CN115711723B - Nonlinear multidirectional wave absorption method and system - Google Patents
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Abstract
The invention provides a nonlinear multidirectional wave absorption method and a nonlinear multidirectional wave absorption system, which are characterized in that a wave equation is decomposed based on a unit vector of wave numbers to obtain a first absorption boundary equation, and an equation of the relation between wave phase velocity and water wave dispersion is approximated by using a Pade approximation method to obtain a second absorption boundary equation; and reconstructing a first relation of the wave number and a velocity potential function in the wave equation, a second relation of the velocity potential function and the velocity of fluid particles at a calculation domain boundary in a numerical water pool, and a third relation of the velocity potential function and the pressure of the fluid particles, obtaining a pressure poisson equation through corresponding formula conversion and dispersion, solving the pressure poisson equation by adopting an ILU-BiCGSTAB algorithm, and judging whether the wave is completely absorbed according to the numerical solution of the wave equation. According to the invention, the waves with different wave directions and steep wave directions can be effectively absorbed without additionally increasing the length of the calculation domain, so that the calculation efficiency is greatly improved, and the method has a good absorption effect on long waves.
Description
Technical Field
The invention relates to the technical field of ship and ocean engineering hydrodynamics, in particular to a nonlinear multidirectional wave absorption method and system.
Background
Clean energy development to accommodate green shipping needs has become a new trend, which has further driven the development of marine equipment (e.g., floating fans) during energy recovery. Marine equipment is often operated in deep water because of the greater renewable energy source in the deep water environment. In addition, the wind and wave current environment in deep water sea is worse, and in the operation process of marine equipment or in the navigation of ships, extreme sea conditions can pose serious threats to the safety of workers and the integrity of structures. Therefore, there is an urgent need to develop a numerical pool capable of finely simulating the fluid-solid coupling effect of wave current and marine equipment under severe sea conditions.
The hydrodynamic performance of marine equipment is studied in a numerical wave current pool, and a numerical solver is required to accurately simulate waves for a long time, including wave generation, propagation, absorption and other technologies. In real sea conditions, marine equipment is installed in open water, and reflected waves generated on the surface of a structure continuously attenuate until disappearing in the open water. In the numerical pool, the secondary reflection of the reflected wave occurs at the boundary of the entrance/exit due to the limitation of artificially introducing the boundary of the calculation domain, thereby disturbing the accuracy and reliability of the flow field calculation in the calculation domain, and therefore, the secondary reflection of the reflected wave needs to be eliminated.
The existing wave-absorbing method is mainly divided into an active wave-absorbing method and a passive wave-absorbing method, wherein the active wave-absorbing method is used for correcting the motion of a wave-making plate by monitoring a feedback signal of waves, so that secondary reflection of the waves is eliminated. The method is based on a linear wave theory, and the reflection coefficient is increased along with the non-linearity enhancement of waves. In addition, reflected wave information such as wave period needs to be estimated, the wave-canceling effect has uncertainty, and uncertainty analysis needs to be performed. The passive wave-cutting method, such as a digital attenuation domain, requires that the calculation domain is increased by at least two times of wavelength, is mainly effective for short waves and has limited wave-cutting effect for long waves.
Disclosure of Invention
In order to solve the problems of increased reflection coefficient, uncertainty of wave elimination effect, limited wave elimination effect and the like in the existing secondary reflection process of eliminating reflected waves, the invention provides a nonlinear multidirectional wave absorption method, based on a nonlinear wave theory, an absorption boundary equation aiming at waves in different directions is designed according to wave directions by decomposing the wave equation, and the equation of the relation between wave phase velocity and water wave dispersion is approximated, so that wave components with different wave steepness (nonlinearity) can be effectively absorbed, the length of a calculation domain is not required to be additionally increased, the calculation efficiency is greatly improved, and the nonlinear multidirectional wave absorption method has good absorption effect on long waves and universality. The invention also relates to a nonlinear multidirectional wave absorbing system.
The technical scheme of the invention is as follows:
a nonlinear multidirectional wave absorbing method, comprising the steps of:
s1: decomposing the wave equation based on the unit vector of the wave number, obtaining a first absorption boundary equation for absorbing wave components in different propagation directions according to the wave propagation directions, and performing approximate treatment on the equation of the relation between the wave phase velocity and the water wave dispersion by using a Pade approximation method to obtain a second absorption boundary equation for absorbing wave components in different nonlinearities;
S2: constructing a first relation of a velocity potential function in the wave number and the wave equation, constructing a second relation of the velocity potential function and the velocity of the fluid particles at the boundary of the calculation domain and a third relation of the velocity potential function and the pressure of the fluid particles according to a definition of the velocity potential function and the Bernoulli equation, calculating the first relation, the first absorption boundary equation and the second absorption boundary equation to obtain a first equation, and calculating and dispersing the first equation, the second relation and the third relation to obtain a pressure Poisson equation;
s3: and solving the pressure poisson equation by adopting an ILU-BiCGSTAB algorithm to obtain the speed and the pressure of the fluid particles as a first speed and a first pressure, and using the speed and the pressure of the fluid particles at the boundary of the calculation domain, which are propagated by the wave, as a second speed and a second pressure, comparing the second speed and the second pressure with the first speed and the first pressure respectively, and if the second speed and the first speed are equal and the second pressure is equal to the first pressure, completely absorbing the wave.
Preferably, in the step S1, decomposing the wave equation based on the unit vector of the wave number includes:
A first step of: decomposing the wave equation into a fourth relation about the wave propagation direction operator based on the unit vector of wave numbers;
And a second step of: applying a wave propagation direction operator to a velocity potential function in the wave equation to obtain a second equation;
And a third step of: and multiplying both sides of the second equation by normal vectors simultaneously to obtain a first absorption boundary equation.
Preferably, in the step S2, the first equation is calculated by substituting the first relational expression and the second absorption boundary equation into the first absorption boundary equation.
Preferably, in the step S2, the pressure poisson equation is obtained by substituting the second relation and the third relation into the first equation, calculating to obtain a third equation, and dispersing the third equation to obtain the pressure poisson equation.
Preferably, in the step S1, the direction of the unit vector of the wave number is the propagation direction of the wave.
A nonlinear multidirectional wave absorbing system is characterized by comprising a first module, a second module and a third module which are sequentially connected,
The wave-absorbing device comprises a first module, a second module and a third module, wherein the first module is used for decomposing a wave equation based on a unit vector of wave number, obtaining a first absorption boundary equation for absorbing wave components in different propagation directions according to wave propagation directions, and performing approximate processing on an equation of a relation between wave phase velocity and water wave dispersion by using a Pade approximation method to obtain a second absorption boundary equation for absorbing wave components in different nonlinearities;
the second module is used for constructing a first relation of the velocity potential function in the wave number and the wave equation, constructing a second relation of the velocity potential function and the velocity of the fluid particles at the boundary of the calculation domain and a third relation of the velocity potential function and the pressure of the fluid particles according to the definition of the velocity potential function and the Bernoulli equation, calculating the first relation, the first absorption boundary equation and the second absorption boundary equation to obtain a first equation, and calculating and dispersing the first equation, the second relation and the third relation to obtain a pressure Poisson equation;
And a third module for solving the pressure poisson equation by using an ILU-BiCGSTAB algorithm to obtain the speed and pressure of the fluid particles as a first speed and a first pressure, and for using the speed and pressure of the fluid particles at the boundary of the calculation domain as a second speed and a second pressure, and comparing the second speed and the second pressure with the first speed and the first pressure respectively, wherein if the second speed and the first speed are equal and the second pressure is equal to the first pressure, the wave is completely absorbed.
Preferably, in the first module, decomposing the wave equation based on the unit vector of wave numbers includes:
decomposing the wave equation into a fourth relation about the wave propagation direction operator based on the unit vector of wave numbers; applying a wave propagation direction operator to a velocity potential function in the wave equation to obtain a second equation; and multiplying both sides of the second equation by normal vectors simultaneously to obtain a first absorption boundary equation.
Preferably, in the second module, the first equation is calculated by substituting the first relation and the second absorption boundary equation into the first absorption boundary equation, and calculating the first equation.
Preferably, in the second module, the obtaining of the pressure poisson equation includes:
substituting the second relation and the third relation into the first equation, calculating to obtain a third equation, and dispersing the third equation to obtain a pressure poisson equation.
Preferably, the direction of the unit vector of the wave number is the propagation direction of the wave.
The beneficial effects of the invention are as follows:
according to the nonlinear multidirectional wave absorption method provided by the invention, based on a nonlinear wave theory, the wave equation is decomposed based on the unit vector of wave number to obtain the first absorption boundary equation, and the absorption boundary condition can be selected according to the wave propagation direction; the equation of the relation between the wave phase velocity and the water wave dispersion is approximated by using the Pade approximation method, so that a second absorption boundary equation is obtained, wave components with different wave steepness (nonlinearity) can be effectively absorbed, the wave steepness (nonlinearity) range of the absorbable wave is further enlarged, and the (secondary) reflection of nonlinear irregular waves is effectively reduced; meanwhile, a relational expression of the wave number and a velocity potential function in the wave equation and a relational expression of the velocity potential function and the velocity and the pressure of fluid particles at a calculation domain boundary in a numerical water tank are constructed, so that an absorption boundary condition is easy to apply to a Navier-Stokes solver, a pressure Poisson equation is finally obtained through conversion of a corresponding formula, the pressure Poisson equation is solved by adopting an ILU-BiCGSTAB algorithm, and whether waves are completely absorbed or not is judged according to comparison of a calculation result and the velocity and the pressure of the fluid particles at the calculation domain boundary of the waves transmitted to the numerical water tank. According to the invention, waves with different wave directions and wave steepness can be effectively absorbed without additionally increasing the length of the calculation domain, so that the calculation efficiency is greatly improved, the absorption effect on long waves is good, in addition, the absorption boundary equation is applied to the calculation domain boundary in the numerical pool, and the target waves can be generated simultaneously, namely, waves are allowed to be simultaneously transmitted and transferred on the same boundary, and the real ocean environment is simulated.
The invention also relates to a nonlinear multidirectional wave absorption system, which corresponds to the nonlinear multidirectional wave absorption method and can be understood as a system for realizing the nonlinear multidirectional wave absorption method, and the system comprises a first module, a second module and a third module which are sequentially connected, wherein the modules work cooperatively with each other, a wave equation is decomposed based on a unit vector of wave number to obtain a first absorption boundary equation, and an equation of a wave phase velocity and water wave dispersion relation is approximated by using a Pade approximation method to obtain a second absorption boundary equation; meanwhile, a relational expression of the wave number and a velocity potential function in the wave equation and a relational expression of the velocity potential function and the velocity and the pressure of fluid particles at a calculation domain boundary in a numerical water tank are constructed, a pressure poisson equation is obtained through relational conversion and dispersion, and the ILU-BiCGSTAB algorithm is adopted to solve the pressure poisson equation and judge whether waves are completely absorbed. According to the wave equation decomposition method, the wave components with different wave steeps (nonlinearity) can be effectively absorbed by decomposing the wave equation and designing the absorption boundary condition operators for waves in different directions according to the wave directions and further approximating the second-order dispersion relation of the water waves. Compared with the existing passive wave-absorbing method, the method can effectively absorb waves with different wave directions and wave steepness without additionally increasing the length of a calculation domain, greatly improves the calculation efficiency, and has good absorption effect on long waves. Compared with the existing active wave-absorbing method, the method can effectively absorb wave components with larger wave steepness based on the nonlinear wave theory, and in addition, the information of reflected waves does not need to be estimated and input manually.
Drawings
FIG. 1 is a flow chart of the nonlinear multidirectional wave absorbing method of the present invention.
Fig. 2 is a preferred flow chart of the nonlinear multidirectional wave absorbing method of the present invention.
FIG. 3 is a graph of velocity and pressure profiles of fluid particles at the boundary of a calculated domain in a numeric pool of water according to the present invention.
Detailed Description
The present invention will be described below with reference to the accompanying drawings.
The invention relates to a nonlinear multidirectional wave absorbing method, which comprises the following steps in sequence, wherein a flow chart of the method is shown in fig. 1:
s1: decomposing the wave equation based on the unit vector of the wave number, obtaining a first absorption boundary equation for absorbing wave components in different propagation directions according to the wave propagation directions, and performing approximate treatment on the equation of the relation between the wave phase velocity and the water wave dispersion by using a Pade approximation method to obtain a second absorption boundary equation for absorbing wave components in different nonlinearities;
Wherein, wave equation is:
In the above-mentioned method, the step of, As a function of the velocity potential, c is the wave phase velocity and t is time.
The unit vector e k of wave number k is:
In the above equation, k x and k y are components of the wave number k in the x-direction and the y-direction, respectively, and the direction of e k is the propagation direction of the wave.
As shown in fig. 2, based on the propagation direction e k of the wave, the wave equation (1) can be decomposed into a relational expression with respect to the wave propagation direction operator (i.e., with respect to the first operator and the second operator):
wherein the first operator is expressed as The second operator is denoted/>
The first operator in the formula (3)Applied to the velocity potential function/>The following second equation can be obtained:
at this time, equation (4) can identify a wave component having a wave propagation direction e k.
Multiplying both sides of equation (4) simultaneously by normal vector n yields the first absorption boundary equation:
Because the actual waves contain components with different frequencies, different amplitudes and phases, the equation of the relation between the wave phase velocity and the water wave dispersion is approximated by using the Pade P-de approximation method, and a second absorption boundary equation is obtained:
Wherein c is the wave phase velocity, g is the gravitational acceleration, k is the wave number, h is the water depth, A 0,a1 and b 1 are approximation parameters, and by selecting appropriate approximation parameters a 0,a1 and b 1, a second absorption boundary equation for different wave steepness can be obtained.
S2: constructing a first relation of a velocity potential function in the wave number and the wave equation, constructing a second relation of the velocity potential function and the velocity of the fluid particles at the boundary of the calculation domain and a third relation of the velocity potential function and the pressure of the fluid particles according to a definition of the velocity potential function and the Bernoulli equation, calculating the first relation, the first absorption boundary equation and the second absorption boundary equation to obtain a first equation, and calculating and dispersing the first equation, the second relation and the third relation to obtain a pressure Poisson equation;
Specifically, a first relation between wave numbers and a velocity potential function in a wave equation is firstly constructed, and the first relation and a second absorption boundary equation are substituted into the first absorption boundary equation to obtain a first equation;
wherein, the first relation is:
Where z represents the vertical coordinate.
Substituting the second absorption boundary equation (6) and the first relation (7) into the first absorption boundary equation (5) to obtain a first equation:
constructing a second relation between the velocity potential function and the velocity of the fluid particles at the boundary of the calculation domain in the numerical pool and a third relation between the velocity potential function and the pressure of the fluid particles according to the definition of the velocity potential function and the linear Bernoulli equation;
wherein the second relation is:
The third relation is:
where u is the velocity of the fluid particles at the computational domain boundary, p is the pressure of the fluid particles at the computational domain boundary, and b is the computational domain exit boundary.
Substituting the second relation (9) and the third relation (10) into the first relation (8), and further finishing to obtain the following third relation:
S3: and (3) performing discretization on the formula (11) to obtain a pressure poisson equation, solving the pressure poisson equation by adopting an ILU-BiCGSTAB algorithm to obtain the speed and the pressure of the fluid particles, taking the speed and the pressure as a first speed and a first pressure, spreading waves to a numerical pool, calculating the speed and the pressure of the fluid particles at the boundary of a domain, taking the speed and the pressure as a second speed and a second pressure, comparing the second speed and the second pressure with the first speed and the first pressure respectively, and completely absorbing the waves if the second speed and the first speed are equal and the second pressure is equal to the first pressure.
Wherein, the poisson equation of pressure is:
Where B and V are coefficient matrices, p i is the pressure vector of the fluid particles at the boundary of the computational domain, To calculate the velocity vector of the fluid particles at the domain boundary, e k represents the direction of wave propagation.
Wherein the coefficient matrices B and V, the pressure vector p i and the velocity vectorIs defined as:
Vzl＝δQ1,Vc＝∈-δQ2,Vzr＝δQs.
The variables appearing in the above definitions are now explained as follows:
Velocity and pressure profiles of fluid particles at the boundary of the computational domain in a numerical pool as shown in FIG. 3, with subscripts i and k representing grid coordinates in the x-and z-directions, respectively, of the computational domain;
C, D are a convection matrix and a dissipation matrix in the momentum equation respectively; f is the volumetric force to which the fluid is subjected; μ represents the dynamic viscosity coefficient of the fluid; ρ represents the fluid density.
Where Δt and Δx represent the time step and the grid size in the x-direction, respectively.
Wherein Δz i,k＝zi,k-zi,k-1;Δzi,k+1＝zi,k+1-zi,k.
And finally, solving the pressure poisson equation by adopting an ILU-BiCGSTAB algorithm to obtain the speed u and the pressure p of the fluid particles as a first speed and a first pressure, spreading the waves to a numerical pool to calculate the speed and the pressure of the fluid particles at the boundary of the domain as a second speed and a second pressure, comparing the second speed and the second pressure with the first speed and the first pressure respectively, and if the second speed and the first speed are equal and the second pressure is equal to the first pressure, completely absorbing the waves, wherein the reflection coefficient is zero, and the reflection coefficient is the ratio of the amplitude of the reflected waves at the boundary to the amplitude of the incident waves. If the second speed and the first speed are not equal or the second pressure is not equal to the first pressure, the waves cannot be absorbed completely, and the reflection coefficient can be controlled below 5% by selecting the appropriate approximate parameters a 0,a1 and b 1, which are equivalent to the reflection coefficient in the pool test.
The invention also relates to a nonlinear multidirectional wave absorbing system, which corresponds to the nonlinear multidirectional wave absorbing method, and can be understood as a system for realizing the method, and comprises a first module, a second module and a third module which are sequentially connected, in particular,
The wave-absorbing device comprises a first module, a second module and a third module, wherein the first module is used for decomposing a wave equation based on a unit vector of wave number, obtaining a first absorption boundary equation for absorbing wave components in different propagation directions according to wave propagation directions, and performing approximate processing on an equation of a relation between wave phase velocity and water wave dispersion by using a Pade approximation method to obtain a second absorption boundary equation for absorbing wave components in different nonlinearities;
the second module is used for constructing a first relation of the velocity potential function in the wave number and the wave equation, constructing a second relation of the velocity potential function and the velocity of the fluid particles at the boundary of the calculation domain and a third relation of the velocity potential function and the pressure of the fluid particles according to the definition of the velocity potential function and the Bernoulli equation, calculating the first relation, the first absorption boundary equation and the second absorption boundary equation to obtain a first equation, and calculating and dispersing the first equation, the second relation and the third relation to obtain a pressure Poisson equation;
And a third module for solving the pressure poisson equation by using an ILU-BiCGSTAB algorithm to obtain the speed and pressure of the fluid particles as a first speed and a first pressure, and for using the speed and pressure of the fluid particles at the boundary of the calculation domain as a second speed and a second pressure, and comparing the second speed and the second pressure with the first speed and the first pressure respectively, wherein if the second speed and the first speed are equal and the second pressure is equal to the first pressure, the wave is completely absorbed.
Preferably, in the first module, decomposing the wave equation based on the unit vector of wave numbers includes: decomposing the wave equation into a fourth relation about the wave propagation direction operator based on the unit vector of wave numbers; applying a wave propagation direction operator to a velocity potential function in the wave equation to obtain a second equation; and multiplying both sides of the second equation by normal vectors simultaneously to obtain a first absorption boundary equation.
Preferably, in the second module, the first equation is calculated by substituting the first relation and the second absorption boundary equation into the first absorption boundary equation.
Preferably, in the second module, the obtaining of the pressure poisson equation includes: substituting the second relation and the third relation into the first equation, calculating to obtain a third equation, and dispersing the third equation to obtain a pressure poisson equation.
Preferably, the direction of the unit vector of wave numbers is the propagation direction of the waves.
The invention provides an objective and scientific nonlinear multidirectional wave absorption method and system, which are characterized in that a wave equation is decomposed based on a unit vector of wave number, and an equation of the relation between wave phase velocity and water wave dispersion is approximated by using a Pade approximation method, so that wave components in different propagation directions and wave components in different wave steeps (nonlinearity) can be effectively absorbed, the (secondary) reflection of nonlinear irregular waves is effectively reduced, and meanwhile, a relation between wave number and a velocity potential function in the wave equation is constructed, so that an absorption boundary condition is easy to apply to a Navier-Stokes solver, the calculation efficiency is greatly improved, and the nonlinear multidirectional wave absorption method has good absorption effect and universality on long waves. The invention discloses a strong nonlinear mechanism of interaction between marine equipment and wave flow, and enhances the understanding and understanding of related basic science by researching the technologies of a wave making method of an absorption boundary of nonlinear waves, an absorption method of wave components parallel to the boundary in a three-dimensional calculation domain, an incident and reflected wave separation method and the like and combining the technologies with a three-dimensional large vortex simulation Navier-Stokes solver, researching the hydrodynamic performance of a complex marine structure in a flow field, wave rolling and crushing (large free surface deformation), the interaction mechanism between waves and flow and the like.
It should be noted that the above-described embodiments will enable those skilled in the art to more fully understand the invention, but do not limit it in any way. Therefore, although the present invention has been described in detail with reference to the drawings and examples, it will be understood by those skilled in the art that the present invention may be modified or equivalent, and in all cases, all technical solutions and modifications which do not depart from the spirit and scope of the present invention are intended to be included in the scope of the present invention.
Claims (10)
1. A nonlinear multidirectional wave absorbing method, comprising the steps of:
S1: decomposing the wave equation based on the unit vector of the wave number, and obtaining a first absorption boundary equation for absorbing wave components in different propagation directions according to the wave propagation directions, wherein the first absorption boundary equation is expressed as:
In the above formula, n is a normal vector, e k is a unit vector of wave number k, c is wave phase velocity, t is time, As a function of velocity potential; and performing approximation processing on an equation of the relation between the wave phase velocity and the water wave dispersion by using a Pade approximation method to obtain a second absorption boundary equation for absorbing wave components with different nonlinearities, wherein the second absorption boundary equation is expressed as:
In the above formula, c is the wave phase velocity, g is the gravitational acceleration, k is the wave number, h is the water depth, and a 0,a1 and b 1 are approximate parameters;
S2: constructing a first relation of a velocity potential function in the wave number and the wave equation, constructing a second relation of the velocity potential function and the velocity of the fluid particles at the boundary of the calculation domain and a third relation of the velocity potential function and the pressure of the fluid particles according to a definition of the velocity potential function and the Bernoulli equation, calculating the first relation, the first absorption boundary equation and the second absorption boundary equation to obtain a first equation, and calculating and dispersing the first equation, the second relation and the third relation to obtain a pressure Poisson equation;
s3: and solving the pressure poisson equation by adopting an ILU-BiCGSTAB algorithm to obtain the speed and the pressure of the fluid particles as a first speed and a first pressure, and using the speed and the pressure of the fluid particles at the boundary of the calculation domain, which are propagated by the wave, as a second speed and a second pressure, comparing the second speed and the second pressure with the first speed and the first pressure respectively, and if the second speed and the first speed are equal and the second pressure is equal to the first pressure, completely absorbing the wave.
2. The nonlinear multidirectional wave absorbing method as defined in claim 1, wherein in the S1 step, decomposing the wave equation based on the unit vector of wave numbers includes:
a first step of: decomposing a wave equation into a fourth relation about a wave propagation direction operator based on a unit vector of wave numbers, wherein the wave equation is:
In the above-mentioned method, the step of, C is the wave phase velocity and t is the time;
The unit vector e k of wave number k is:
In the above formula, k x and k y are components of the wave number k in the x direction and the y direction, respectively, and the direction of e k is the propagation direction of waves;
Based on the wave propagation direction e k, decomposing the wave equation into a fourth relation with respect to the wave propagation direction operator:
Wherein the wave propagation direction operator comprises a first operator and a second operator, the first operator is expressed as The second operator is denoted/>
And a second step of: applying the wave propagation direction operator to a velocity potential function in the wave equation to obtain a second equation, and applying the first operator to the wave propagation direction operatorApplied to the velocity potential function/>A second equation is obtained:
And a third step of: and multiplying both sides of the second equation by normal vectors simultaneously to obtain a first absorption boundary equation.
3. The nonlinear multidirectional wave absorbing method according to claim 1, wherein in the step S2, the first equation is calculated by substituting the first relational expression and the second absorption boundary equation into the first absorption boundary equation.
4. The nonlinear multidirectional wave absorbing method according to claim 3, wherein in the step S2, the pressure poisson equation is obtained by substituting the second relation and the third relation into the first equation, calculating a third relation, and dispersing the third relation to obtain the pressure poisson equation.
5. The nonlinear multidirectional wave absorbing method as defined in claim 1, wherein in the step S1, the direction of the unit vector of wave number is the propagation direction of the wave.
6. A nonlinear multidirectional wave absorbing system is characterized by comprising a first module, a second module and a third module which are sequentially connected,
The first module is used for decomposing the wave equation based on the unit vector of the wave number, and obtaining a first absorption boundary equation for absorbing wave components in different propagation directions according to the wave propagation directions, wherein the first absorption boundary equation is expressed as:
In the above formula, n is a normal vector, e k is a unit vector of wave number k, c is wave phase velocity, t is time, As a function of velocity potential; and performing approximation processing on an equation of the relation between the wave phase velocity and the water wave dispersion by using a Pade approximation method to obtain a second absorption boundary equation for absorbing wave components with different nonlinearities, wherein the second absorption boundary equation is expressed as:
In the above formula, c is the wave phase velocity, g is the gravitational acceleration, k is the wave number, h is the water depth, and a 0,a1 and b 1 are approximate parameters;
the second module is used for constructing a first relation of the velocity potential function in the wave number and the wave equation, constructing a second relation of the velocity potential function and the velocity of the fluid particles at the boundary of the calculation domain and a third relation of the velocity potential function and the pressure of the fluid particles according to the definition of the velocity potential function and the Bernoulli equation, calculating the first relation, the first absorption boundary equation and the second absorption boundary equation to obtain a first equation, and calculating and dispersing the first equation, the second relation and the third relation to obtain a pressure Poisson equation;
And a third module for solving the pressure poisson equation by using an ILU-BiCGSTAB algorithm to obtain the speed and pressure of the fluid particles as a first speed and a first pressure, and for using the speed and pressure of the fluid particles at the boundary of the calculation domain as a second speed and a second pressure, and comparing the second speed and the second pressure with the first speed and the first pressure respectively, wherein if the second speed and the first speed are equal and the second pressure is equal to the first pressure, the wave is completely absorbed.
7. The nonlinear multidirectional wave absorbing system of claim 6, wherein in the first module, decomposing the wave equation based on a unit vector of wave numbers includes:
decomposing a wave equation into a fourth relation about a wave propagation direction operator based on a unit vector of wave numbers, wherein the wave equation is:
In the above-mentioned method, the step of, C is the wave phase velocity and t is the time;
The unit vector e k of wave number k is:
In the above formula, k x and k y are components of the wave number k in the x direction and the y direction, respectively, and the direction of e k is the propagation direction of waves;
Based on the wave propagation direction e k, decomposing the wave equation into a fourth relation with respect to the wave propagation direction operator:
Wherein the wave propagation direction operator comprises a first operator and a second operator, the first operator is expressed as The second operator is denoted/>Applying a wave propagation direction operator to a velocity potential function in the wave equation to obtain a second equation, and applying a first operator/>Applied to the velocity potential function/>A second equation is obtained:
And multiplying both sides of the second equation by normal vectors simultaneously to obtain a first absorption boundary equation.
8. The nonlinear multidirectional wave absorbing system of claim 6, wherein in the second module, a first equation is calculated by substituting the first relation and a second absorption boundary equation into the first absorption boundary equation.
9. The nonlinear multidirectional wave absorbing system of claim 8, wherein in the second module, the obtaining of the pressure poisson equation includes:
substituting the second relation and the third relation into the first equation, calculating to obtain a third equation, and dispersing the third equation to obtain a pressure poisson equation.
10. The nonlinear multidirectional wave absorbing system of claim 6, wherein the direction of the unit vector of wave numbers is the wave propagation direction.
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| CN111241756A (en) * | 2020-01-08 | 2020-06-05 | 大连理工大学 | Numerical wave water tank wave making method based on Fluent UDF |
| CN114624002A (en) * | 2022-03-15 | 2022-06-14 | 浙江大学 | Intelligent wave generation method based on machine learning |
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| US6611736B1 (en) * | 2000-07-01 | 2003-08-26 | Aemp Corporation | Equal order method for fluid flow simulation |
| CN111241756A (en) * | 2020-01-08 | 2020-06-05 | 大连理工大学 | Numerical wave water tank wave making method based on Fluent UDF |
| CN114624002A (en) * | 2022-03-15 | 2022-06-14 | 浙江大学 | Intelligent wave generation method based on machine learning |
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