Sea wave numerical mode second-order space advection method based on SCVT unstructured grid

Abstract

The embodiment of the invention discloses a sea wave numerical mode second-order space advection method based on an SCVT unstructured grid, and the method comprises the steps: constructing an SCVT unstructured grid system, building an index mapping relation between a unit and an edge, configuring a wave action quantity at the center of the unit, and configuring an advection speed at the midpoint of the edge of the grid; spatial discretization is carried out on geographic space advection items based on a finite volume method; for flux calculation on each discrete grid edge, a second-order windward format is adopted, an upstream unit is determined according to the flow velocity direction, the wave action quantity and gradient of the upstream unit are obtained, and a high-precision wave action quantity value at the midpoint of the grid edge is obtained through linear reconstruction; and finally, combining spectrum space advection and a source convergence item to finish time integration and sea wave forecasting. According to the method, sea wave advection calculation of the second-order windward format is achieved in the SCVT grid, the precision of sea wave simulation is remarkably improved, numerical dissipation is effectively restrained, meanwhile, variable-resolution grid configuration is supported, and the calculation efficiency is improved on the premise that the simulation precision of key areas such as a near-shore area is guaranteed.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation and computational fluid dynamics of ocean waves, specifically to a second-order spatial advection method for a numerical model of ocean waves based on SCVT unstructured meshes. Background Technology

[0002] Ocean wave numerical simulation is an important technical means in fields such as marine engineering, weather forecasting, ship navigation, and coastal protection. Its core lies in the high-precision and high-efficiency numerical solution of the ocean wave spectral equilibrium equation. The ocean wave spectral equation consists of two parts: geographic spatial advection and spectral spatial advection. Among them, geographic spatial advection determines the propagation process of ocean wave energy in geographic space, which directly affects the simulation accuracy and forecasting capability of ocean waves.

[0003] Currently, most mainstream third-generation numerical wave models internationally employ structured grids (such as equal-latitude and longitude grids) or unstructured grids (such as triangular grids) for spatial discretization. Among these, the Spherical Centroidal Voronoi Tessellation (SCVT) grid, as an unstructured grid, is increasingly being used in global or regional ocean models due to its advantages such as regular grid cell shapes, flexible resolution, and suitability for spherical simulations. The SCVT grid allows for high resolution in key areas such as nearshore and straits, while lower resolution is used in open sea areas, thus significantly improving computational efficiency while maintaining accuracy.

[0004] However, numerical discretization schemes for geospatial advection terms in wave models based on the SCVT grid still face significant challenges. Currently, published literature and practical applications mostly employ a first-order upwind scheme for advection calculations on the SCVT grid. While this scheme boasts advantages such as strong numerical stability and simplicity, its truncation error is only first-order, leading to substantial numerical dissipation and phase errors during wave propagation simulations. Specifically:

[0005] Insufficient simulation accuracy: First-order schemes are prone to fuzziness when capturing wave spectrum and spatial gradient changes in wave energy (such as peak wave height at the center of a typhoon and nearshore wave energy focusing), making it difficult to accurately reflect the detailed distribution of wave energy.

[0006] Severe non-physical energy dissipation: To ensure stability, the first-order upwind scheme introduces a large numerical dissipation, which leads to non-physical attenuation of wave energy during propagation, affecting wave energy conservation, and is particularly unfavorable for simulating processes such as long-distance propagation of swells, nearshore wave reflection and diffraction.

[0007] Highly resolution-dependent: To achieve higher simulation accuracy, it is often necessary to significantly increase the grid resolution, which leads to a sharp increase in computational costs. Summary of the Invention

[0008] To address this, this invention provides a second-order spatial advection method for wave numerical models based on SCVT unstructured grids, in order to solve the technical problems of low advection calculation accuracy and high energy dissipation in existing SCVT grid wave models.

[0009] To achieve the above objectives, the embodiments of the present invention provide the following technical solutions:

[0010] According to a first aspect of the present invention, a second-order spatial advection method for ocean wave numerical models based on SCVT unstructured grids is provided, the method comprising:

[0011] Construct an unstructured SCVT mesh system for the simulation region and establish index mapping relationships for all mesh cells and mesh edges. The index mapping relationships include at least the correspondence between each mesh cell and its adjacent mesh cells, the correspondence between each mesh cell and its contained mesh edges, and the correspondence between each mesh edge and its two adjacent mesh cells.

[0012] The wave action is placed at the center of each grid cell, and the advection velocity in geographic space is placed at the midpoint of each grid edge.

[0013] Based on the finite volume method, the geospatial advection term in the wave spectrum equilibrium equation is spatially discretized on the SCVT unstructured grid to obtain the discrete equation of wave action as a function of time for each grid cell.

[0014] For the wave flux on each grid edge in the obtained discrete equation, a second-order upwind scheme is used for calculation: the upstream grid cell is determined based on the direction of the advection velocity on the grid edge, the wave flux and its gradient at the center of the upstream grid cell are obtained, and the second-order accurate wave flux value at the midpoint of the grid edge is obtained through linear reconstruction.

[0015] Substitute the calculated edge fluxes of each grid into the discrete equation, and combine the advection term and source-sink term in the spectral space to complete the integral calculation of the wave model in the time dimension, and output the wave forecast results.

[0016] Furthermore, the index mapping relationship is established using the following data structure:

[0017] Define arrays cellsOnCell, edgesOnCell, and cellsOnEdge respectively;

[0018] The array cellsOnCell stores the indices of all adjacent grid cells for each grid cell, the array edgesOnCell stores the indices of all grid edges that make up each grid cell, and the array cellsOnEdge stores the indices of the two grid cells adjacent to each grid edge.

[0019] Furthermore, based on the finite volume method, the geospatial advection term in the wave spectral equilibrium equation is spatially discretized on the SCVT unstructured grid to obtain a discrete equation for the wave action of each grid cell as a function of time, including:

[0020] The discrete equation is the rate of change of the wave action at the center of any grid cell with time, which is equal to the ratio of the negative sum of the normal wave action fluxes on all edges of the cell to the area of ​​the cell, plus the sum of the spectral space advection term and the source-sink term.

[0021] Furthermore, the second-order accurate wave action value at the midpoint of the grid edge is obtained through linear reconstruction, including:

[0022] The wave action value at the center of the upstream grid cell is added to the dot product of the wave action gradient at that center and the displacement vector pointing from that center to the midpoint of the current grid edge to obtain the reconstructed wave action value at the midpoint of the grid edge.

[0023] Furthermore, the wave action gradient at the center of the upstream grid cell is calculated using the Green-Gauss formula or the least squares method.

[0024] Furthermore, for the wave action flux at each grid edge in the obtained discrete equation, a second-order upwind scheme is used for calculation: the upstream grid cell is determined based on the advection velocity direction at the grid edge, the wave action and its gradient at the center of the upstream grid cell are obtained, and the second-order accurate wave action value at the midpoint of the grid edge is obtained through linear reconstruction. This also includes:

[0025] A limiter is introduced to restrict the values ​​obtained by the linear reconstruction in order to prevent numerical oscillations in regions with large wave action gradients.

[0026] Furthermore, the limiter is a Barth-Jespersen limiter.

[0027] Furthermore, the SCVT unstructured mesh is a variable resolution mesh, using high resolution in key areas of the simulation region where wave energy changes drastically, and low resolution in other areas.

[0028] Furthermore, the integral calculation of the wave pattern in the time dimension adopts a parallel computing method, and the parallel task is based on the cells or edges of the SCVT unstructured mesh.

[0029] Furthermore, the upstream grid cells are determined by detecting the normal group velocity on the grid edges, specifically including:

[0030] If the normal group velocity is positive, the upstream grid cell is defined as the current grid cell corresponding to the discrete equation. If the normal group velocity is negative, the adjacent grid cell on the other side of the edge is obtained as the upstream grid cell through the index mapping relationship.

[0031] The embodiments of the present invention have the following advantages:

[0032] This invention constructs an unstructured SCVT grid system and establishes an index mapping relationship between cells and edges. Wave action is positioned at the cell center, and advection velocity at the midpoint of the grid edge. Then, the geospatial advection term is spatially discretized using the finite volume method. For flux calculation on each discretized grid edge, a second-order upwind scheme is used. The upstream cell is determined based on the velocity direction, and its wave action and gradient are obtained. High-precision wave action values ​​at the midpoint of the grid edge are obtained through linear reconstruction. Finally, time integration and wave forecasting are completed by combining spectral spatial advection and source / sink terms. This invention significantly improves the accuracy of wave simulation and effectively suppresses numerical dissipation. It also supports variable resolution grid configuration, improving computational efficiency while ensuring simulation accuracy in key areas such as nearshore regions. It is suitable for global and regional operational wave forecasting and marine engineering applications. Attached Figure Description

[0033] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0034] The structures, proportions, sizes, etc. illustrated in this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed herein, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0035] Figure 1 A flowchart illustrating a second-order spatial advection method for a wave numerical model based on an SCVT unstructured grid, provided for an embodiment of the present invention;

[0036] Figure 2 This is a schematic diagram of SCVT grid discretization in a second-order spatial advection method for a wave numerical model based on an SCVT unstructured grid, provided in an embodiment of the present invention.

[0037] Figure 3This invention provides an effective wave height scatter plot for ocean buoy verification in a second-order spatial advection method for a wave numerical model based on an SCVT unstructured grid, as provided in an embodiment of the invention. Detailed Implementation

[0038] The following specific embodiments illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] The motion of ocean waves can be described by the wave spectrum equation. Ocean wave numerical models discretize the wave spectrum equation into grids in geographic space and spectral space for numerical solution. Currently, the mainstream wave model is the third-generation wave model. The advection transport part of the wave spectrum equation includes geographic advection and spectral space advection. Geographic advection determines the propagation of ocean waves in geographic space, while spectral space advection determines how ocean waves propagate in frequency and direction.

[0040] The accuracy of wave model simulations is closely related to the numerical discretization schemes used for various advection processes; higher-order numerical discretization schemes often yield better results. The numerical discretization scheme for geospatial advection is also closely related to the discretization grid used. Therefore, choosing the right grid for discretization and designing a high-order numerical advection scheme for that grid is one of the important issues in solving wave model problems. The grid will affect the forecasting performance and application scope of the ocean model.

[0041] Currently, the mainstream third-generation wave numerical models internationally employ grids that can be categorized into structured and unstructured grids. Structured grids are primarily isotropic grids, while unstructured grids mainly include triangular grids and SCVT grids. In wave models using isotropic and triangular grids, first- or second-order accuracy geospatial advection schemes have been successfully implemented. However, in SCVT grids, existing work only uses first-order accuracy upwind schemes; there are currently no second-order accuracy schemes designed specifically for this grid in wave numerical models.

[0042] The first-order upwind schemes of the SCVT grid currently in use all have certain shortcomings. The core advantage of the second-order accurate schemes over the first-order upwind schemes is that they significantly improve simulation accuracy while ensuring numerical stability, and at the same time significantly suppress numerical dissipation and phase error. They are particularly suitable for processes such as wave spectrum evolution and wave energy transfer, which have high requirements for spectral shape and energy conservation.

[0043] The core advantage of the second-order precision scheme over the first-order upwind scheme is that it significantly improves simulation accuracy while ensuring numerical stability, and at the same time significantly suppresses numerical dissipation and phase error. It is especially suitable for processes such as wave spectrum evolution and wave energy transfer, which have high requirements for spectral shape and energy conservation.

[0044] Advantage 1: The second-order algorithm has higher numerical accuracy and reduces truncation error.

[0045] The accuracy of numerical schemes is dominated by truncation error. The truncation error of a first-order upwind scheme is first-order (O(Δx)), while that of a second-order scheme is second-order (O(Δx²)) (Δx is the grid step size). For wave models, this means that, at the same grid resolution, the second-order scheme can more accurately capture the spatial distribution of the spectrum (such as the gradual change in nearshore wave energy and the shift of spectral peaks at the typhoon center) and the details of the spectral shape (such as energy attenuation in the high-frequency band and the separation of multi-peak spectra). The low accuracy of the first-order scheme leads to the "blurring" of spectral peaks, especially when simulating wave propagation. The error of the first-order scheme accumulates with the propagation distance, while the second-order scheme better preserves the spectral characteristics of the wave.

[0046] Advantage 2: The second-order algorithm significantly reduces numerical dissipation and protects wave energy conservation.

[0047] The core drawback of the first-order upwind scheme is its excessive numerical dissipation—to ensure stability, it artificially causes wave energy to attenuate during grid propagation. This non-physical dissipation is fatal to wave simulation. For open ocean areas where wind input and dissipation are balanced, the first-order scheme underestimates wave height (especially the energy of high-frequency waves). For nearshore reflection and diffraction processes, the first-order scheme causes the energy of reflected waves to "disappear" rapidly, failing to accurately simulate the superposition of nearshore waves. The second-order scheme reduces numerical dissipation by an order of magnitude, more closely approximating the energy conservation characteristics of wave evolution, and can accurately simulate the long-distance propagation of wave energy (such as ocean swells).

[0048] This invention applies a second-order precision geospatial advection scheme to a wave model based on an unstructured SCVT grid, which can overcome the problem of low numerical precision in previous first-order schemes, reduce truncation error, significantly reduce numerical dissipation, and protect wave energy conservation.

[0049] refer to Figure 1 This invention discloses a second-order spatial advection method based on an SCVT unstructured grid numerical model of ocean waves, the method comprising:

[0050] Construct an unstructured SCVT mesh system for the simulation region and establish index mapping relationships for all mesh cells and mesh edges. The index mapping relationships include at least the correspondence between each mesh cell and its adjacent mesh cells, the correspondence between each mesh cell and its contained mesh edges, and the correspondence between each mesh edge and its two adjacent mesh cells.

[0051] The wave action is placed at the center of each grid cell, and the advection velocity in geographic space is placed at the midpoint of each grid edge.

[0052] Based on the finite volume method, the geospatial advection term in the wave spectrum equilibrium equation is spatially discretized on the SCVT unstructured grid to obtain the discrete equation of wave action as a function of time for each grid cell.

[0053] For the wave flux on each grid edge in the obtained discrete equation, a second-order upwind scheme is used for calculation: the upstream grid cell is determined based on the direction of the advection velocity on the grid edge, the wave flux and its gradient at the center of the upstream grid cell are obtained, and the second-order accurate wave flux value at the midpoint of the grid edge is obtained through linear reconstruction.

[0054] Substitute the calculated edge fluxes of each grid into the discrete equation, and combine the advection term and source-sink term in the spectral space to complete the integral calculation of the wave model in the time dimension, and output the wave forecast results.

[0055] The conservation formula for the action of ocean waves is as follows:

[0056] (1)

[0057] The first term on the left side of the equation is the local variation of the wave action N over time, the second is the variation of N caused by the advection in geographic space, the third and fourth terms are the advection in the spectral space, and the right side of the equation is the source and sink terms.

[0058] This embodiment of the invention only involves geospatial transport, which is the second term of the above equation, i.e., the geospatial transport term. For ease of discussion, the above formula is simplified to the following form, that is, only the local temporal variation term and the geospatial advection term are retained, and the remaining terms are merged into F:

[0059] (2)

[0060] (3)

[0061] In this way, the model discretizes the wave action in continuous space into a grid for numerical solution, and finally predicts or simulates the waves.

[0062] Based on the concept of finite volume, a second-order upwind advection scheme is adopted, and the wave spectrum equilibrium equation is applied to the SCVT unstructured grid:

[0063] S1: All grid cells within the simulation region are uniquely numbered using the subscript iCell, numbered 1, 2…nCells. Each grid cell has nEOC edges and nCOC adjacent grid cells, where nEOC and nCOC are typically 6. All grid edges within the simulation region are uniquely numbered using the subscript iEdge, numbered 1, 2…nEdges. Each edge has two adjacent grid cells on its left and right.

[0064] S2: Indexing method between grid cells and edges. The `cellsOnCell(nCOC, nCells)` array is used to determine the indices of the adjacent grid cells of a grid cell. For the i-th grid cell, the indices of its adjacent grid cells are, in order, `cellsOnCell(1, iCell)`, `cellsOnCell(2, iCell)`, ..., `cellsOnCell(nCOC, iCell)`. The `edgesOnCell(nEOC, nCells)` array is used to determine the indices of the grid edges corresponding to a grid cell. For the i-th grid cell, the indices of the grid edges that make up that grid cell are, in order, `edgesOnCell(1, iCell)`, `edgesOnCell(2, iCell)`, ..., `edgesOnCell(nEOC, iCell)`. The array cellsOnEdge(2,nEdges) is used to determine the indices of two adjacent grid cells of a grid edge. For the i-th edge, the indices of its left and right adjacent grid cells are cellsOnEdge(1,nEdges) and cellsOnEdge(2,nEdges), respectively.

[0065] S3: Variable Configuration. The wave action N is distributed in the center of the grid (cell), while the advection velocity in geographic space is distributed on the edge of the grid (edge). Two adjacent grids share an edge, and their advection velocities are of the same magnitude but opposite in direction.

[0066] S4: Spatial Discretization. Discretize formula (2), assuming the prediction of the i-th cell is calculated, its expression is as follows:

[0067] (4)

[0068] In the above formula, For the first on the iCell grid The group velocity on the edge normal (positive outwards), For the first Wave action at the midpoint of the edge, For the first The length of an edge is used as a variable on the edge. Once the index of iCell is determined, it can be obtained using edgesOnCell(i, iCell). The area of ​​the grid ( Figure 2 (Medium gray grid), where F represents the advection term and source / sink term in the spectral space. Its principle is based on the idea of ​​finite volume, that is, for a certain grid, its local variation is the net flux of inflow and outflow along the six edges.

[0069] S5: Second-order upwind advection scheme, the key lies in calculation. That is, the first The wave action at the midpoint of the edge. Ocean wave geospatial transmission has significant physical meaning, primarily influenced by upstream information. Therefore, using an upwind pattern more closely approximates the actual flow, where information originates from upstream. In this discrete scheme, the specific second-order upwind pattern is as follows:

[0070] (5)

[0071]

[0072] If it is greater than 0, it flows outward. Based on the upwind pattern, its upstream grid is the grid iCell itself. If it is less than 0, it flows inward. Based on the upwind pattern, its upstream is the adjacent grid, which can be obtained by indexing cellsOnCell(i,iCell). If it is equal to 0, there is no flux, and there is no need to consider upstream and downstream. Let N be the gradient of N. The subscript c,0 represents the gradient of N calculated from the current grid center N and the nEdges N around it. It can be obtained by looping i=0,nEOC and indexing through edgesOnCell(i,iCell). The specific calculation formula is (6). This represents the distance from the center of the grid to the edge.

[0073] (6)

[0074] In the above formula For the first The wave action at the midpoint of the edge is indicated by the superscript 'a', which is the average of N values ​​of the two cells on the left and right sides of the edge.

[0075] S6: Calculate the other parts of formula (1), complete the wave pattern integral calculation, and obtain the forecast result.

[0076] The embodiments of the present invention use the Green-Gauss formula or the least squares method to calculate the gradient of the variable based on the center values ​​of the cell and its neighbors; the gradient is used to linearly reconstruct the variable distribution within the cell, thereby improving the format from first-order to second-order accuracy; a limiter (such as the Barth-Jespersen limiter) is introduced to restrict the reconstructed value at places with large gradients (such as near fronts) to prevent numerical oscillations.

[0077] The SCVT unstructured grid was applied to the wave numerical model, and the unstructured grid was applied to the wave geospatial advection model using the upwind mode.

[0078] Using the SCVT grid allows wave forecasting to focus on simulations of key areas, gradually transitioning from a resolution of 10km in the far seas to 2km near the Chinese coast in the Northwest Pacific. This ensures the accuracy of wave forecasts in China's coastal areas while conserving computational resources for non-critical areas in the far seas.

[0079] With a global 10km resolution SCVT grid configuration, the simulation results of this embodiment of the invention show reasonable distribution characteristics, such as the westerly wind belts in the Northern and Southern Hemispheres, which have high wind speeds throughout the year and correspond to large significant wave heights; there are also some strong cyclones, whose rotating wind areas also drive large significant wave heights.

[0080] Figure 3 The scatter plot of effective wave height based on ocean buoy testing shows that the root mean square error (RMSE) is 0.54 m, which is based on a year of statistical data of effective wave height observed by ocean buoy stations. This indicates that the application of the SCVT unstructured grid to the geospatial advection of the wave model has good application effect based on the finite volume approach.

[0081] Table 1. Statistics on the significant wave height error of marine buoy stations

[0082] Buoy Station Name Number of samples / Significant wave height RMSE / m MF02001 8722 0.56 MF03003 8731 0.35 MF06001 8473 0.56 MF06005 8472 0.54 MF14001 8095 0.41 MF17001 7644 0.84 average 8356 0.54

[0083] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A second-order spatial advection method based on a numerical wave model using an SCVT unstructured grid, characterized in that, The method includes: Construct an unstructured SCVT mesh system for the simulation region and establish index mapping relationships for all mesh cells and mesh edges. The index mapping relationships include at least the correspondence between each mesh cell and its adjacent mesh cells, the correspondence between each mesh cell and its contained mesh edges, and the correspondence between each mesh edge and its two adjacent mesh cells. The wave action is placed at the center of each grid cell, and the advection velocity in geographic space is placed at the midpoint of each grid edge. Based on the finite volume method, the geospatial advection term in the wave spectrum equilibrium equation is spatially discretized on the SCVT unstructured grid to obtain the discrete equation of wave action as a function of time for each grid cell. For the wave flux on each grid edge in the obtained discrete equation, a second-order upwind scheme is used for calculation: the upstream grid cell is determined based on the direction of the advection velocity on the grid edge, the wave flux and its gradient at the center of the upstream grid cell are obtained, and the second-order accurate wave flux value at the midpoint of the grid edge is obtained through linear reconstruction. Substitute the calculated edge fluxes of each grid into the discrete equation, and combine the advection term and source-sink term in the spectral space to complete the integral calculation of the wave model in the time dimension, and output the wave forecast results.

2. The second-order spatial advection method for ocean wave numerical models based on SCVT unstructured grids as described in claim 1, characterized in that, The index mapping relationship is established using the following data structure: Define arrays cellsOnCell, edgesOnCell, and cellsOnEdge respectively; The array cellsOnCell stores the indices of all adjacent grid cells for each grid cell, the array edgesOnCell stores the indices of all grid edges that make up each grid cell, and the array cellsOnEdge stores the indices of the two grid cells adjacent to each grid edge.

3. The second-order spatial advection method for ocean wave numerical models based on SCVT unstructured grids as described in claim 1, characterized in that, Based on the finite volume method, the geospatial advection term in the wave spectral equilibrium equation is spatially discretized on the SCVT unstructured grid, yielding a discrete equation for the wave action as a function of time for each grid cell, including: The discrete equation is the rate of change of the wave action at the center of any grid cell with time, which is equal to the ratio of the negative sum of the normal wave action fluxes on all edges of the cell to the area of ​​the cell, plus the sum of the spectral space advection term and the source-sink term.

4. The second-order spatial advection method for ocean wave numerical models based on SCVT unstructured grids as described in claim 1, characterized in that, The second-order accurate wave action value at the midpoint of the grid edge is obtained through linear reconstruction, including: The wave action value at the center of the upstream grid cell is added to the dot product of the wave action gradient at that center and the displacement vector pointing from that center to the midpoint of the current grid edge to obtain the reconstructed wave action value at the midpoint of the grid edge.

5. The second-order spatial advection method for ocean wave numerical models based on SCVT unstructured grids as described in claim 4, characterized in that, The wave action gradient at the center of the upstream grid cell is calculated using the Green-Gauss formula or the least squares method.

6. The second-order spatial advection method for ocean wave numerical models based on SCVT unstructured grids as described in claim 1, characterized in that, For the wave flux at each grid edge in the obtained discrete equations, a second-order upwind scheme is used for calculation: the upstream grid cell is determined based on the advection velocity direction at the grid edge, the wave flux and its gradient at the center of the upstream grid cell are obtained, and the second-order accurate wave flux value at the midpoint of the grid edge is obtained through linear reconstruction. The calculation also includes: A limiter is introduced to restrict the values ​​obtained by the linear reconstruction in order to prevent numerical oscillations in regions with large wave action gradients.

7. The second-order spatial advection method for ocean wave numerical models based on SCVT unstructured grids as described in claim 6, characterized in that, The limiter is a Barth-Jespersen limiter.

8. The second-order spatial advection method for ocean wave numerical models based on SCVT unstructured grids as described in claim 1, characterized in that, The SCVT unstructured mesh is a variable resolution mesh, using high resolution in key areas of the simulation region where wave energy changes drastically, and low resolution in other areas.

9. The second-order spatial advection method for ocean wave numerical models based on SCVT unstructured grids as described in claim 1, characterized in that, The integral calculation of the wave pattern in the time dimension adopts a parallel computing method, and the parallel task is based on the cells or edges of the SCVT unstructured mesh.

10. The second-order spatial advection method for ocean wave numerical models based on SCVT unstructured grids as described in claim 1, characterized in that, The upstream grid cells are determined by detecting the normal group velocity on the grid edges, specifically including: If the normal group velocity is positive, the upstream grid cell is defined as the current grid cell corresponding to the discrete equation. If the normal group velocity is negative, the adjacent grid cell on the other side of the edge is obtained as the upstream grid cell through the index mapping relationship.

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