Generalized mixed bottom coordinate ocean numerical model construction method

Abstract

The invention relates to the technical field of numerical simulation, in particular to a generalized mixed bottom coordinate ocean numerical model construction method, which comprises the following steps of: defining coordinate transformation and vertical speed, introducing a continuously changing vertical layer sequence number as an independent variable, and constructing generalized vertical coordinate transformation; based on the coordinate transformation and the vertical speed definition, deriving a seawater motion equation under a generalized vertical coordinate by taking a vertical layering serial number lambda as an independent variable; designing a novel sigma-z mixed generalized follow-bottom coordinate; and calculating the oblique pressure gradient force and introducing a local density layer junction concept to improve the calculation method.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation technology, and in particular to a method for constructing a generalized hybrid bottom coordinate ocean numerical model. Background Technology

[0002] In regional oceanographic numerical simulations, internationally widely used three-dimensional flow field numerical models primarily employ z-coordinates or σ-coordinates. However, using z-coordinates for spatial discretization creates unnatural stepped topography on the seabed, introducing computational errors to physical processes near the seabed. σ-coordinates, on the other hand, perfectly coincide with both the sea surface and seabed, and employ relative vertical stratification, providing high vertical resolution even in shallower waters. Many mainstream international oceanographic numerical models currently utilize this vertical coordinate system, such as POM, ECOM, ROMS, and FVCOM. The FVCOM model, in particular, employs unstructured triangular meshes and finite volume numerical calculation methods, offering greater horizontal mesh flexibility and computational efficiency. This model is more suitable for numerical studies of the South China Sea, which features irregular and complex coastlines and steep, varied topography.

[0003] The drawbacks of existing technologies are: in steep terrain, the σ coordinate will cause the seabed topography to be discrete in a stepped manner, which will affect the calculation accuracy of near-bottom physical processes; the connection between the z-plane and the σ-plane depends on the minimum transformation depth, which means that the z-plane cannot extend sufficiently into the deep water area, and there may be a reverse "pseudo-slope" or excessive slope at the transformation point; the traditional method of subtracting the overall average density stratification cannot eliminate the influence of local density changes, resulting in a large error in the baroclinic gradient force. Summary of the Invention

[0004] The main objective of this invention is to provide a method for constructing a generalized hybrid bottom coordinate ocean numerical model, which effectively solves the problems mentioned in the background art.

[0005] The technical solution of the present invention is as follows:

[0006] A method for constructing a generalized hybrid bottom-coordinate ocean numerical model is proposed, which includes the following steps:

[0007] S1. Define coordinate transformation and vertical velocity, introduce continuously changing vertical layer number as independent variable, and construct generalized vertical coordinate transformation;

[0008] S2. Based on the above coordinate transformation and definition of vertical velocity, the equation of seawater motion in the generalized vertical coordinate system with the vertical layer number λ as the independent variable is derived.

[0009] S3. Design a novel σ-z hybrid generalized base-dependent coordinate system;

[0010] S4. Calculate the baroclinic gradient force and introduce the concept of local density stratification to improve the calculation method.

[0011] A further improvement of the present invention is that step S1 includes the following specific steps:

[0012] S11. Introduce the continuously varying vertical layer index λ as the independent variable to construct a generalized vertical coordinate transformation: z = ξ(x,y,t) + s(x,y,λ,t). When λ = 1, s = 0, at which point z = ξ, and the coordinate plane is at the sea surface; 1 ≤ λ ≤ k b k b This represents the total number of vertical floors.

[0013] S12. Define the expression for the vertical velocity ω′ in the generalized vertical coordinate system as follows: Simultaneously define w = ω′ + (s) x +η x )u+(s y +η y )v+s t +η t Where u and v are horizontal velocity components, η is the free sea surface height, and s x s y s t Let s be the partial derivatives of s with respect to x, y, and t, respectively, and η be the x η y η t Similarly.

[0014] A further improvement of the present invention is that step S2 includes the following specific steps:

[0015] S21. Based on coordinate transformation and the definition of vertical velocity, the equations of seawater motion in the generalized vertical coordinate system with the vertical stratification index λ as the independent variable are derived. The expression for the momentum equation is:

[0016]

[0017] In the formula, f is the Coriolis force parameter, g is the gravitational acceleration, and K is the acceleration due to gravity. m F is the vertical eddy viscosity coefficient. u F v These are the horizontal momentum diffusion terms, B x B y This represents the component of the baroclinic gradient force.

[0018] S22. The expression for the continuity equation is:

[0019] S23. The expression for the temperature-salinity diffusion equation is:

[0020]

[0021] In the formula, T is the temperature, S is the salinity, and K h is the thermal vertical eddy friction coefficient, is the heat source term, F T and F S are the heat and salinity diffusion terms respectively;

[0022] The relationships between S24, the horizontal density gradient, and the baroclinic gradient force expression are as follows:

[0023]

[0024] S25. Furthermore, the expressions for B x and B y are as follows:

[0025]

[0026] A further improvement of the present invention is that the S3 includes the following specific steps:

[0027] S21. Preset a series of equal z planes, and the total number of layers is denoted as k z , k z satisfies the condition z0(k z ) < H. The positions of each z plane are z0(k) (k = 1, 2,..., k z ), and according to the formula k1 < λ ≤ k z convert z0 to the generalized bottom-following coordinate γ0(x, y, λ);

[0028] S22. Select a traditional σ coordinate (σ(λ)) and apply it to the entire calculation sea area. Finally, according to γ(x, y, λ) = max[σ(λ), γ0(x, y, λ)], k1 < λ ≤ k z judge to generate the generalized bottom-following coordinate.

[0029] A further improvement of the present invention is that the specific content of the generalized bottom-following coordinate in S22 is:

[0030] S221. The B1 coordinate is a generalized bottom-following coordinate in which the uniform σ stratification and the equal z-plane stratification are fully mixed; in the vertical layer where λ ≤ k1 or λ ≥ k z , γ(x, y, λ) = σ1; in the vertical layer where k1 < λ < k z , if σ1 ≥ γ0, then γ(x, y, λ) = σ1, otherwise γ(x, y, λ) = γ0;

[0031] S222. The B2 coordinate is a generalized bottom-following coordinate in which the exponential function σ stratification and the equal z-plane stratification are fully mixed; in the vertical layer where λ ≤ k1 or λ ≥ k z γ(x, y, λ) = σ2; in the vertical layer where k1 < λ < kz For the vertical layer, if σ2≥γ0, then γ(x,y,λ)=σ2, otherwise γ(x,y,λ)=γ0;

[0032] The coordinates S223 and B3 are generalized base-dependent coordinates that are a complete mixture of hyperbolic function σ-layers and isozymatic layers; when λ≤k1 or λ≥k z The vertical layer, γ(x,y,λ)=σ1; when k1<λ <k z For the vertical layer, if σ3≥γ0, then γ(x,y,λ)=σ3, otherwise γ(x,y,λ)=γ0.

[0033] A further improvement of the present invention is that the specific content of S4 is as follows:

[0034] S41. Calculate the baroclinic gradient force B in the x-direction using the finite volume method on an unstructured triangular mesh. x The formula is:

[0035] S42, baroclinic gradient force B in the y direction y The calculation formula is:

[0036]

[0037] A further improvement of the present invention is that S4 further includes: subtracting the local average density layering from the calculated density ρ to obtain the remaining density ρ′. L This is used to replace ρ in the original formula for calculating the baroclinic gradient force, ρ′ L The expression is

[0038]

[0039] in It is a local average density stratification.

[0040] The technical effects of this invention are as follows:

[0041] A generalized hybrid bottom-coordinate ocean numerical model construction method is proposed. This invention replaces the σ layer with a preset iso-z-surface, smoothly connects the σ and z coordinates, reduces the tilt slope of the vertical layer, and thus reduces baroclinic gradient force error. It avoids the limitation of minimum transformation depth in A4 coordinates, allowing the iso-z-surface to extend to deeper regions as much as possible, improving vertical resolution. It solves the inapplicability of traditional γ coordinates in generalized bottom-coordinates, ensuring that λ on the same vertical layer is independent of horizontal position, avoiding errors in baroclinic gradient force calculation. It compensates for local density variations, significantly reducing baroclinic gradient force error. Attached Figure Description

[0042] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0043] Figure 1 This is a flowchart illustrating a method for constructing a generalized hybrid bottom-coordinate ocean numerical model according to Embodiment 1 of the present invention. Detailed Implementation

[0044] This invention aims to propose a method for constructing a generalized hybrid bottom-coordinate ocean numerical model. This invention replaces the σ layer with a pre-defined isozyme, smoothly connecting the σ and z coordinates, reducing the vertical slope of the layers, and thus lowering the baroclinic gradient force error. It avoids the minimum transformation depth limitation in A4 coordinates, allowing the isozyme to extend to deeper regions as much as possible, improving vertical resolution. It solves the inapplicability of traditional γ coordinates in generalized bottom-coordinates, ensuring that λ on the same vertical layer is independent of horizontal position, avoiding errors in baroclinic gradient force calculation. It also compensates for local density variations, significantly reducing baroclinic gradient force error.

[0045] Example 1:

[0046] This embodiment proposes a method for constructing a generalized hybrid bottom-coordinate ocean numerical model, such as... Figure 1 As shown, the specific steps include the following:

[0047] S1. Define coordinate transformation and vertical velocity, introduce continuously changing vertical layer number as independent variable, and construct generalized vertical coordinate transformation;

[0048] S2. Based on the above coordinate transformation and definition of vertical velocity, the equation of seawater motion in the generalized vertical coordinate system with the vertical layer number λ as the independent variable is derived.

[0049] S3. Design a novel σ-z hybrid generalized base-dependent coordinate system;

[0050] S4. Calculate the baroclinic gradient force and introduce the concept of local density stratification to improve the calculation method.

[0051] In this embodiment, step S1 includes the following specific steps:

[0052] S11. Introduce the continuously varying vertical layer index λ as the independent variable to construct a generalized vertical coordinate transformation: z = ξ(x,y,t) + s(x,y,λ,t). When λ = 1, s = 0, at which point z = ξ, and the coordinate plane is at the sea surface; 1 ≤ λ ≤ k b k b This represents the total number of vertical floors.

[0053] S12. Define the expression for the vertical velocity ω′ in the generalized vertical coordinate system as follows: Simultaneously define w = ω′ + (s) x+η x )u+(s y +η y )v+s t +η t Where u and v are horizontal velocity components, η is the free sea surface height, and s x s y s t Let s be the partial derivatives of s with respect to x, y, and t, respectively, and η be the x η y η t Similarly.

[0054] In this embodiment, step S2 includes the following specific steps:

[0055] S21. Based on coordinate transformation and the definition of vertical velocity, the equations of seawater motion in the generalized vertical coordinate system with the vertical stratification index λ as the independent variable are derived. The expression for the momentum equation is:

[0056]

[0057] In the formula, f is the Coriolis force parameter, g is the gravitational acceleration, and K is the acceleration due to gravity. m F is the vertical eddy viscosity coefficient. u F v These are the horizontal momentum diffusion terms, B x B y This represents the component of the baroclinic gradient force.

[0058] S22. The expression for the continuity equation is:

[0059] S23. The expression for the temperature-salinity diffusion equation is:

[0060]

[0061] In the formula, T is temperature, S is salinity, and K is temperature. h The coefficient of thermal vertical eddy friction is . For the heat source term, F T F S These are the heat and salinity diffusion terms, respectively;

[0062] S24, the relationship between horizontal density gradient and baroclinic gradient force are as follows:

[0063]

[0064] S25, thus obtaining B x B y The expression is:

[0065]

[0066] In this embodiment, step S3 specifically includes the following steps:

[0067] S21. Preset a series of equal z - planes, and the total number of layers is denoted as k z , k z satisfies the condition z0(k z ) < H. The positions of each z - plane are z0(k) (k = 1, 2, …, k z ), and according to the formula k1 < λ ≤ k z transform z0 into the generalized bottom - following coordinate γ0(x, y, λ);

[0068] S22. Select a traditional σ - coordinate (σ(λ)) and apply it to the entire calculation sea area. Finally, judge and generate the generalized bottom - following coordinate according to γ(x, y, λ) = max[σ(λ), γ0(x, y, λ)], k1 < λ ≤ k z

[0069] In this embodiment, the specific content of the generalized bottom - following coordinate in S22 is as follows:[[ID=?]] [[ID=?]]

[0070] S221. The B1 coordinate is the generalized bottom - following coordinate with the full mixing of uniform σ - layer and equal z - plane layer; in the vertical layer where λ ≤ k1 or λ ≥ k z , γ(x, y, λ) = σ1; in the vertical layer where k1 < λ < k z , if σ1 ≥ γ0, then γ(x, y, λ) = σ1, otherwise γ(x, y, λ) = γ0;

[0071] S222. The B2 coordinate is the generalized bottom - following coordinate with the full mixing of exponential - function σ - layer and equal z - plane layer; in the vertical layer where λ ≤ k1 or λ ≥ k z , γ(x, y, λ) = σ2; in the vertical layer where k1 < λ < k z , if σ2 ≥ γ0, then γ(x, y, λ) = σ2, otherwise γ(x, y, λ) = γ0;

[0072] S223. The B3 coordinate is the generalized bottom - following coordinate with the full mixing of hyperbolic - function σ - layer and equal z - plane layer; in the vertical layer where λ ≤ k1 or λ ≥ k z , γ(x, y, λ) = σ1; in the vertical layer where k1 < λ < k z , if σ3 ≥ γ0, then γ(x, y, λ) = σ3, otherwise γ(x, y, λ) = γ0.

[0073] In this embodiment, the specific content of S4 is as follows:

[0074] S41. On the unstructured triangular grid, calculate the baroclinic gradient force B in the x - direction by finite - volume method integration x , and the formula is:​

[0075] S42, baroclinic gradient force B in the y direction y The calculation formula is:

[0076]

[0077] In this embodiment, step S4 further includes: subtracting the local average density layering from the calculated density ρ to obtain the remaining density ρ′. L This is used to replace ρ in the original formula for calculating the baroclinic gradient force, ρ′ L The expression is

[0078]

[0079] in It is a local average density stratification.

[0080] Example 2:

[0081] This embodiment provides an electronic device, including a processor and a memory, wherein the memory stores a computer program that can be called by the processor; the processor executes the above-described method for constructing a generalized hybrid bottom coordinate ocean numerical model by calling the computer program stored in the memory.

[0082] The electronic device can vary considerably depending on its configuration and performance. It may include one or more Central Processing Units (CPUs) and one or more memories, wherein the memory stores at least one computer program, which is loaded and executed by the processor to implement the generalized hybrid bottom-coordinate ocean numerical model construction method provided in the above-described embodiment. The electronic device may also include other components for implementing its functions; for example, it may have wired or wireless network interfaces and input / output interfaces for data input and output. Details will not be elaborated upon in this embodiment.

[0083] Those skilled in the art will recognize that this invention can be implemented as a system, method, or computer program product. Therefore, this disclosure can be embodied in the following forms: it can be entirely hardware, entirely software (including firmware, resident software, microcode, etc.), or a combination of hardware and software, generally referred to herein as a "circuit," "module," or "system." Furthermore, in some embodiments, the invention can also be implemented as a computer program product contained in one or more computer-readable media, which includes computer-readable program code.

[0084] Any combination of one or more computer-readable media may be used. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. More specific examples (a non-exhaustive list) of computer-readable storage media include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in connection with an instruction execution system, apparatus, or device.

[0085] This invention is described with reference to flowchart illustrations and block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and block diagrams, as well as combinations of blocks in the flowchart illustrations and block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart. Figure 1 One or more processes and boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0086] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and boxes Figure 1 The steps of the function specified in one or more boxes.

[0087] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for constructing a generalized hybrid bottom-coordinate ocean numerical model, characterized in that: The specific steps include the following: S1. Define coordinate transformation and vertical velocity, introduce continuously changing vertical layer number as independent variable, and construct generalized vertical coordinate transformation; S2. Based on the above coordinate transformation and vertical velocity definition, the vertical layer sequence number is derived. The equations of seawater motion in the generalized vertical coordinate system with the independent variable as the equations. S3, New Design Mixed generalized base-dependent coordinates; S4. Calculate the baroclinic gradient force and introduce the concept of local density stratification to improve the calculation method.

2. The method for constructing a generalized hybrid bottom-coordinate ocean numerical model according to claim 1, characterized in that: S1 includes the following specific steps: S11. Introduce continuously varying vertical layer numbers. As the independent variable, construct a generalized vertical coordinate transformation: ,when hour, ,at this time The coordinate plane is located at the sea surface; , This represents the total number of vertical floors. S12. Define the vertical velocity in the generalized vertical coordinate system. The expression is: Simultaneously define Where u and v are horizontal velocity components, The height of the free sea surface. , , Let be the partial derivatives of s with respect to x, y, and t, respectively. , , Similarly.

3. The method for constructing a generalized hybrid bottom-coordinate ocean numerical model according to claim 2, characterized in that: S2 includes the following specific steps: S21. Based on coordinate transformation and the definition of vertical velocity, the vertical layering sequence number is derived. The equations of motion for seawater in the generalized vertical coordinate system, with denoted by ... ； ； In the formula, f is the Coriolis force parameter, and g is the acceleration due to gravity. The vertical eddy viscosity coefficient is... , These are the horizontal momentum diffusion terms. , This represents the component of the baroclinic gradient force. S22. The expression for the continuity equation is: ; S23. The expression for the temperature-salinity diffusion equation is: ； ； In the formula, T is temperature and S is salinity. The coefficient of thermal vertical eddy friction is . For heat source items, , These are the heat and salinity diffusion terms, respectively; S24, the relationship between horizontal density gradient and baroclinic gradient force are as follows: ； ； S25, and thus obtain , The expression is: ； 。 4. The method for constructing a generalized hybrid bottom-coordinate ocean numerical model according to claim 3, characterized in that: S3 includes the following specific steps: S21. Pre-set a series of equal z-planes, the total number of layers is denoted as... , Meet the conditions The positions of each z-plane are And according to the formula Will Transformation into generalized base coordinates ; S22. Select a tradition coordinate( And apply it to the entire computational sea, and finally according to Determine the generalized base coordinates generated.

5. The method for constructing a generalized hybrid bottom-coordinate ocean numerical model according to claim 4, characterized in that: The specific content of the generalized base-dependent coordinates in S22 is as follows: The coordinates of S221 and B1 are uniform. Stratification and Equality Generalized base-dependent coordinates of fully mixed surface layers; in or The vertical layer, ;exist The vertical layer, if ,but ,otherwise ; The coordinates of S222 and B2 are exponential functions. Stratification and Equality Generalized base-dependent coordinates of fully mixed surface layers; in or The vertical layer, ;exist The vertical layer, if ,but ,otherwise ; The coordinates S223 and B3 are hyperbolic functions. Stratification and Equality Generalized base-dependent coordinates of fully mixed surface layers; in or The vertical layer, ;exist The vertical layer, if ,but ,otherwise .

6. The method for constructing a generalized hybrid bottom-coordinate ocean numerical model according to claim 5, characterized in that: The specific content of S4 is as follows: S41. Calculate the baroclinic gradient force in the x-direction using the finite volume method on an unstructured triangular mesh. The formula is: ; S42, baroclinic gradient force in the y direction The calculation formula is: 。 7. The method for constructing a generalized hybrid bottom-coordinate ocean numerical model according to claim 6, characterized in that: The S4 further includes: from the calculated density The remaining density is obtained by subtracting the local average density stratification. This replaces the original formula. Perform baroclinic gradient force calculation. The expression is ； in It is a local average density stratification.

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