Smooth particle improvement method for simulating wave impact on single pile foundation

Abstract

The invention discloses an improved smoothed particle method for simulating wave impact on a single pile foundation, and belongs to the field of computational fluid mechanics. The invention provides an improved smoothed particle fluid dynamics method for solving the problems that in the prior art, an SPH method is low in precision and remarkable in numerical dissipation, an FPM method cannot simulate free surface flow, and a particle method is low in calculation efficiency and difficult to achieve three-dimensional simulation. According to the method, the FPM format with the second-order precision is adopted in the fluid to improve the calculation precision, the SPH method is reserved near the free surface to guarantee the free surface capturing capacity, particle distribution is optimized in combination with the ASPH multi-resolution technology, and the calculation efficiency is remarkably improved. Through SPH-FPM-ASPH multi-method coupling, high-precision and high-efficiency three-dimensional simulation of interaction of waves and a single pile is achieved, and a reliable numerical analysis tool is provided for safety evaluation and optimization design of ocean engineering structures.

Description

Technical Field

[0001] The invention belongs to the field of computational fluid dynamics, and in particular relates to an improved smooth particle method for simulating wave impact on a single pile foundation. Background Art

[0002] Wave impact on monopile foundations is a key issue in marine engineering. Monopile structures (such as offshore wind turbine towers, pier pile foundations, and oil platform support columns) are subjected to long-term periodic wave impacts, which directly affect the safety and durability of the structures. Extreme waves (such as typhoons or huge waves) can trigger strong instantaneous impact loads, leading to pile foundation vibration, fatigue damage, and even structural failure. In addition, the interaction between waves and piles can also produce vortex-induced vibrations, local scouring, and other phenomena, further threatening the stability of the structure. Accurately predicting wave impact loads and dynamic responses is crucial for optimizing monopile design, extending service life, and reducing maintenance costs. It is a core challenge to ensure the safe operation of marine engineering. Therefore, accurately simulating the interaction between waves and monopile structures is crucial for evaluating the stability of structures, optimizing design parameters, and predicting structural responses under extreme wave loads. Traditional mesh-based numerical methods (such as the finite volume method and the finite element method) often face problems such as difficulty in free surface tracking and reduced accuracy due to mesh distortion when dealing with such problems. Especially under complex flow conditions such as wave breaking and strong nonlinear impact, computational stability and accuracy are difficult to guarantee.

[0003] Meshless methods, especially smoothed particle hydrodynamics (SPH) methods, have become effective tools for simulating wave impact problems due to their Lagrangian characteristics and natural free surface processing capabilities. However, the traditional SPH method has defects such as low accuracy (only first-order convergence) and significant numerical dissipation, which may lead to load prediction errors when simulating wave impact on single piles. As an improved particle method, the finite particle method (FPM) can greatly improve the calculation accuracy through second-order accuracy, but its disadvantage is that its dependence on the integrity of the particle support domain makes it unable to solve the flow near the free surface. In addition, the FPM method requires additional solution of the coefficient matrix in the calculation, resulting in lower computational efficiency than the traditional SPH method. On the other hand, the interaction process between waves and single piles is a three-dimensional problem and cannot be simplified to a two-dimensional simulation, which greatly limits the computational efficiency and scale.

[0004] ASPH (Anisotropic Smoothed Particle Hydrodynamics, SPH), an emerging particle multi-resolution algorithm, significantly accelerates the solution of numerical problems requiring different resolutions in different directions. For example, traditional wave-structure interaction simulations require different resolutions for the wave's forward direction and the water depth. This has been demonstrated in numerous grid-based numerical simulations. From this perspective, ASPH is highly suitable for simulating wave-structure interaction problems, alleviating the decreased computational efficiency associated with the FPM method. However, to date, the application of ASPH to fluid simulation has been largely unsuccessful. The reason is that, firstly, in the existing ASPH work applied to solid mechanics, the particle motion amplitude is small and the neighbor relationship remains unchanged, but the irregular particle motion caused by fluid motion and the constantly updated particle neighbor relationship significantly increase the simulation difficulty; secondly, the classical SPH method has the characteristic of reduced accuracy under the condition of uneven particles, which limits its application in complex problems such as wave-single pile interaction. This problem is solved in the present invention by the SPH-FPM coupling framework; finally, the applicability of important auxiliary technologies in fluid simulation, such as particle displacement technology, under the ASPH framework has not yet been confirmed. Summary of the Invention

[0005] In response to the problems in the prior art, this application proposes an improved smooth particle method for simulating wave impact on a single pile foundation.

[0006] The present invention intends to improve the accuracy of numerical calculations by using the FPM method to calculate the particles inside the fluid; by coupling the SPH-FPM method, the traditional SPH method is used to replace the FPM method near the free surface to solve the problem that the FPM method cannot simulate the free surface; by coupling the ASPH method, the particle spacing is increased in the water depth direction, and a sparser particle resolution is used in the other two directions, ultimately achieving the purpose of accurately and efficiently simulating the problem of wave impact on single pile foundations.

[0007] To solve the above technical problems, the technical solution adopted by the present invention is an improved smooth particle method for simulating wave impact on a single pile foundation, which specifically includes the following steps:

[0008] 1) At the initial moment, based on the simulated wave elements and the pile dimensions, SPH particles are used to discretize the water body and the pile boundary in the ocean waves, and a numerical model of the interaction between ocean waves and piles is established. The wave elements include water depth, wave period, and wave height; the pile dimensions include the pile center point position, pile radius, and pile height.

[0009] 2) Assigning initial values ​​of required physical quantities to all SPH particles, including pressure, velocity, density, mass, and smooth length, and starting the time step iterative calculation in the numerical simulation after the initialization is completed;

[0010] 3) SPH particles include boundary particles and fluid particles. In each time step, before calculating the fluid particles, we first determine whether the particle is a free surface particle. Among them, the 3-4 layers of particles from the outermost free surface inward are all free surface particles.

[0011] 4) If a fluid particle i is a free surface particle, its density increment is calculated using the SPH discretized continuity equation. The velocity increment of particle i is calculated using the Navier-Stokes equation discretized by the SPH method. All kernel functions and their gradients used in the calculation are determined by the normalized distance vector η.

[0012] 5) If a fluid particle i is not a free surface particle, the density increment of particle i is calculated using the continuity equation after FPM discretization, and the velocity increment of particle i is calculated using the Navier-Stokes equation after FPM discretization; all kernel functions and their gradients used in the calculation are determined by the normalized distance vector η;

[0013] 6) If a particle is a boundary particle, use Shepard interpolation to solve the particle's pressure, density, and velocity;

[0014] 7) For all fluid particles, after obtaining the particle velocity increment and density increment according to steps 4) and 5), update the particle density and velocity and proceed to the next time step solution.

[0015] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0016] High computational accuracy: When simulating wave impacts on single pile foundations, the SPH-FPM-ASPH coupled numerical model proposed in this application leverages the particle method's advantages in capturing free surfaces and addressing large deformations, avoiding the accuracy degradation associated with traditional mesh methods due to mesh distortion. Furthermore, the use of the second-order FPM format within the fluid significantly improves computational accuracy.

[0017] Computational efficiency optimization: By introducing ASPH multi-resolution technology, the particle distribution is dynamically adjusted according to the characteristics of wave-structure interaction (such as high resolution along the water depth direction and low resolution in the horizontal direction), which greatly reduces the number of calculated particles and improves the computational efficiency of 3D simulation while ensuring the simulation accuracy of key areas.

[0018] Wide Applicability: This model accurately simulates strong nonlinear phenomena (such as vortex-induced vibration and transient impact loads) under the impact of extreme waves (e.g., typhoons and giant waves), providing a reliable basis for the safety assessment and optimized design of monopile structures. Furthermore, the SPH-FPM coupling strategy effectively overcomes the FPM method's inability to simulate free surfaces, resulting in a model with both high accuracy and stability.

[0019] Strong engineering practicality: This technology can provide efficient and accurate numerical tools for the design and safety analysis of single pile structures such as offshore wind turbine towers and wharf pile foundations, helping to reduce engineering risks and maintenance costs, and has important engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 is a flow chart of the method of the present invention;

[0021] Figure 2 The model setting for simulating wave impact on a single pile foundation is shown as an example;

[0022] Figure 3 Velocity distribution of the flow field at t = 20s (viewed from above);

[0023] Figure 4 Velocity distribution of the flow field (side view) at t = 20s;

[0024] Figure 5 Pressure distribution around a single pile on the centerline section of the water tank at t = 20s. DETAILED DESCRIPTION

[0025] The present invention will be further described and illustrated below in conjunction with specific embodiments. The embodiments are merely illustrative of the present disclosure and do not limit its scope. The technical features of the various embodiments of the present invention may be combined accordingly, provided that there is no conflict between them.

[0026] like Figure 1 As shown, the improved smooth particle method for simulating wave impact on a single pile foundation in this embodiment includes the following steps:

[0027] 1) At the initial moment, based on the simulated wave elements and the pile dimensions, SPH particles are used to discretize the water body and the pile boundary in the ocean waves, and a numerical model of the interaction between ocean waves and piles is established. The wave elements include water depth, wave period, and wave height; the pile dimensions include the pile center point position, pile radius, and pile height.

[0028] 2) Assigning initial values ​​of required physical quantities to all SPH particles, including pressure, velocity, density, mass, and smooth length, and starting the time step iterative calculation in the numerical simulation after the initialization is completed;

[0029] 3) SPH particles include boundary particles and fluid particles. In each time step, before calculating the fluid particles, we first determine whether the particle is a free surface particle. Among them, the 3-4 layers of particles from the outermost free surface inward are all free surface particles.

[0030] 4) If a fluid particle i is a free surface particle, its density increment is calculated using the SPH discretized continuity equation. The velocity increment of particle i is calculated using the Navier-Stokes equation discretized by the SPH method. All kernel functions and their gradients used in the calculation are determined by the normalized distance vector η.

[0031] Specifically, the density increment is calculated according to the SPH format discretized continuity equation, specifically:

[0032]

[0033] Among them, ρ i is the density of particle i, t represents time, particle j is a particle in the support domain of particle i, u i 、u j are the velocity vectors of particles i and j, is the kernel function gradient, m j , ρ j are the mass and density of particle j, respectively.

[0034] The velocity increment of particle i is calculated using the Navier-Stokes equation discretized by the SPH method, specifically:

[0035]

[0036] in,

[0037] π ij =(u j -u i )·(x j -x i ) / |x ij | 2 ,

[0038] In the above formula, g is the gravitational acceleration vector, c is the speed of sound, and ρ 0,i is the reference density of particle i, ρ i is the density of particle i at the current time step, p i 、p j is the pressure of particles i and j, W ij is the kernel function value determined by the distance between particles j and i, α is the artificial viscosity coefficient, h is the smoothing length, and x i 、x j is the position vector of particles i and j, xij =x i -x j is the distance vector between particles i and j.

[0039] As the core idea of ​​ASPH, all kernel functions and kernel function gradients are determined by the normalized distance vector η, rather than the position vector x in classic SPH. ij Determine the distance vector x before normalization ij The relationship between the normalized distance vector η is:

[0040] η=Gx ij

[0041] In the above formula, G is a deformation tensor:

[0042]

[0043] h x 、h y 、h z are the smooth lengths of the particles in the x, y, and z directions respectively;

[0044] The kernel function gradient expressed as the normalized distance vector η for:

[0045]

[0046] η=|η| is the length of the distance vector η.

[0047] 5) If a fluid particle i is not a free surface particle, the density increment of particle i is calculated using the continuity equation after FPM discretization, and the velocity increment of particle i is calculated using the Navier-Stokes equation after FPM discretization; all kernel functions and their gradients used in the calculation are determined by the normalized distance vector η;

[0048] Step 5) specifically includes:

[0049] The density increment and velocity increment after FPM discretization are calculated as follows:

[0050]

[0051]

[0052] Among them, W is the kernel function value, is the kernel function gradient The components in the x, y, and z directions, u i 、v i 、w i is the velocity vector u of particle i iThe components in the x, y, and z directions, τ i,x , τ i,y , τ i,z is the component of the viscous force τ in the x, y, and z directions, F i,x 、F i,y 、F i,z is the component of the body force F in the x, y, and z directions, V j =m j / ρ j is the volume of particle j; a mn are the elements in the coefficient matrix, m = 1, 2, 3, 4; n = 1, 2, 3, 4:

[0053]

[0054] Among them, x ji =-x ij ,y ji =-y ij , z ji =-z ij , x ij 、y ij 、z ij is the distance vector x between particles i and j ij Components in the x, y, and z directions.

[0055] Similar to step 4), as the core idea of ​​ASPH, all kernel functions and kernel function gradients in step 5) are also determined by the normalized distance vector η. The kernel function gradient represented by the normalized distance vector η is the same as that in step 4).

[0056] 6) If a particle is a boundary particle, use Shepard interpolation to solve the particle's pressure, density, and velocity;

[0057] Pressure and velocity are solved according to the following formula:

[0058]

[0059]

[0060] Where f represents the fluid particles, p f 、m f , ρ f are the pressure, mass and density of the fluid particles, u f is the velocity vector of the fluid particle f, W if is the kernel function value determined by the normalized distance η = |η| between the boundary particle i and the fluid particle f; the density of the boundary particle i is determined by its pressure p i Combining the weakly compressible state equation gives:

[0061] ρi = ρ0 + p i / c 2

[0062] Where c is the artificial sound speed in the simulation; in addition, to ensure that there is no non - physical particle penetration under strong non - linear conditions such as wave impinging on a monopile foundation and wave breaking, the following correction is applied to the acceleration of fluid particles near the boundary particles of the monopile:

[0063]

[0064] Where h min is the minimum of the smoothing lengths of the boundary particle i in the x, y, and z directions, n i is the normal vector of the boundary particle, pointing from the center of the monopile foundation to the outside, and u f and u i are the velocity vectors of the fluid particle f and the boundary particle i, respectively.

[0065] 7) For all fluid particles, after obtaining the velocity increment and density increment of the particles according to steps 4) and 5), update the density and velocity of the particles and enter the solution of the next time step. After updating the particle positions, use the linked - list search method or the tree - search method to quickly traverse all particles i to obtain the sequence numbers of all their adjacent particles; the basis for determining whether two particles i and j are adjacent particles is: the length of the distance vector between particles i and j, η < R, where R is the radius of the selected kernel function.

[0066] According to the preferred embodiment of the present invention, after step 7) is completed, the particle displacement technique is also used for the fluid particles on the non - free surface to ensure that the particle distribution is as uniform as possible, thereby avoiding the generation of ill - conditioned matrices in the calculation of the FPM method, ensuring calculation stability while obtaining higher calculation accuracy.

[0067] Example 1 takes the interaction between a linear regular wave and a monopile foundation as an example to illustrate the technical solution of the present invention. In this simulation, the main computing content is calculated on the GPU through the CUDA language, and only the initialization, result output, and operation scheduling are completed in the CPU. The specific process can be seen in the appendix Figure 1 . The simulation includes the following steps:

[0068] 1) At the initial moment, a corresponding numerical model is established based on the specific problem being simulated, and all particles are assigned initial values ​​of the required physical quantities, including pressure, velocity, density, mass, and smooth length. Calculation begins after initialization is complete. In the simulation, the wave-structure interaction process in a wave numerical tank is used to simulate the wave-structure interaction process in a scaled-down real sea area. The tank dimensions are 20m (length) * 1m (height) * 2m (width). The water depth is d = 0.7m, the single pile radius is R = 0.15m, and the single pile foundation is arranged on the center axis of the tank (1m away from both sides) and 8m away from the wave-making plate. The specific dimensions can be seen in the attached figure. Figure 2 Wave height H = 0.06m, period T = 1.12s, speed of sound c = 20m / s, artificial viscosity coefficient α = 0.05, reference density ρ 0,i =1000kg / m 3 For ease of understanding, this example uses anisotropy r = 1 and particle spacing Δ x =Δ y =Δ z =0.02m. After initialization, the calculation begins, and the kernel function is the Gaussian function. In the ASPH method, the Gaussian kernel function represented by the normalized distance vector η and its gradient are:

[0069]

[0070] Where η=|η| is the length of the distance vector η, α d =1 / (π 1.5 h x h y h z ) is the coefficient of the Gaussian kernel function in the ASPH framework in three-dimensional simulation;

[0071] 2) In a certain time step, before calculating a fluid particle, first determine whether the particle is on the free surface or close to the free surface. Among them, the particles 3-4 layers from the outermost free surface are called free surface particles.

[0072] 3) If a fluid particle i is a free surface particle, its density increment is calculated according to the SPH format discretized continuity equation.

[0073] 4) If a fluid particle i is not a free surface particle, the density increment of particle i is calculated using the continuity equation after the FPM method, and the velocity increment of particle i is calculated using the Navier-Stokes equation after the FPM method. 5) If a particle i is a boundary particle, the pressure and velocity of particle i are solved using Shepard interpolation.

[0074] 6) For all fluid particles, after obtaining the particle velocity increment and density increment according to steps 3) and 4), update the particle density and velocity according to the time advancement format used in the calculation and enter the solution of the next time step.

[0075] 7) Perform particle displacement operations on all internal fluid particles to obtain a more uniform particle distribution.

[0076] Attachment Figure 3 , Attachment Figure 4 The x-direction velocity u around the structure 20 seconds after the start of wave generation is given. The velocity unit in the legend is m / s. Figure 3 For top view, attached Figure 4 It is an oblique upper side view. Figure 5 The fluid pressure distribution along the section y = 1m (the center axis of the water tank) at the same time is given, where P is the pressure coefficient, P = p / ρ0gd. It can be seen that the proposed method can effectively simulate the interaction between waves and single pile structures.

[0077] The above-described embodiments merely illustrate several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. Persons skilled in the art will readily appreciate that variations and modifications may be made without departing from the scope of the present invention, all of which fall within the scope of protection of the present invention.

Claims

1. An improved smooth particle method for simulating wave impact on a single pile foundation, characterized in that: It includes the following steps: 1) At the initial moment, according to the simulated wave elements and the monopile size, use SPH particles to discretize the water body and the monopile boundary in the ocean wave, and establish a numerical model of the interaction between the ocean wave and the monopile. The wave elements include water depth, wave period, and wave height; the monopile size includes the position of the monopile center point, the monopile radius, and the monopile height; 2) Assign initial values of the required physical quantities to all SPH particles. The required physical quantities include pressure, velocity, density, mass, and smoothing length. After initialization, start the time-step iteration calculation in the numerical simulation; 3) SPH particles include boundary particles and fluid particles; in each time step, before calculating the fluid particles, first determine whether the particle is a free-surface particle. Among them, the 3-4 layers of particles from the outermost side of the free surface inward are all free-surface particles; 4) If a certain fluid particle i belongs to the free-surface particle, calculate its density increment according to the SPH-formatted discretized continuity equation; calculate the velocity increment of particle i using the Navier-Stokes equation discretized by the SPH method; all kernel functions and their gradients used in the calculation are determined by the normalized distance vector η; 5) If a certain fluid particle i does not belong to the free-surface particle, calculate the density increment of particle i using the continuity equation discretized by the FPM method, and calculate the velocity increment of particle i using the Navier-Stokes equation discretized by the FPM method; all kernel functions and their gradients used in the calculation are determined by the normalized distance vector η; 6) If a certain particle belongs to the boundary particle, use Shepard interpolation to solve the pressure, density, and velocity of the particle; 7) For all fluid particles, after obtaining the velocity increment and density increment of the particles according to steps 4) and 5), update the position, velocity, and density of the particles, and enter the solution of the next time step.

2. The improved smooth particle method for simulating wave impact on a single pile foundation according to claim 1, characterized in that: Step 4) calculates the density increment according to the SPH format discretized continuity equation, specifically: Among them, ρ i is the density of particle i, t represents time, particle j is a particle in the support domain of particle i, u i 、u j are the velocity vectors of particles i and j, is the kernel function gradient, m j , ρ j are the mass and density of particle j, respectively.

3. The improved smooth particle method for simulating wave impact on a single pile foundation according to claim 2, characterized in that: The calculation of the velocity increment of particle i using the Navier-Stokes equation discretized by the SPH method in step 4) is specifically as follows: Where, π ij =(u j -u i )·(x j -x i ) / |x ij | 2 , In the above formula, g is the gravitational acceleration vector, c is the speed of sound, and ρ 0,i is the reference density of particle i, ρ i is the density of particle i at the current time step, p i 、p j is the pressure of particles i and j, W ij is the kernel function value determined by the distance between particles j and i, α is the artificial viscosity coefficient, h is the smoothing length, and x i 、x j is the position vector of particles i and j, x ij =x i -x j is the distance vector between particles i and j.

4. The improved smooth particle method for simulating wave impact on a single pile foundation according to claim 3, characterized in that: Step 5) specifically includes: The density increment and velocity increment discretized by the FPM method are calculated as follows: Among them, W is the kernel function value, is the kernel function gradient The components in the x, y, and z directions, u i 、v i 、w i is the velocity vector u of particle i i The components in the x, y, and z directions, τ i,x , τ i,y , τ i,z is the component of the viscous force τ in the x, y, and z directions, F i,x 、F i,y 、F i,z is the component of the body force F in the x, y, and z directions, V j =m j / ρ j is the volume of particle j; a mn are the elements in the coefficient matrix, m = 1, 2, 3, 4; n = 1, 2, 3, 4: Among them, x ji =-x ij ,y ji =-y ij , z ji =-z ij , x ij 、y ij 、z ij is the distance vector x between particles i and j ij Components in the x, y, and z directions.

5. The improved smooth particle method for simulating wave impact on a single pile foundation according to claim 4, characterized in that: In step 4) and step 5), all kernel functions and kernel function gradients are determined by the normalized distance vector η. The distance vector x before normalization is ij The relationship between and the normalized distance vector η is: η=Gx ij In the above formula, G is a deformation tensor: h x 、h y 、h z are the smooth lengths of the particles in the x, y, and z directions respectively; The kernel function gradient expressed as the normalized distance vector η for: η = |η| is the length of the distance vector η.

6. The improved smooth particle method for simulating wave impact on a single pile foundation according to claim 1, characterized in that: In step 6), the pressure and velocity are solved according to the following formula: Where f represents the fluid particles, p f 、m f , ρ f are the pressure, mass and density of the fluid particles, u f is the velocity vector of the fluid particle f, W if is the kernel function value determined by the normalized distance η = |η| between the boundary particle i and the fluid particle f; the density of the boundary particle i is determined by its pressure p i Combining the weakly compressible state equation gives: r i =ρ0+p i / c 2 Where, c is the artificial sound speed in the simulation.

7. The improved smooth particle method for simulating wave impact on a single pile foundation according to claim 6, characterized in that: To ensure that there is no non-physical particle penetration under the physical processes of strong nonlinear conditions such as wave impact on the monopile foundation and wave breaking, the following correction is applied to the acceleration of the fluid particles near the monopile boundary particles: Among them, h min is the minimum value of the smooth length of the boundary particle i in the x, y, and z directions, n i is the normal vector of the boundary particle, pointing from the center of the single pile foundation to the outside, u f 、u i are the velocity vectors of fluid particle f and boundary particle i respectively.

8. The improved smooth particle method for simulating wave impact on a single pile foundation according to claim 1, characterized in that: After step 7) is completed, the particle displacement technique is also used for the fluid particles that are not free surfaces to ensure that the particle distribution is as uniform as possible, so as to avoid the generation of ill-conditioned matrices in the calculation of the FPM method, and to obtain higher calculation accuracy while ensuring calculation stability.

9. The improved smooth particle method for simulating wave impact on a single pile foundation according to claim 1, characterized in that: In step 7), after updating the particle position, use the linked list search method or the tree search method to quickly traverse all particles i to obtain the serial numbers of all its adjacent particles; the basis for judging whether two particles i and j are adjacent particles is: the length of the distance vector between particles i and j, η < R, where R is the radius of the selected kernel function.

10. The improved smooth particle method for simulating wave impact on a single pile foundation according to claim 1, characterized in that: The main computing content is deployed on the GPU, and the CPU only retains basic initialization, output, and instruction scheduling operations, thereby achieving faster computing efficiency.

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