CN-121981010-A - Sea wave numerical mode second-order spatial advection method based on SCVT unstructured grid

CN121981010ACN 121981010 ACN121981010 ACN 121981010ACN-121981010-A

Abstract

The embodiment of the invention discloses a second-order spatial advection method of an ocean wave numerical mode based on SCVT unstructured grids, which comprises the steps of constructing a SCVT unstructured grid system, establishing an index mapping relation between units and edges, configuring wave action quantity at the center of the units, configuring advection speed at the middle point of the grid edges, further performing spatial dispersion on geospatial advection items based on a finite volume method, calculating flux on each grid edge after dispersion, determining an upstream unit according to a flow velocity direction, acquiring wave action quantity and gradient of the upstream unit, obtaining high-precision wave action quantity value at the middle point of the grid edges through linear reconstruction, and finally combining spectrum space advection with source sink items to finish time integration and ocean wave forecast. According to the invention, the second-order windward format ocean wave advection calculation is realized through SCVT grids, so that the ocean wave simulation precision is remarkably improved, the numerical dissipation is effectively inhibited, meanwhile, the variable resolution grid configuration is supported, and the calculation efficiency is improved on the premise of ensuring the near-shore and other key area simulation precision.

Inventors

GAO YUANYONG
YU FUJIANG
YUAN YE
Pang Renbo
ZHANG YU

Assignees

国家海洋环境预报中心

Dates

Publication Date: 20260505
Application Date: 20260127

Claims (10)

1. The sea wave numerical mode second-order spatial advection method based on SCVT unstructured grids is characterized by comprising the following steps of: Establishing SCVT unstructured grid systems of the simulation area, and establishing index mapping relations for all grid cells and grid edges, wherein the index mapping relations at least comprise the corresponding relation between each grid cell and adjacent grid cells, the corresponding relation between each grid cell and the grid edges contained in each grid cell, and the corresponding relation between each grid edge and two adjacent grid cells; the wave action quantity is configured at the center of each grid unit, and the advection speed of the geographic space is configured at the middle point of each grid side; Based on a finite volume method, carrying out space dispersion on geospatial advection items in the ocean wave spectrum balance equation on the SCVT unstructured grids to obtain a discrete equation of the wave action quantity of each grid unit changing along with time; Determining an upstream grid unit based on the advection speed direction of the grid edge, acquiring the wave action quantity and gradient of the center of the upstream grid unit, and obtaining a second-order-precision wave action quantity value at the midpoint of the grid edge through linear reconstruction; Substituting the calculated grid edge flux into the discrete equation, combining the spectrum space advection term and the source sink term, completing integral calculation of the wave mode in the time dimension, and outputting a wave forecasting result.
2. The method for ocean wave numerical mode second order spatial advection based on SCVT unstructured grids according to claim 1, wherein the index mapping relation is established through the following data structure: Defining an array cellsOnCell, an array edgesOnCell, and an array cellsOnEdge, respectively; Wherein the array cellsOnCell is used for storing indexes of all adjacent grid cells of each grid cell, the array edgesOnCell is used for storing indexes of all grid edges constituting each grid cell, and the array cellsOnEdge is used for storing indexes of two adjacent grid cells of each grid edge.
3. The method for ocean wave numerical mode second order spatial advection based on SCVT unstructured grids according to claim 1, wherein the method for spatially dispersing geospatial advection terms in an ocean wave spectrum balance equation on the SCVT unstructured grids based on a finite volume method to obtain a discrete equation of wave action quantity of each grid unit changing with time comprises the following steps: The discrete equation is the change rate of wave action quantity of the center of any grid unit along with time, which is equal to the ratio of the negative value of the sum of normal wave action quantity flux on all sides of the unit to the area of the unit, and the sum of the spectrum space advection term and the source sink term.
4. A method of ocean wave numerical mode second order spatial advection based on SCVT unstructured grids as claimed in claim 1, wherein obtaining the second order precision wave action magnitude at the midpoint of the grid edge by linear reconstruction comprises: And adding the dot product of the wave action gradient at the center and the displacement vector pointing to the midpoint of the current grid edge from the center to the wave action value at the center of the upstream grid cell to obtain the wave action reconstruction value at the midpoint of the grid edge.
5. The method for ocean wave numerical mode second order spatial advection based on SCVT unstructured grids according to claim 4, wherein the wave action gradient of the center of the upstream grid unit is calculated by using a green-Gao Sigong method or a least square method.
6. The method for ocean wave numerical mode second order spatial advection based on SCVT unstructured grids according to claim 1, wherein for wave action quantity flux on each grid edge in the obtained discrete equation, a second order windward format is adopted to calculate, wherein an upstream grid unit is determined based on an advection speed direction on the grid edge, wave action quantity and gradient of the center of the upstream grid unit are obtained, and a wave action quantity value of second order precision at a midpoint of the grid edge is obtained through linear reconstruction, and the method further comprises the steps of: A limiter is introduced to limit the value obtained by the linear reconstruction to prevent numerical oscillation in a region where the wave action gradient is large.
7. A method of ocean wave numerical mode second order spatial advection based on a SCVT unstructured grid as defined in claim 6 wherein the limiter is a Barth-Jespersen limiter.
8. A method of ocean wave numerical mode second order spatial advection based on SCVT unstructured grids as claimed in claim 1 wherein the SCVT unstructured grid is a variable resolution grid with high resolution in critical areas of intense ocean wave energy variation in the analogue region and low resolution in other areas.
9. The method for performing second-order spatial advection of the ocean wave numerical mode based on the SCVT unstructured grid according to claim 1, wherein integral calculation of the ocean wave mode in a time dimension adopts a parallel calculation mode, and parallel tasks are divided based on units or edges of the SCVT unstructured grid.
10. A method of ocean wave numerical mode second order spatial advection based on SCVT unstructured grids as claimed in claim 1, wherein the upstream grid cell is determined by detecting the normal group velocity on the grid edge, comprising in particular: And if the normal group velocity is positive, an upstream grid cell is defined as the current grid cell corresponding to the discrete equation, and if the normal group velocity is negative, acquiring an adjacent grid cell positioned on the other side of the edge through an index mapping relation to serve as the upstream grid cell.

Description

Sea wave numerical mode second-order spatial advection method based on SCVT unstructured grid Technical Field The embodiment of the invention relates to the technical field of wave numerical simulation and computational fluid dynamics, in particular to a SCVT non-structural grid-based wave numerical mode second-order spatial advection method. Background The wave numerical simulation is an important technical means in the fields of ocean engineering, weather forecast, ship navigation, coast protection and the like, and is characterized in that the wave spectrum balance equation is subjected to high-precision and high-efficiency numerical solution. The ocean wave spectrum equation comprises two parts of geospatial advection and spectral space advection, wherein the geospatial advection determines the propagation process of ocean wave energy in the geospatial, and directly influences the simulation precision and forecasting capability of ocean waves. Currently, the third generation of wave numerical modes in the international mainstream mostly adopts structural grids (such as equal longitude and latitude grids) or non-structural grids (such as triangular grids) for space dispersion. The SCVT (Spherical Centroidal Voronoi Tessellation) grid is used as an unstructured grid, and is gradually applied to a global or regional ocean mode because of the advantages of regular grid cell shape, flexible variation of resolution, suitability for spherical simulation and the like. SCVT grids allow high resolution to be used in critical areas such as offshore, strait and the like, and low resolution to be used in open sea, so that the accuracy is guaranteed and the calculation efficiency is remarkably improved. However, in SCVT grid-based ocean wave modes, the numerical discrete scheme of geospatial advection terms still faces significant challenges. In the currently disclosed literature and practice, the SCVT grids mostly adopt a first-order windward format to carry out advection calculation. The proposal has the advantages of strong numerical stability and simple realization, but the cut-off error is only of a first order, which results in larger numerical dissipation and phase error in the process of simulating wave propagation, and is specifically expressed as follows: The simulation precision is insufficient, namely, the first-order format is easy to have a blurring phenomenon when capturing the wave spectrum shape and the wave energy spatial gradient change (such as typhoon center wave peak value and near shore wave energy focusing), and the fine distribution of the wave energy is difficult to accurately reflect; The energy non-physical dissipation is serious, namely, in order to ensure stability, a first-order windward format introduces larger value dissipation, so that the wave energy is not physically attenuated in the propagation process, the wave energy conservation is influenced, and the simulation of the long-distance propagation of the swell, the reflection and diffraction of the off-shore waves and other processes is particularly unfavorable; the resolution dependence is strong, and in order to achieve higher simulation precision, the resolution of the grid is often required to be greatly improved, so that the calculation cost is increased sharply. Disclosure of Invention Therefore, the embodiment of the invention provides a SCVT unstructured grid-based ocean wave numerical mode second-order spatial advection method, which aims to solve the technical problems of low advection calculation precision and large dissipation in the existing SCVT grid ocean wave mode. In order to achieve the above object, the embodiment of the present invention provides the following technical solutions: According to a first aspect of an embodiment of the present invention, there is provided a method for ocean wave numerical mode second order spatial advection based on SCVT unstructured grids, the method comprising: Establishing SCVT unstructured grid systems of the simulation area, and establishing index mapping relations for all grid cells and grid edges, wherein the index mapping relations at least comprise the corresponding relation between each grid cell and adjacent grid cells, the corresponding relation between each grid cell and the grid edges contained in each grid cell, and the corresponding relation between each grid edge and two adjacent grid cells; the wave action quantity is configured at the center of each grid unit, and the advection speed of the geographic space is configured at the middle point of each grid side; Based on a finite volume method, carrying out space dispersion on geospatial advection items in the ocean wave spectrum balance equation on the SCVT unstructured grids to obtain a discrete equation of the wave action quantity of each grid unit changing along with time; Determining an upstream grid unit based on the advection speed direction of the grid edge, acquiring the wave action quantity and gradient o