CN104331599A - Unstructured grid nesting wave numerical simulation method - Google Patents
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Abstract
The invention discloses an unstructured grid nesting wave numerical simulation method, which includes the following main steps: an unstructured grid is adopted to create a mathematical model of waves in a large area; an unstructured grid is adopted to create a mathematical model of waves in a shallow-water engineering sea area; according to computational domains of different sizes, the numerical simulation of the waves is carried out. The unstructured grid nesting wave numerical simulation method achieves the following advantages: on the basis of bringing the unstructured grid wave mathematical models into full play, by applying the grid nesting technology, the unstructured grid nesting wave numerical simulation method greatly reduces the number of the grids in the computational domains, and increases the speed of computation; by applying the grid nesting technology, the unstructured grid nesting wave numerical simulation method can deploy finer computational grids in order to adapt to complex terrains and irregular coast boundaries, so that the accuracy of computed results can be increased.
Description
Technical Field
The invention relates to an unstructured grid nesting wave numerical simulation method, and belongs to the technical field of wave field numerical simulation and prediction.
Background
In recent years, with the construction of coastal projects such as port and channel projects, artificial islands, artificial beaches, reclamation, wind power and the like in China, higher requirements are put forward on numerical simulation and prediction of engineering sea area waves. The method has the advantages that the mathematical models of the sea wave of the unstructured grid estuary, coast and offshore engineering are built, the wave elements of the engineering sea area are accurately forecasted, and the method has important practical significance for optimizing the engineering design scheme, saving the engineering investment and improving the engineering safety.
In order to simulate the wave propagation process of estuaries, seacoasts and offshore water areas more accurately, a grid nesting method is often adopted to establish large and small-range wave mathematical models. At present, the nesting technology of structured grids is commonly used at home and abroad, but because the topography of the water areas is very complex, the land line is tortuous and changeable, and meanwhile, the influence of multiple projects is received, the wave propagation cannot be simulated accurately.
With the development of wave numerical simulation technology, compared with structured grids, unstructured grids have more advantages and are widely applied, and although the unstructured grid simulation technology applied at home and abroad has many successful cases, simulation results are to be further improved due to the complexity and higher precision requirements of wave simulation at estuaries, coasts and offshore water areas.
Disclosure of Invention
In order to solve the defects of the prior art, the invention aims to provide a numerical simulation method for the nested waves of the unstructured grid, which is used for establishing a large-area nested wave mathematical model and a small-area nested wave mathematical model considering the influence of the change of the sea level so as to accurately predict the wave propagation process of complex terrains, tortuous boundaries and engineering influence.
In order to achieve the above object, the present invention adopts the following technical solutions:
an unstructured grid nesting wave numerical simulation method is characterized by comprising the following steps:
1) establishing an unstructured grid wave mathematical model of a large area, wherein a control equation is as follows:
the first term on the left side of the above equation is the change rate of the wave action amount N with time, where N (σ, θ) is E (σ, θ)/σ, E (σ, θ) is the energy spectrum density, σ is the wave frequency, and θ is the wave direction;
the second term and the third term on the left side of the above expression respectively represent the propagation of N (sigma, theta) in the x and y directions of the space;
the fourth term on the left of the above equation represents the variation of N (σ, θ) in σ space due to the flow field and water depth;
the fifth term on the left side of the above equation represents the propagation of N (σ, θ) in θ space, i.e., the refraction caused by water depth and flow field;
s on the right side of the equation represents the source-sink term expressed in spectral density, including wind energy input, wave-to-wave nonlinear interaction, and energy loss due to ground friction, white waves, deep induced fragmentation;
said C isx、Cy、Cσ、CθRespectively representing wave propagation speeds in x, y, sigma and theta spaces; wherein, Cx、Cy、Cσ、CθRespectively as follows:
whereinIs wave number, kx,kyX and u space components, k wave number, d water depth,is the flow rate, Ux,UyThe components of x and y space, s is the space coordinate along theta direction, m is the coordinate perpendicular to s, and relative frequencyω is the natural frequency of the wave; operatorIs defined as <math><mrow>
<mfrac>
<mi>d</mi>
<mi>dt</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mo>∂</mo>
<mrow>
<mo>∂</mo>
<mi>t</mi>
</mrow>
</mfrac>
<mo>+</mo>
<mover>
<mi>C</mi>
<mo>→</mo>
</mover>
<mo>·</mo>
<msub>
<mo>▿</mo>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
</mrow>
</msub>
<mo>;</mo>
</mrow></math> Is the wave velocity; t is time.
2) Establishing a shallow sea engineering sea wave mathematical model nested with unstructured grids; establishing a shallow sea engineering sea wave mathematical model according to the completely nested frequency spectrum and direction spectrum boundary conditions (including the coordinate, frequency, direction, energy spectrum or variable density and other elements of the node at the boundary of the calculation domain to be nested) provided by the large-area unstructured grid wave mathematical model, and then applying the control equation and related auxiliary equations in the step 1) to simulate the engineering sea wave;
3) and solving the unstructured grid nested wave mathematical model.
The method for simulating the numerical value of the unstructured grid nested wave is characterized in that in the step 1), the expression of a source function term S is as follows:
S＝Swind+Snl+Sbottom+Swhite+Sbreaking (6)；
Swindrepresenting the effect of wind on waves; snlRepresents nonlinear wave-wave interaction; sbottomRepresenting the energy loss caused by bottom friction; swhiteRepresenting the energy loss caused by the white waves; sbreakingRepresenting the energy loss caused by the deep induced disruption.
The numerical simulation method of the unstructured grid nested waves is characterized in that SwindI.e. Swind(σ, θ), representing the effect of wind on waves, can be expressed as a linear and exponential growth component, i.e.: swind(σ, θ) ═ a + BE (σ, θ), where a and B depend on the frequency, direction of the wave, and the magnitude and direction of the wind.
The numerical simulation method of the unstructured grid nested waves is characterized in that SnlRepresenting nonlinear wave-wave interaction, waves grow after gaining energy from the wind, and the energy is redistributed among different frequencies; triphase wave-wave interaction according to E1 debarky (1996)Obtaining the scheme and solving by using an LTA (sampled Triad application) method; the calculation of the four-phase wave-wave interaction adopts the scheme proposed by Hasselmann (1985) and adopts the DIA (discrete interaction adaptation) method
The numerical simulation method of the unstructured grid nested waves is characterized in that SbottomRepresenting the energy loss caused by bottom friction, the expression is:
d is water depth, sigma, k and theta represent frequency, wave number and wave direction respectively, g is gravity acceleration, CbottomIs the bottom coefficient of friction.
The numerical simulation method of the unstructured grid nested waves is characterized in that SwhiteRepresenting the energy loss caused by the white waves, the expression is as follows:
wherein d represents water depth and is a wave steepness coefficient, E (sigma, d) is wave energy, k is wave number,it is meant that the average frequency is,the average wave number is shown.
The numerical simulation method of the unstructured grid nested waves is characterized in that SbreakingRepresenting the energy loss caused by deep induced disruption, the expression is:
wherein E istotAs a total wave energy, DtotTo average dissipation ratio of energy per unit area due to wave breaking, the expression is:
wherein, alpha in SWAN modelBJ＝1，Is the average frequency, QbDetermined by the wave of fragmentation:
Hmmaximum wave height, from H, that can be supported for a given depth without breaking of the wavesmWhere d is the water depth and γ is the crushing parameter, taken as a constant, with a default value of 0.73.
The numerical simulation method for the unstructured grid nested waves is characterized in that in the step 3), a third generation wave model SWAN is taken as a tool, a basic equation and a related equation in the formula (1) in the step 1) are combined, the result in the step 2) is applied, and a fully implicit finite difference format and a one-time iteration four-time scanning technology are adopted to solve the unstructured grid nested wave mathematical model.
The invention achieves the following beneficial effects: on the basis of giving full play to the unstructured grid wave mathematical model, the grid nesting technology is applied, the number of grids in a calculation domain is greatly reduced, the difference between the maximum grid and the minimum grid is reduced, and the calculation speed is improved. By applying the grid nesting technology, finer computational grids can be arranged, the method is suitable for complex terrains and tortuous shoreline boundaries, and the accuracy of computational results is improved.
Drawings
Drawing (A)1 is the SWAN large-scale model calculation range;
drawing (A)2 is a SWAN large-scale model mesh;
drawing (A)3 is the effective wave height distribution of the large-range calculation region during typhoon (No. 8615)Drawing (A)；
Drawing (A)4, calculating the range of the SWAN engineering area model;
drawing (A)5, SWAN engineering area model calculation grid;
drawing (A)Effective wave height distribution of engineering region during typhoon (No. 8615)Drawing (A)；
Drawing (A)7 is spectrum and direction spectrum boundary condition schematicDrawing (A)；
Drawing (A)Wave calculation control point schematic 8Drawing (A)；
Drawing (A)9 is H13% wave height distribution in NE direction of wide area with +5 grade wind in 2 yearsDrawing (A)；
Drawing (A)10 is H13% wave height distribution in NE direction of 2-year-one-meeting + 5-level wind engineering areaDrawing (A)。
Detailed Description
The following is combined withDrawing (A)The invention is further described. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
An unstructured grid nesting wave numerical simulation method is combined with some typical methods in the past, and comprises the following steps:
1) establishing an unstructured grid wave mathematical model of a large area, wherein a control equation is as follows:
the first term on the left side of the above equation is the change rate of the wave action amount N with time, where N (σ, θ) is E (σ, θ)/σ, E (σ, θ) is the energy spectrum density, σ is the wave frequency, and θ is the wave direction;
the second term and the third term on the left side of the above expression respectively represent the propagation of N (sigma, theta) in the x and y directions of the space;
the fourth term on the left of the above equation represents the variation of N (σ, θ) in σ space due to the flow field and water depth;
the fifth term on the left side of the above equation represents the propagation of N (σ, θ) in θ space, i.e., the refraction caused by the water depth and the flow field;
s on the right side of the equation represents the source-sink term expressed in spectral density, including wind energy input, wave-to-wave nonlinear interaction, and energy loss due to ground friction, white waves, deep induced fragmentation;
Cx、Cy、Cσ、Cθrespectively representing wave propagation speeds in x, y, sigma and theta spaces; wherein, Cx、Cy、Cσ、CθRespectively as follows:
whereinIs wave number, kx,kyX and y space components, k wave number, d water depth,is the flow rate, Ux,UyThe components of x and y space, s is the space coordinate along theta direction, m is the coordinate perpendicular to s, and relative frequencyω is the natural frequency of the wave; operatorIs defined as <math><mrow>
<mfrac>
<mi>d</mi>
<mi>dt</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mo>∂</mo>
<mrow>
<mo>∂</mo>
<mi>t</mi>
</mrow>
</mfrac>
<mo>+</mo>
<mover>
<mi>C</mi>
<mo>→</mo>
</mover>
<mo>·</mo>
<msub>
<mo>▿</mo>
<mrow>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
</mrow>
</msub>
<mo>;</mo>
</mrow></math> Is the wave velocity; t is time.
The expression of the source function term S is:
S＝Swind+Snl+Sbottom+Swhite+Sbreaking (6)；
Swindrepresenting the effect of wind on waves; snlRepresents nonlinear wave-wave interaction; sbottomRepresenting the energy loss caused by bottom friction; swhiteRepresenting the energy loss caused by the white waves; sbreakingRepresenting the energy loss caused by the deep induced disruption.
SwindI.e. Swind(σ, θ), representing the effect of wind on the waves, can be expressed as a linear and exponential growth portion, using a combination of the "resonance" mechanism proposed by Phillips (1957) and the parallel flow instability wave generation theory proposed by Miles (1957), namely: swind(σ, θ) ═ a + BE (σ, θ), where a and B depend on the frequency and direction of the wave and the magnitude and direction of the wind, the selection of the coefficient A, B directly affects the simulation results of the ocean waves.
SnlRepresenting a nonlinear wave-wave interaction, waves grow after they gain energy from the wind, which in turn redistributes their energy between different frequencies. In deep water situations, the four-phase wave-wave interaction controls the development of the wave spectrum of the sea wave, and transfers part of energy from high frequency to low frequency, so that the peak frequency gradually moves to the low frequency; in shallow water, the three-phase wave-wave interaction plays a major role, converting low frequency energy to high frequency. In the shallow water area near the shore, the three waves S are generally considered due to the complex and variable submarine topographynl3(sigma, theta) and four-wave Snl4(σ, θ) interaction between them.
The triphase wave-wave interaction was obtained according to the protocol of E1 debarky (1996) and solved using the method of LTA (lumped Triad application):
the expression of the interaction coefficient J is:
wherein,when 10 > UrCalculated when the temperature is higher than 0.1.
αEBTo adjustable proportionality coefficient, HsIs the effective wave height, sigma is the wave frequency, theta is the wave direction, k is the wave number, d is the water depth, g is the gravitational acceleration, C is the wave velocitygE (σ, θ) is the spectral density, T,Mean wave period and mean wave frequency, respectively.
The calculation of the four-phase wave-wave Interaction was carried out using the scheme proposed by Hasselmann (1985) and using the DIA (diffraction Interaction analysis) method:
frequency of the four waves is:
σ1＝σ2＝σ，σ3＝σ(1+λ)＝σ+,σ4＝σ(1-λ)＝σ-λ is a constant, and λ is 0.25.
In the DIA method, two sets of four waves are considered, the first set beingThe second group isThen the source item Snl4(σ, θ) can be expressed as:
wherein,expression andthe mirror image directions are consistent.
In the formula, Cnl4Is constant, take 3 × 107Energy spectral density E (σ)+,θ+)、E(σ-,θ-) And obtaining the four values through bilinear interpolation according to the surrounding four values.
SbottomRepresenting the energy loss caused by bottom friction, the expression is:
d is water depth, sigma, k and theta represent frequency, wave number and wave direction respectively, g is gravity acceleration, E (sigma, theta) is energy spectrum density, CbottomIs the bottom coefficient of friction, Hasselmann et al (1973) values in the JONSWAP test of 0.038m2s-3Bouws and Komen (1983) took 0.067m in a fully grown state in shallow water2s-3。
SwhiteRepresenting energy loss caused by the white waves, the sea surface continuously generates and grows under the continuous action of wind (particularly strong wind), one part of the wind waves are broken, the waves are broken to directly form ocean white waves, and foams left after the white waves decline can disappear for a long time; meanwhile, bubbles in seawater and droplets in air are also associated with the wave. The white waves play an important role in the sea-gas exchange process. The expression of WAMDIgroup (1988) was chosen:
where d represents water depth, is the steepness factor, depends on the mean square wave steepness, and uses the formula of Kurther et al (1992).
SbreakingRepresenting the energy loss caused by deep induced disruption, the expression is:
wherein Etot is total wave energy, Dtot is average dissipation ratio of energy in unit area caused by wave breaking, and the expression is as follows:
wherein, alpha in SWAN modelBJ＝1，Is the average frequency, QbDetermined by the wave of fragmentation:
Hmmaximum wave height, from H, that can be supported for a given depth without breaking of the wavesmWhere d is the water depth and γ is the crushing parameter, taken as a constant, with a default value of 0.73.
2) And establishing a shallow sea engineering sea area wave mathematical model nested with unstructured grids. And (2) according to the completely nested frequency spectrum and direction spectrum boundary conditions (including the coordinate, frequency, direction, energy spectrum or variable density and other elements of the node at the boundary of the calculation domain to be nested) provided for the engineering sea wave mathematical model by the large-area unstructured grid wave mathematical model, then applying the control equation and related auxiliary equations in the step 1), establishing the shallow sea engineering sea wave mathematical model, and carrying out the numerical calculation of the engineering sea wave.
3) And solving the unstructured grid nested wave mathematical model.
And (3) taking a third generation wave model SWAN as a tool, combining a basic equation and a related equation in the formula (1) in the step 1), and applying the result in the step 2) to solve the unstructured grid nested wave mathematical model by adopting a fully-implicit finite difference format and a one-iteration four-time scanning technology.
The combination examples: the wave propagation conditions of the channel and the water area at the front edge of the wharf are analyzed and explained aiming at the navigation safety problem of channel and river combined transportation of the Hongyang harbor channel and the channel.
(1) Establishing large-area unstructured grid wave mathematical model
According to the general plan of salt city harbor, the belonged harbor area is divided into an inland river operation area and a estuary operation area, wherein the north area of the belonged harbor of the estuary operation area is a key development area in the near term planning and mainly takes coal, bulk cargo, containers, liquid chemical industry and petroleum product transportation as main parts.
According to the channel engineering requirements of the Yangtze river channel, the Yangtze river channel directly realizes the sea and river combined transportation by using the yellow sand harbor, and the inland river ship directly drives into the Yangtze river mouth sea harbor wharf to realize the seamless connection of the sea and river combined transportation.
Therefore, in order to fully demonstrate the feasibility of the inland river ship directly entering the Yangtze river mouth harbor area, scientific basis is provided for the design and decision department of the Yangtze river channel engineering of the Yangtze river channel, and wave propagation numerical simulation of the channel and the water area at the front edge of the wharf in the navigation safety problem of the channel and river combined transportation of the Yangtze river channel is developed.
In order to accurately simulate the wave propagation of the channel and the water area at the front edge of the wharf in the sea-river transport, a control equation and related auxiliary equations in the step 1) are firstly applied to establish a large-range wave model SWAN, and the underwater topography and grids of the corresponding calculation area such asDrawing (A)1 anddrawing (A)2, calculating to obtain wave elements at a water depth of-12 meters according to the wave elements at the deep line of-17 meters and the like in the engineering stage, and performing simulation verification on a wave field in the sea area near the sunport during the No. 8615 typhoon, wherein the effective wave height is distributed asDrawing (A)3, the wave height of H4% at the deep line of-12 m is 5.24 m, which is close to the wave height of 5.3 m obtained by analyzing the measured data of the ocean I, and provides boundary conditions for the engineering area model.
(2) Shallow sea engineering sea wave mathematical model for establishing unstructured grid nesting
Applying step 2) to establish a wave model of an engineering area according to boundary conditions (including elements such as coordinates, frequency, direction, energy spectrum or variable density of nodes at the boundary of the computational domain to be nested) provided by the large-scale wave model, wherein the distance between the north and the south of the area is about 17 kilometers,things (Earthwest)The length is about 34 kilometers, in order to more accurately simulate the influence of engineering and terrain change on wave propagation, local encryption is carried out on engineering area grids, 48094 nodes are totally arranged, 93883 triangle units are arranged, the minimum side length of the grids is 10m, and underwater terrains and grids in the area are calculated by the methodDrawing (A)4 anddrawing (A)5, if the calculation domain is subdivided according to the 10m × 10m grids, 5780000 rectangular grids are formed, which are 60 times of triangular grids, so that the method can greatly save calculation time and improve benefits. Effective wave height distribution of the sea area near the estuary of the shooting harbor and the channel water area of the dredging harbor during the typhoon No. 8615Drawing (A)And 6, the method is mainly used for researching the influence of the breakwater engineering and the dredging channel engineering on the wave elements of nearby sea areas and providing the wave elements for ship seakeeping, berthing calculation and operation simulation.
(3) Implementation of unstructured grid nested wave mathematical model
According to bigThe fully nested spectral and directional spectral boundary conditions (including the coordinate, frequency, direction, energy spectrum or variable density of nodes at the boundary of the computational domain to be nested) provided by the region wave model, and the boundary conditions thereof are schematicDrawing (A)Such asDrawing (A)And 7, performing engineering sea wave simulation calculation for a finer grid (the minimum grid side length is 10 m).
(4) The influence of coast engineering, port engineering and the like on wave fields in nearby sea areas is researched by applying an unstructured grid nested wave mathematical model.
Applying the established unstructured grid nested wave mathematical model, solving the unstructured grid nested wave mathematical model according to the step 3), researching the influence of a breakwater project and a dredging channel project on a wave field of a sea area near a sun-shooting port, calculating wave elements of each calculation point when a sea river integrated transportation wharf harbor pool and a ship enter and exit the sea river integrated transportation wharf from a yellow sand port under various working conditions, providing necessary wave conditions for simulation of dredging channel and sea river integrated transportation conditions of a ship manipulation simulator, calculating the wave elements of three recurrence periods of 50 year one meeting, 25 year one meeting and 2 year one meeting in NE and ENE under the designed high water level condition in two directions to obtain H13% wave height, wherein, the wind speed is calculated by adopting 8-grade wind as the wind speed for the first time of 25 years and the first time of 50 years, and the wind speed is calculated by adopting 5-grade wind and 6-grade wind as the wind speed for the first time of 2 years. Wave calculation control points such asDrawing (A)Shown in fig. 8.
Wherein the corresponding large range and the NE direction effective wave height distribution of the engineering regionDrawing (A)Such asDrawing (A)9、Drawing (A)Shown at 10.
Wherein, the statistics of the effective wave height of each calculation control point is designed for the high water level plus 2 yearsAs shown in Table 1As shown.
Under the condition of meeting waves in 2 years, the wave heights of the harbor basin of the sea and river combined transport wharf and the nearby points (P1-P7) are gradually reduced from P1 to P7, the maximum value of the H13% wave height is 0.618m under the condition of grade 5 wind, and the maximum value of the H13% wave height is 0.66m under the condition of grade 6 wind, and the wave heights are all generated in the NE direction; and the H13% wave height of each calculation control point (Q1-Q20) from the Huangshahong to the sea-river joint transport code head section is basically less than 0.4m under the conditions of 5-grade wind and 6-grade wind.
The invention achieves the following beneficial effects: on the basis of giving full play to the unstructured grid wave mathematical model, the grid nesting technology is applied, the number of grids in a calculation domain is greatly reduced, the difference between the maximum grid and the minimum grid is reduced, and the calculation speed is improved. By applying the grid nesting technology, finer computational grids can be arranged, the method is suitable for complex terrains and tortuous shoreline boundaries, and the accuracy of computational results is improved. The calculation range of the unstructured grid nested wave mathematical model established by the invention covers the whole engineering water area from a deep water sea area to a river mouth and a river channel, the verification of the nested wave mathematical model is carried out by utilizing the actually measured wave data, the calculation result is reasonable, the model is applied, the wave numerical simulation of the channel and the water area at the front edge of the wharf is carried out aiming at the navigation safety problem of channel and river combined transportation of the channel of the Hongyang harbor and the harbor, and the distribution characteristics of the waves are analyzed on the basis.
TABLE 1High water level +2 year-one-encounter calculation control point effective wave height statistics
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
Claims (8)
1. An unstructured grid nesting wave numerical simulation method is characterized by comprising the following steps:
1) establishing an unstructured grid wave mathematical model of a large area, wherein a control equation is as follows:
the first term on the left side of the above equation is the change rate of the wave action amount N with time, where N (σ, θ) is E (σ, θ)/σ, E (σ, θ) is the energy spectrum density, σ is the wave frequency, and θ is the wave direction;
the second term and the third term on the left side of the above expression respectively represent the propagation of N (sigma, theta) in the x and y directions of the space;
the fourth term on the left of the above equation represents the variation of N (σ, θ) in σ space due to the flow field and water depth;
the fifth term on the left side of the above equation represents the propagation of N (σ, θ) in θ space, i.e., the refraction caused by water depth and flow field;
s on the right side of the equation represents the source-sink term expressed in spectral density, including wind energy input, wave-to-wave nonlinear interaction, and energy loss due to ground friction, white waves, deep induced fragmentation;
said C isx、Cy、Cσ、CθRespectively representing wave propagation speeds in x, y, sigma and theta spaces; wherein, Cx、Cy、Cσ、CθRespectively as follows:
wherein,is wave number, kx，kyX and y space components, k wave number, d water depth,is the flow rate, Ux，uy2 components of x and y space, s is space coordinate along theta direction, m is coordinate perpendicular to s, and relative frequencyω is the natural frequency of the wave; operatorIs defined as Is the wave velocity; t is time.
2) Establishing a shallow sea engineering sea wave mathematical model nested with unstructured grids; and (2) providing completely nested frequency spectrum and direction spectrum boundary conditions (including elements such as coordinates, frequency, direction, energy spectrum or variable density of nodes at the boundary of a calculation domain to be nested) for the shallow sea engineering sea wave mathematical model according to the large-area unstructured grid wave mathematical model, and then applying the control equation and related auxiliary equations in the step 1) to establish the shallow sea engineering sea wave mathematical model for carrying out numerical calculation of the engineering sea wave.
3) And solving the unstructured grid nested wave mathematical model.
2. The unstructured grid nested wave numerical simulation method of claim 1, wherein in the step 1), the expression of a source function term S is as follows:
S＝Swind+Snl+Sbottom+Swhite+Sbreaking (6)；
Swindrepresenting the effect of wind on waves; snlRepresents nonlinear wave-wave interaction; sbottomRepresenting the energy loss caused by bottom friction; swhiteRepresenting the energy loss caused by the white waves; sbreakingRepresenting the energy loss caused by the deep induced disruption.
3. The method according to claim 2, wherein S is the number of waves in the unstructured grid nestingwindI.e. Swind(σ, θ), representing the effect of wind on waves, is represented as a linear and exponential growth component, namely: swind(σ, θ) ═ a + BE (σ, θ), where E (σ, θ) is the energy spectral density, depending on the frequency and direction of the wave, and the magnitude and direction of the wind.
4. The method according to claim 2, wherein S is the number of waves in the unstructured grid nestingnlRepresenting nonlinear wave-wave interaction, waves grow after gaining energy from the wind, and the energy is redistributed among different frequencies; said involving three-phase wave-wave interaction Snl3And four-phase wave-wave interaction Snl4。
5. The method according to claim 2, wherein S is the number of waves in the unstructured grid nestingbottomRepresenting the energy loss caused by bottom friction, the expression is:
wherein d is water depth, σ, k and θ represent frequency, wave number and wave direction, respectively, and CbottomIs the bottom friction coefficient, and E (σ, θ) is the spectral density.
6. The method according to claim 2, wherein S is the number of waves in the unstructured grid nestingwhiteRepresenting the energy loss caused by the white waves, the expression is as follows:
wherein d represents the water depth and is the steepness factor,it is meant that the average frequency is,the average wave number is shown.
7. The unstructured grid nested wave numerical simulation method of claim 2, wherein in the step 1),
said SbreakingRepresenting the energy loss caused by deep induced disruption, the expression is:
wherein E istotAs a total wave energy, DtotTo average dissipation ratio of energy per unit area due to wave breaking, the expression is:
wherein, alpha in SWAN modelBJ＝1，Is the average frequency, QbDetermined by the wave of fragmentation:
Hmmaximum wave height, from H, that can be supported for a given depth without breaking of the wavesmWhere d is the water depth and γ is the crushing parameter.
8. The method according to claim 1, wherein in the step 3), a third generation wave model SWAN is used as a tool, the control equation (1) and related auxiliary formulas in the step 1) are combined, the nesting method of the unstructured grid wave model in the step 2) is applied, and a fully-implicit finite difference format and an iterative four-time scanning technique are adopted to solve the unstructured grid nested wave mathematical model.
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