along ACG1 and the grids on its left and right sides: (13) (14) The local coordinates are ： (15) so: (16) The flux can be expressed as: (17) The local coordinates of the upper left vertex of meshes VFG1, VFG2, VFG3 and the upper right vertex of VFG3 are denoted by , , and ,like Figure 5 As shown. Then the upper flux of the three grids VFG1, VFG2 and VFG3 is: (18) To maintain flux balance: (19) Substituting equations (10) to (12) into equation (2), we can obtain the finite difference equations of the continuity equations in VFG1, VFG2, and VFG3. Taking VFG1 as an example, the difference equation can be finally simplified to: (20) Taking the north side as an example, in the nested boundary ACG3 ( Figure 5 ), the finite difference equation of formula (5) is: (twenty one) (twenty two) (twenty three) The flux at the southern boundary of ACG3 is equal to the sum of the fluxes at the northern boundaries of AFG1, AFG2, and AFG3: (twenty four) Substituting equation (23) into equation (2), we can obtain the finite difference equation of the continuity equation at ACG3: (25) Thus, a closed set of equations can be constructed to solve the positive pressure gradient force term in the momentum equation and the continuity equation. In order to maintain consistency and flux conservation, the boundary flux of the VCG grid is updated using the calculation results of AFG, and then the water level and flow rate of step n+1 are obtained for other calculations.

[0056] The time splitting operator method is used to solve the momentum equation. The time term of the momentum equation is split into three steps by integrating the time terms in the equation. Figure 2 As shown:

[0057] Step 1: The time variation term is processed in the time forward difference format, the advection term is processed in the high-precision HSIMT format, and the baroclinic term, curvature term, Coriolis force term and horizontal diffusion term are processed in the spatial central difference format to obtain the actual grid and virtual fine grid. , .

[0058] (26) (27) Step 2: Implicit processing of the vertical diffusion term to calculate the actual grid and virtual fine grid , ; Then, according to the flux conservation, replace the virtual coarse grid , The tridiagonal matrix generated by this step can be solved using the tridiagonal matrix algorithm (Thomas, 1949): (28) (29) Step 3: Consider only the positive pressure term generated by the external gravity wave, substitute it into the continuity equation and use the implicit format to solve the water level to obtain the actual grid and virtual fine grid Compared with explicit solution, the implicit format can maximize the model time step, without being restricted by the CFL criterion to constrain the time step and prevent the model calculation from being unstable: (1) (2) (3) According to the flux conservation, replace the virtual coarse grid , and then Bring back , replace the virtual coarse grid Finally, the actual grid is obtained by updating the continuity equation , and then perform subsequent calculations.

[0059] The present invention utilizes implicit solution to increase the time step, thereby shortening the overall model calculation time; at the same time, the bidirectional information transmission between nested grids ensures the flux conservation between high and low resolution grids, and significantly improves the model stability and calculation accuracy.

[0060] The calculation of the material transport equation also uses the time operator splitting method. In the first step of the material transport equation, the advection term and the horizontal diffusion term are processed using the HSIMT format and the Euler format respectively: (30) In the second step of the material transport equation, the vertical diffusion term is implicitly processed to obtain a tridiagonal matrix, which is solved by the tridiagonal matrix algorithm: (31) Embodiment 2 The present invention provides a water level implicit calculation system for a bidirectional local nested ocean model. The water level implicit calculation system for a bidirectional local nested ocean model can be implemented by executing the process steps of the water level implicit calculation method for the bidirectional local nested ocean model, that is, those skilled in the art can understand the water level implicit calculation method for the bidirectional local nested ocean model as a preferred implementation of the water level implicit calculation system for the bidirectional local nested ocean model.

[0061] A water level implicit calculation system for a bidirectional local nested ocean model provided by the present invention comprises: Module M1: Read input file and perform mode initialization.

[0062] Module M2: Determine whether the current mode time is greater than the preset end time. If so, end the calculation process. If not, execute module M3. The mode boundary condition refers to the physical information at the boundary of the mode grid. The physical information includes tidal current, tide level, salinity and humidity. The values ​​of the corresponding boundary points are different at different times.

[0063] Module M3: Read the mode boundary conditions according to the current mode time, and use the operator splitting method to solve the momentum equation in three steps, and bring the positive pressure term in the third step into the continuity equation to solve the water level value implicitly. The momentum equation includes the following:

[0064] in, and represents the horizontal flow velocity in the curvilinear coordinate system, n represents the time step, a represents one-third of the time step, b represents two-thirds of the time step, represents the time step, D represents the total water depth, that is, the water depth plus the water level, and J represents the Jacobian function.

[0065] The material transport equation includes the salinity transport equation and the temperature transport equation: The salinity transport equation is:

[0066] The temperature transport equation is:

[0067] Where S represents salinity, and Indicates that the definition is and The velocity in the normal direction, Indicated in The vertical velocity in the coordinate system is: represents the vertical turbulent diffusion coefficient, Indicates time, and Represents the two directions of the grid, Indicates the vertical direction.

[0068] Module M3 includes: Module M3.1: The time variation term adopts the time forward difference format, the advection term adopts the high-precision HSIMT format, the baroclinic term, curvature term, Coriolis force term and horizontal diffusion term adopt the spatial central difference explicit processing, and the velocity information of the actual grid and virtual fine grid is calculated. and Module M3.2: Implicit treatment of vertical diffusion terms, calculating the velocity information of the actual grid and virtual fine grid and , and then replace the velocity information of the virtual coarse grid according to the flux conservation and Module M3.3: Only consider the positive pressure term generated by external gravity waves, substitute the positive pressure term into the continuity equation, and use the implicit format to solve the water level to obtain the n+1th step water level value of the actual grid and the virtual fine grid Module M3.4: Replace the water level value of the virtual coarse grid according to flux conservation , and then the water level value The velocity information of the virtual coarse grid is obtained by back-tracking , replace the velocity information of the virtual coarse grid according to the flux conservation Module M3.5: Obtaining the actual grid velocity information through continuity equation update ,in Indicates the flow velocity information in the vertical direction.

[0069] Module M4: Substitute the water level value into the Mellor-Yamada 2.5-order turbulence closed model to calculate the vertical turbulent viscosity coefficient and vertical turbulent diffusion coefficient.

[0070] Module M5: Through the vertical turbulent viscosity coefficient and the vertical turbulent diffusion coefficient, the material transport equation is solved in two steps using the operator splitting method to obtain the corresponding physical information. In the first step, the advection term and the horizontal diffusion term are processed using the HSIMT format and the Euler format respectively. In the second step, the vertical diffusion term is implicitly processed according to the vertical turbulent viscosity coefficient and the vertical turbulent diffusion coefficient. The material transport equation includes the salinity transport equation and the temperature transport equation: The salinity transport equation is:

[0071] The temperature transport equation is:

[0072] Where S represents salinity, and Indicates that the definition is and The velocity in the normal direction, Indicated in The vertical velocity in the coordinate system is: represents the vertical turbulent diffusion coefficient, Indicates time, and Represents the two directions of the grid, Indicates the vertical direction.

[0073] Module M6: Transfers the required physical information to the virtual coarse grid and updates the model time and model boundary conditions, and returns to module M2.

[0074] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0075] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A water level implicit calculation method for a bidirectional local nested ocean model, characterized in that: include: Step S1: read the input file and initialize the mode; Step S2: determine whether the current mode time is greater than the preset end time, if so, end the calculation process; if not, execute step S3; Step S3: reading the mode boundary conditions according to the current mode time, and solving the momentum equation in three steps using the operator splitting method, bringing the positive pressure term in the third step into the continuity equation to solve the water level value implicitly; Step S4: Substituting the water level value into the Mellor-Yamada 2.5-order turbulence closed model to calculate the vertical turbulent viscosity coefficient and the vertical turbulent diffusion coefficient; Step S5: using the vertical turbulent viscosity coefficient and the vertical turbulent diffusion coefficient, and using the operator splitting method to solve the material transport equation in two steps to obtain corresponding physical information; Step S6: transfer the required physical information to the virtual coarse grid and update the model time and model boundary conditions, and return to step S2.

2. The water level implicit calculation method of the bidirectional local nested ocean model according to claim 1 is characterized in that: The pattern boundary condition refers to the physical information at the pattern grid boundary; The physical information includes tidal current, tide level, salinity and temperature, and the values ​​corresponding to the boundary points are different at different times.

3. The water level implicit calculation method of the bidirectional local nested ocean model according to claim 1 is characterized in that: The formula for the time variation term in the momentum equation is as follows: Among them, u and v represent the horizontal flow velocity in the curvilinear coordinate system, n represents the time step, a represents one-third of the time step, b represents two-thirds of the time step, Δt represents the time step, D represents the total water depth, and J represents the Jacobian function; The material transport equation includes the salinity transport equation and the temperature transport equation: The salinity transport equation is: The temperature transport equation is: Where S represents salinity, and represents the velocity defined in the normal direction of ξ and η, ω represents the vertical velocity in the σ coordinate system, K h represents the vertical turbulent diffusion coefficient, t represents time, ξ and η represent the two directions of the grid, and σ represents the vertical direction.

4. The water level implicit calculation method of the bidirectional local nested ocean model according to claim 1 is characterized in that: The step S3 comprises: Step S3.1: The time variation term is calculated using the time forward difference format, the advection term is calculated using the high-precision HSIMT format, and the baroclinic term, curvature term, Coriolis force term and horizontal diffusion term are calculated using the spatial central difference explicit processing to obtain the velocity information of the actual grid and the virtual fine grid. and Step S3.2: Implicit processing of the vertical diffusion term to calculate the velocity information of the actual grid and the virtual fine grid and Then, according to the flux conservation, replace the velocity information of the virtual coarse grid and Step S3.3: Only the positive pressure term generated by the external gravity wave is considered, and the positive pressure term is substituted into the continuity equation and the water level is solved using the implicit format to obtain the n+1 step water level value ζ of the actual grid and the virtual fine grid n+1 ; Step S3.4: Replace the water level value ζ of the virtual coarse grid according to the flux conservation n+1 , and then the water level value ζ n+1 The velocity information of the virtual coarse grid is obtained by back-tracking Replace the velocity information of the virtual coarse grid according to the flux conservation Step S3.5: Obtain the actual grid velocity information through the continuity equation update Where ω represents the flow velocity information in the vertical direction.

5. The water level implicit calculation method of the bidirectional local nested ocean model according to claim 1 is characterized in that: The method of solving the material transport equation in two steps by using the operator splitting method in step S5 includes: In the first step, the advection term and horizontal diffusion term are processed using the HSIMT format and the Euler format, respectively; The second step is to perform implicit processing on the vertical diffusion term according to the vertical turbulent viscosity coefficient and the vertical turbulent diffusion coefficient.

6. A water level implicit calculation system for a bidirectional local nested ocean model, characterized in that: include: Module M1: reads input file and initializes the mode; Module M2: Determine whether the current mode time is greater than the preset end time. If so, end the calculation process; if not, execute module M3; Module M3: Reading the mode boundary conditions according to the current mode time, and solving the momentum equation in three steps using the operator splitting method, bringing the positive pressure term in the third step into the continuity equation to solve the water level value implicitly; Module M4: Substituting the water level value into the Mellor-Yamada 2.5-order turbulence closed model to calculate the vertical turbulent viscosity coefficient and the vertical turbulent diffusion coefficient; Module M5: by using the vertical turbulent viscosity coefficient and the vertical turbulent diffusion coefficient, the material transport equation is solved in two steps using the operator splitting method to obtain corresponding physical information; Module M6: Transfers the required physical information to the virtual coarse grid and updates the model time and model boundary conditions, and returns to module M2.

7. The water level implicit calculation system of the bidirectional local nested ocean model according to claim 6 is characterized in that: The pattern boundary condition refers to the physical information at the pattern grid boundary; The physical information includes tidal current, tide level, salinity and temperature, and the values ​​corresponding to the boundary points are different at different times.

8. The water level implicit calculation system of the bidirectional local nested ocean model according to claim 6 is characterized in that: The formula for the time variation term in the momentum equation is as follows: Among them, u and v represent the horizontal flow velocity in the curvilinear coordinate system, n represents the time step, a represents one-third of the time step, b represents two-thirds of the time step, Δt represents the time step, D represents the total water depth, and J represents the Jacobian function; The material transport equation includes the salinity transport equation and the temperature transport equation: The salinity transport equation is: The temperature transport equation is: Where S represents salinity, and represents the velocity defined in the normal direction of ξ and η, ω represents the vertical velocity in the σ coordinate system, K h represents the vertical turbulent diffusion coefficient, t represents time, ξ and η represent the two directions of the grid, and σ represents the vertical direction.

9. The water level implicit calculation system of the bidirectional local nested ocean model according to claim 6, characterized in that: The module M3 comprises: Module M3.1: The time variation term uses the time difference format, the advection term uses the high-precision HSIMT format, the baroclinic term, curvature term, Coriolis force term and horizontal diffusion term use the spatial central difference explicit processing, and the velocity information of the actual grid and virtual fine grid is calculated. and Module M3.2: Implicit treatment of vertical diffusion terms, calculating the velocity information of the actual grid and virtual fine grid and Then, according to the flux conservation, replace the velocity information of the virtual coarse grid and Module M3.3: Only the positive pressure term generated by external gravity waves is considered. The positive pressure term is substituted into the continuity equation and the water level is solved using the implicit format to obtain the n+1 step water level value ζ of the actual grid and the virtual fine grid. n+1 ; Module M3.4: Replace the water level value ζ of the virtual coarse grid according to flux conservation b+1 , and then the water level value ζ n+1 The velocity information of the virtual coarse grid is obtained by back-tracking Replace the velocity information of the virtual coarse grid according to the flux conservation Module M3.5: Obtaining flow velocity information of the actual grid through continuity equation update Where ω represents the flow velocity information in the vertical direction.

10. The water level implicit calculation system of the bidirectional local nested ocean model according to claim 6, characterized in that: The two-step method of solving the material transport equation using the operator splitting method in the module M5 includes: In the first step, the advection term and horizontal diffusion term are processed using the HSIMT format and the Euler format, respectively; The second step is to perform implicit processing on the vertical diffusion term according to the vertical turbulent viscosity coefficient and the vertical turbulent diffusion coefficient.

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