A method for simulating wetting phenomena based on pseudo-potential lattice Boltzmann method

Abstract

The present invention provides a method for simulating wetting phenomena based on a pseudo-potential lattice Boltzmann method, the method comprising the following steps: transforming the velocity distribution function f i (x, t), equilibrium velocity distribution function f i eq (x, t) and discrete force F i (x, t) collides on the grid points according to the collision model; the velocity distribution function f i (x, t) migrates to a neighboring grid point according to a migration rule; the density ρ at the grid point is solved according to the formula #imgabs0# to obtain a density value; a pseudopotential is solved based on the density value and the non-ideal gas state equation; the force F(x, t) at the grid point is solved based on the pseudopotential; a wetting angle is set at the grid representing the wall surface; the velocity value at the grid point is solved; and a termination judgment is made. The method of the present invention can explicitly set the contact angle, effectively expanding the range of contact angle representation, and is beneficial for improving the stability of numerical simulations and the efficiency of parallel computing.

Description

Technical Field

[0001] The present invention relates to the field of computational fluid dynamics, and in particular to a method for simulating wetting phenomena based on a pseudo-potential lattice Boltzmann method. Background Art

[0002] Wetting phenomena are common in nature and industrial applications, such as the self-cleaning effect of lotus leaves, paint spraying, waterproof coatings, and flotation beneficiation. Computational fluid dynamics (CFD) is a key method for studying such problems. Its low cost and high repeatability make it widely used in scientific research and industrial production.

[0003] Wetting is a typical phenomenon of gas-liquid two-phase flow. Numerical simulations of such flow problems can be solved using a variety of methods, including molecular dynamics, smoothed particle fluid dynamics, and the lattice Boltzmann method. The lattice Boltzmann method is widely used for numerical simulations of two-phase and multiphase flow problems due to its explicit evolution, simple programming, and suitability for parallelism. Commonly used lattice Boltzmann methods for multiphase flow include the color model, pseudo-potential model, free energy model, and phase field model. Compared with the other three models, the pseudo-potential model directly describes the interphase interaction forces at the microscopic level, characterizing the merging and separation of phases through the interphase forces, without the need to explicitly track changes in the phase interface, and the calculation is extremely concise.

[0004] The wetting angle is an important indicator of the wetting phenomenon. It is the angle formed by the tangent line of the gas-liquid interface at the gas-liquid-solid three-phase junction and the solid-liquid interface, represented by θ. The specific definition of the wetting angle is shown in the following figure: Figure 1 As shown. When numerically simulating multiphase flows with wetting phenomena, the wetting angle needs to be set in advance. Since the size of the wetting angle has a significant impact on the flow phenomenon, the wetting angle model is crucial for the accurate implementation of the numerical simulation. In the pseudo-potential lattice Boltzmann method, the existing wetting angle models are divided into two categories. One category is to establish the liquid-solid interaction force by imitating the form of the liquid-solid interaction force, and set the wetting angle by adjusting the liquid-solid interaction force strength. The defect of this type of format is that it is impossible to quantify the relationship between the liquid interaction force strength and the wetting angle. The relationship between the two must be obtained through numerical experiments, making it impossible to explicitly set the wetting angle. The other category is the geometric wetting model. This model can explicitly set the wetting angle, but when the gas-liquid density is relatively large, the wetting angle range that can be represented by this model is relatively narrow. When the wetting angle is set beyond the representation range, the computational instability increases, making it impossible to perform the calculation normally. Summary of the Invention

[0005] In response to the defects in the prior art, the purpose of the present invention is to provide a wetting phenomenon simulation method based on the pseudo-potential lattice Boltzmann method, which can be used for numerical simulation of wetting phenomena. This method can explicitly set the contact angle and effectively expand the contact angle characterization range of the geometric wetting model, which is conducive to improving the stability of numerical simulation and parallel computing efficiency.

[0006] To achieve the above object, the present invention provides a method for simulating wetting phenomena based on a pseudo-potential lattice Boltzmann method, the method comprising the following steps:

[0007] The velocity distribution function f i (x, t), equilibrium velocity distribution function and the discrete force F i (x, t) collides on the grid points according to the collision model;

[0008] The velocity distribution function f i (x, t) migrates to the adjacent grid point according to the migration rule;

[0009] The density ρ at the grid point is calculated according to the formula Solve to get the density value;

[0010] solving a pseudopotential based on the density value and the non-ideal gas state equation;

[0011] Solve the force F(x, t) at the grid point according to the pseudo potential;

[0012] The wetting angle is set at the grid representing the wall surface, specifically including: giving the wetting angle θ value, which ranges from 0 to 180°, and for two-dimensional numerical simulation, implementing the formula for the force acting on the grid point at the boundary representing the solid wall Or for three-dimensional numerical simulations, implement the formula for the grid points at the boundary representing the solid wall in is the partial derivative of pressure with respect to density, subscripts n and τ represent the normal and tangential directions of the wall, respectively, and subscripts τ1 and τ2 represent any pair of orthogonal tangential directions of the wall;

[0013] Solve for the velocity value at the grid points;

[0014] Make a termination judgment.

[0015] Optionally, the collision model can adopt a single relaxation model or a multi-relaxation model, wherein the control equation of the single relaxation model is The control equation of the multi-relaxation model is Where δt is the unit time, τ v is the relaxation time, which is related to the viscosity υ, and the relationship between the two is v=(2τ v -1) / 6, M is the two-dimensional transformation matrix of size q×q associated with the grid template, M -1 is its inverse matrix, I is the q-order identity matrix, and Λ is a two-dimensional diagonal matrix of size q×q, representing the relaxation time.

[0016] Optionally, the equilibrium velocity distribution function The definition is Where ρ and u are the density and velocity at the grid points, respectively, and c s is the lattice sound speed, w i is the weight coefficient associated with the grid template.

[0017] Optionally, the discrete force F i There are many models for (x, t), including the Guo external force format, the Shan-Chen format, the exact difference format, and the Li correction format.

[0018] Optionally, the migration velocity distribution function f i (x, t + δt) = f i (xc i δt, t+δt), where x represents the grid point position. For two-dimensional and three-dimensional uniform Cartesian grids, x is (x, y) and (x, y, z), respectively. Where i = 0, 1, 2, 3, ... (q-1), q is the number of discrete velocities, which is related to the grid template used. The grid template type can be expressed as DdQq, d represents the dimension of the grid template, which is usually 2 and 3, indicating that the grid type is two-dimensional and three-dimensional, respectively, and also indicating that the simulation is a two-dimensional numerical simulation and a three-dimensional numerical simulation, respectively. t is the current time, c i is the discrete grid velocity, and its value is determined by the grid template used.

[0019] Optionally, the pseudopotential is defined as Where G is the force intensity, usually -1, c is the grid velocity, usually 1, and P is the pressure at the grid point.

[0020] Optionally, the pressure P at the grid point can be solved by a non-ideal gas state equation, which includes the de Waals equation, the Peng-Robinson gas state equation, and the Camahan-Starling gas state equation.

[0021] Optionally, the step of solving the force F(x, t) at the grid point according to the pseudo potential specifically includes: solving the force F(x, t) at the grid point follows the formula

[0022] Optionally, the partial derivative of pressure with respect to density The solution is performed using non-ideal gas state equations, which include the de Waals equation, the Peng-Robinson gas state equation, and the Carnahan-Starling gas state equation.

[0023] Optionally, the step of solving the velocity value at the grid point specifically includes: according to the formula Solve for the velocity value.

[0024] Optionally, the termination judgment step specifically includes: for two-dimensional numerical simulation, the termination judgment formula is For three-dimensional numerical simulation, the termination judgment condition is Where N represents a certain time interval, ε is the convergence target, and the calculation ends when the set number of cycles or the convergence condition is met. If the termination condition is not met, the above steps are repeated.

[0025] Compared with the prior art, the beneficial effect of the present invention is that the wetting phenomenon simulation method based on the pseudo-potential lattice Boltzmann method can explicitly set the contact angle and effectively expand the contact angle characterization range of the geometric wetting model, which is beneficial to improving the stability of numerical simulation and parallel computing efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Other features, objects and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments with reference to the following drawings:

[0027] Figure 1 Define a schematic diagram for the wetting angle;

[0028] Figure 2 A flowchart of a method for simulating wetting phenomena based on the pseudo-potential lattice Boltzmann method provided by an embodiment of the present invention;

[0029] Figures 3A-3D A comparison diagram between the simulated value and the set value of the wetting angle when the saturation temperatures are 0.90Tc, 0.80Tc, 0.70Tc, and 0.60Tc, respectively, provided for one embodiment of the present invention;

[0030] Figures 4A-4C A diagram showing the morphology of liquid droplets attached to a wall at different wetting angles when the saturation temperature is 0.60Tc according to one embodiment of the present invention;

[0031] Figures 5A-5D A comparison diagram between simulated and set values ​​of the wetting angle when the saturation temperatures are 0.90Tc, 0.80Tc, 0.70Tc, and 0.60Tc, respectively, provided in another embodiment of the present invention;

[0032] Figures 6A-6C Another embodiment of the present invention provides a diagram of the morphology of bubbles attached to the wall at different wetting angles when the saturation temperature is 0.60Tc. DETAILED DESCRIPTION

[0033] The present invention will be described in detail below with reference to specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those skilled in the art, several changes and improvements can be made without departing from the scope of the present invention. These all fall within the scope of protection of the present invention.

[0034] like Figure 2 The steps of the pseudo-potential lattice Boltzmann method for simulating wetting phenomena are as follows:

[0035] Step S21: The velocity distribution function f i (x, t), equilibrium velocity distribution function and the discrete force F i (x, t) collides on the grid points according to the collision model;

[0036] Specifically, the collision model can adopt a single relaxation model or a multi-relaxation model, wherein the control equation of the single relaxation model is The control equation of the multi-relaxation model is Where δt is the unit time, usually 1, τ v is the relaxation time, which is related to the viscosity υ, and the relationship between the two is v=(2τ v -1) / 6, M is the two-dimensional transformation matrix of size q×q associated with the grid template, M -1 is its inverse matrix, I is the q-order unit matrix, and Λ is a two-dimensional diagonal matrix of size q×q, which represents the relaxation time and its value is usually between 0 and 2.

[0037] The equilibrium velocity distribution function The definition is Where ρ and u are the density and velocity at the grid points, respectively, and c s is the lattice sound speed, w I is the weight coefficient associated with the grid template.

[0038] The discrete force F i There are many models for (x, t), including the Guo external force format, the Shan-Chen format, the exact difference format, and the Li correction format.

[0039] Step S22: The velocity distribution function f i (x, t) migrates to the adjacent grid point according to the migration rule;

[0040] Specifically, the migration velocity distribution function f i (x, t + δt) = f i (xc iδt, t+δt), where x represents the grid point position. For two-dimensional and three-dimensional uniform Cartesian grids, x is (x, y) and (x, y, z), respectively. Where i = 0, 1, 2, 3, ... (q-1), q is the number of discrete velocities, which is related to the adopted grid template. The grid template type can be expressed as DdQq, where d represents the dimension of the grid template, usually taking the values ​​of 2 and 3, indicating that the grid type is two-dimensional and three-dimensional, respectively, and also representing that the simulation is a two-dimensional numerical simulation and a three-dimensional numerical simulation, respectively. For two-dimensional numerical simulation, the commonly used two-dimensional grid template is: D2Q9 template. For three-dimensional numerical simulation, the commonly used three-dimensional grid template is: D3Q15 template, D3Q19 template, D3Q27 template. t is the current time, c I is the discrete grid velocity, and its value is determined by the grid template used.

[0041] Step S23: The density ρ at the grid point is calculated according to the formula Solve to get the density value;

[0042] Step S24: solving the pseudo potential according to the density value and the non-ideal gas state equation;

[0043] Specifically, the pseudopotential is defined as Where G is the force intensity, c is the grid velocity, and P is the pressure at the grid point. The pressure P at the grid point can be solved using non-ideal gas state equations, including the de Waals equation, the Peng-Robinson gas state equation, and the Carnahan-Starling gas state equation.

[0044] Step S25: solving the force F(x, t) at the grid point according to the pseudo potential;

[0045] Specifically, the force F(x, t) at the grid point is solved according to the formula Where G is the force intensity, usually -1.

[0046] Step S26: setting a wetting angle at the grid representing the wall surface;

[0047] Specifically, the step of setting the wetting angle at the grid representing the wall includes: giving a wetting angle θ value in the range of 0 to 180°, and for a two-dimensional numerical simulation, implementing the formula for the grid point force at the boundary representing the solid wall: For three-dimensional numerical simulations, the force at the grid points representing the boundaries of the solid wall is formulated as in is the partial derivative of pressure with respect to density, which can be solved with the help of the selected non-ideal gas state equation. The subscripts n and τ represent the normal and tangential directions of the wall, respectively, and the subscripts τ1 and τ2 represent any pair of orthogonal tangential directions of the wall.

[0048] Step S27: Calculate the velocity value at the grid point;

[0049] Specifically, solve the velocity value at the grid point: According to the formula Solve for the velocity value.

[0050] Step S28: Perform termination judgment.

[0051] Specifically, for two-dimensional numerical simulation, the termination judgment formula is: For three-dimensional numerical simulation, the termination judgment formula is: Where N represents a certain time interval, ε is the convergence target, and the calculation is terminated when the calculation meets the set number of cycles or meets the convergence condition. When the termination condition is not met, the above steps S21 to S27 are repeated.

[0052] The following specific example 1 is a numerical simulation of a liquid droplet adhering to a solid surface. By setting different wetting angles, the droplet morphology and contact angle in a stable state are investigated. This example uses a two-dimensional grid for numerical simulation and uses the D2Q9 model. The values ​​of the discrete velocity ci and weight coefficient wi in this model are shown in Table 1 below:

[0053]

[0054] Table 1

[0055] The collision process uses a multi-relaxation collision model. The relaxation time matrix Λ is shown in Equation 1, the conversion matrix M is shown in Equation 2, and the external force format uses the Li correction format. The value of MFi(x, t) during the collision process is given by Equation 3, where σ is the adjustment coefficient and is taken as 1.275. The non-ideal gas state equation used to calculate the pseudopotential is the Peng-Robinson gas state equation, shown in Equation 4, where the coefficients w, a, b, and R are 0.344, 1 / 49, 2 / 21, and 1, respectively. is the critical temperature, Ts is the saturation temperature, and its value range is 0.55 to 1 times the critical temperature. Its change corresponds to the change of the vapor-liquid two-phase density ratio.

[0056] Λ=diagg(1.0, 0.8, 0.8, 1.0, 1.1, 1.0, 1.1, 1.25, 1.25) (1)

[0057]

[0058]

[0059]

[0060] In this example, a uniform Cartesian grid with a length of 300 and a width of 100 is used as the computational domain. Periodic boundary conditions are used for the left and right boundaries, and no-slip wall conditions are used for the upper and lower boundaries. A wetting angle θ is set for the lower boundary. The center of the semicircular droplet with a radius of 30 is initially located at (150, 0). The upper limit of the number of computational cycles is set to 2*10. 5 Each cycle is 100 times, and a convergence judgment is performed. The convergence target value is ε=10 -6 .

[0061] In this embodiment, the vapor-liquid two-phase density ratio (ρ * =ρ liquid / ρ gas ), when the saturation temperatures Ts are 0.90Tc, 0.80Tc, 0.70Tc, and 0.60Tc, the corresponding vapor-liquid two-phase density ratio ρ * They are 10.1, 36.8, 148.6 and 865.1 respectively.

[0062] In this embodiment, by setting different wetting angle θ values, the calculated equilibrium state droplet morphology is different. At this time, the angle formed by the vapor-liquid interface and the solid wall (this angle is the calculated wetting angle) is also different. The closer the calculated wetting angle is to the set wetting angle, the more accurate the wetting angle setting method of the present invention is, and the closer the simulated wetting phenomenon is to reality.

[0063] In order to fully examine the scope of application and accuracy of the infiltration angle setting method of the present invention, this embodiment forms four groups of calculation conditions by adjusting the saturation temperature Ts and the infiltration angle θ. The calculation condition grouping settings are shown in Table 2 below.

[0064]

[0065] Table 2

[0066] Figures 3A-3D The comparison diagram between the simulated value and the theoretical value of the wetting angle when the saturation temperature is 0.90Tc, 0.80Tc, 0.70Tc, and 0.60Tc respectively is shown in the figure. Figure 3C and 3D As shown in the figure, when the saturation temperatures are 0.70Tc and 0.60Tc, the two-phase density ratios are 148.6 and 865.1, respectively. The wetting angle range that can be characterized by this method is 15-150°, which far exceeds the wetting angle characterization range that can be achieved by the existing geometric wetting format, and is in good agreement with the theoretical solution, showing good calculation accuracy and stability, reflecting that this method has the characteristics of high accuracy and wide value range in a wide range of vapor-liquid density ratios. Figures 4A-4CThe figure shows the droplet morphology in equilibrium state when the saturation temperature is 0.60Tc and the wetting angle is different. Figure 4A Indicates that the set value of the infiltration angle is 15° and the simulated value of the infiltration angle is 19.5°. Figure 4B Indicates that the set value of the infiltration angle is 90° and the simulated value of the infiltration angle is 88.1°. Figure 4C It indicates that the set value of the wetting angle is 145° and the simulated value of the wetting angle is 143.9°.

[0067] Yet another embodiment of the present invention is to numerically simulate bubbles attached to a solid wall, and to explore the bubble morphology and contact angle size in a stable state by setting different wetting angles.

[0068] In this embodiment, a two-dimensional grid is used for numerical simulation, and the D2Q9 model is selected. In this model, the discrete velocity c i and weight coefficient w i The values ​​are shown in Table 1. The collision process adopts the multi-relaxation collision model, the relaxation time matrix Λ is shown in Formula 1, the conversion matrix M is shown in Formula 2, and the external force format adopts the Li correction format. Then, in the collision process, MF i (x, t) is taken as the above formula 3, where σ is the adjustment coefficient and is taken as 1.40. The non-ideal gas state equation used to calculate the pseudopotential is the Peng-Robinson gas state equation, see the above formula 4, where the coefficients w, a, b, and R are taken as 0.344, 1 / 49, 2 / 21, and 1 respectively. is the critical temperature, Ts is the saturation temperature, and its value range is 0.55 to 1 times the critical temperature. Its change corresponds to the change of the vapor-liquid two-phase density ratio.

[0069] In this example, a uniform Cartesian grid with a length of 300 and a width of 100 is used as the computational domain. Periodic boundary conditions are used for the left and right boundaries, and no-slip wall conditions are used for the upper and lower boundaries. A wetting angle θ is set for the lower boundary. The center of the semicircular bubble with a radius of 30 is initially located at (150, 0). The upper limit of the number of computational cycles is set to 2*10. 5 Each cycle is 100 times, and a convergence judgment is performed. The convergence target value is ε=10 -6 .

[0070] In this embodiment, the vapor-liquid two-phase density ratio (ρ * =ρ liquid / ρ gas ), when the saturation temperatures Ts are 0.90Tc, 0.80Tc, 0.70Tc, and 0.60Tc, the corresponding vapor-liquid two-phase density ratio ρ * They are 10.1, 36.8, 148.6 and 865.1 respectively.

[0071] In this embodiment, by setting different wetting angle θ values, the calculated equilibrium bubble morphology is different. At this time, the angle formed by the vapor-liquid interface and the solid wall (this angle is the calculated wetting angle) is also different. The closer the calculated wetting angle is to the set wetting angle, the more accurate the wetting angle setting method of the present invention is, and the closer the simulated wetting phenomenon is to reality.

[0072] In order to fully examine the scope of application and accuracy of the infiltration angle setting method of the present invention, this embodiment forms four groups of calculation conditions by adjusting the saturation temperature Ts and the infiltration angle θ. The calculation condition grouping settings are shown in Table 2 above.

[0073] Figures 5A-5D The comparison diagram between the simulated value and the theoretical value of the wetting angle when the saturation temperature is 0.90Tc, 0.80Tc, 0.70Tc, and 0.60Tc respectively is shown in the figure. Figure 5C and 5D As shown in the figure, when the saturation temperatures are 0.70Tc and 0.60Tc, the two-phase density ratios are 148.6 and 865.1, respectively. The wetting angle range that can be characterized by this method is 15-150°, which far exceeds the wetting angle characterization range that can be achieved by the existing geometric wetting format, and is in good agreement with the theoretical solution, showing good calculation accuracy and stability, reflecting that this method has the characteristics of high accuracy and wide value range in a wide range of vapor-liquid density ratios. Figures 6A-6C The figure shows the bubble morphology in the equilibrium state when the saturation temperature is 0.60Tc and the different wetting angles are taken. Figure 6A Indicates that the set value of the infiltration angle is 15° and the simulated value of the infiltration angle is 21.9°; Figure 6B Indicates that the set value of the infiltration angle is 90° and the simulated value of the infiltration angle is 91.9°; Figure 6C Indicates that the set value of the wetting angle is 145° and the simulated value of the wetting angle is 144.0°.

[0074] The above describes specific embodiments of the present invention. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art may make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. The embodiments of this application and the features in the embodiments may be combined with each other in any manner unless there is a conflict.

Claims

1. A method for simulating wetting phenomena based on the pseudo-potential lattice Boltzmann method, characterized by: The method comprises the following steps: The velocity distribution function f i (x, t), equilibrium velocity distribution function and the discrete force F i (x, t) collides on the grid points according to the collision model; The velocity distribution function f i (x, t) migrates to the adjacent grid point according to the migration rule; The density ρ at the grid point is calculated according to the formula Solve to get the density value, q is the number of discrete velocities, x is the grid point position, and t is the current time; solving a pseudopotential based on the density value and the non-ideal gas state equation; Solve the force F(x, t) at the grid point according to the pseudo potential; The wetting angle is set at the grid representing the wall, specifically including: giving the wetting angle θ value, which ranges from 0 to 180°, For two-dimensional numerical simulations, the force acting on the grid points at the boundary representing the solid wall is formulated as Or for three-dimensional numerical simulations, implement the formula for the force acting on the grid points at the boundary representing the solid wall in is the partial derivative of pressure with respect to density, subscripts n and τ represent the normal and tangential directions of the wall, subscripts τ1 and τ2 represent any pair of orthogonal tangential directions of the wall, and c s is the lattice sound speed; Solve for the velocity value at the grid points; Make a termination judgment.

2. The method for simulating wetting phenomena based on the pseudo-potential lattice Boltzmann method according to claim 1, characterized in that: The collision model can adopt a single relaxation model or a multi-relaxation model, wherein the control equation of the single relaxation model is The control equation of the multi-relaxation model is Where δt is the unit time, τv is the relaxation time, which is related to the viscosity υ, and the relationship between the two is v = (2τ v -1) / 6, M is the two-dimensional transformation matrix of size q×q associated with the grid template, M -1 is its inverse matrix, I is the q-order identity matrix, and Λ is a two-dimensional diagonal matrix of size q×q, representing the relaxation time.

3. The method for simulating wetting phenomena based on the pseudo-potential lattice Boltzmann method according to claim 1, characterized in that: The equilibrium velocity distribution function The definition is Where ρ and u are the density and velocity at the grid points, respectively, and c s is the lattice sound speed, w i is the weight coefficient associated with the grid template.

4. The method for simulating wetting phenomena based on the pseudo-potential lattice Boltzmann method according to claim 1, characterized in that: The discrete force F i There are many models for (x, t), including the Guo external force format, the Shan-Chen format, the exact difference format, and the Li correction format.

5. The method for simulating wetting phenomena based on the pseudo-potential lattice Boltzmann method according to claim 1, characterized in that: The migration velocity distribution function f i (x, t + δt) = f i (xc i δt, t+δt), where x represents the grid point position. For two-dimensional and three-dimensional uniform Cartesian grids, δt is the unit time, x is (x, y) and (x, y, z), respectively, where i = 0, 1, 2, 3, ... (q-1), q is the number of discrete velocities, which is related to the grid template used. The grid template type can be expressed as DdQq, d represents the dimension of the grid template, usually 2 and 3, indicating that the grid type is two-dimensional and three-dimensional, respectively, and also indicating that the simulation is a two-dimensional numerical simulation and a three-dimensional numerical simulation, respectively. t is the current time, c i is the discrete grid velocity, and its value is determined by the grid template used.

6. The method for simulating wetting phenomena based on the pseudo-potential lattice Boltzmann method according to claim 1, characterized in that: The pseudopotential is defined as Where G is the force intensity, c is the grid velocity, and P is the pressure at the grid point.

7. The method for simulating wetting phenomena based on the pseudo-potential lattice Boltzmann method according to claim 6, characterized in that: The pressure P at the grid point can be solved using non-ideal gas state equations, which include the de Waals equation, the Peng–Robinson gas state equation, and the Carnahan-Starling gas state equation.

8. The method for simulating wetting phenomena based on the pseudo-potential lattice Boltzmann method according to claim 1, characterized in that: The step of solving the force F(x, t) at the grid point according to the pseudo potential specifically includes: solving the force F(x, t) at the grid point follows the formula w i is the weight coefficient related to the grid template, c i is the discrete lattice velocity, δt is the unit time, ψ(x, t) is the pseudopotential, and G is the force intensity.

9. The method for simulating wetting phenomena based on the pseudo-potential lattice Boltzmann method according to claim 1, characterized in that: The partial derivative of pressure with respect to density The solution is performed using non-ideal gas state equations, which include the de Waals equation, the Peng–Robinson gas state equation, and the Carnahan-Starling gas state equation.

10. The method for simulating wetting phenomena based on the pseudo-potential lattice Boltzmann method according to claim 1, characterized in that: The step of solving the velocity value at the grid point specifically includes: according to the formula ρ, u are the density and velocity at the grid points, respectively, c i is the discrete lattice velocity, δt is the unit time, and the velocity value is solved.

11. The method for simulating wetting phenomena based on the pseudo-potential lattice Boltzmann method according to claim 1, characterized in that: The termination judgment step specifically includes: for two-dimensional numerical simulation, the termination judgment formula is: Where u is the velocity at the grid point, δt is the unit time, and for three-dimensional numerical simulation, the termination judgment formula is: Where N represents a certain time interval, ε is the convergence target, and the calculation ends when the set number of cycles is met or the convergence condition is met. If the termination condition is not met, the above steps are repeated.

Images