Dendritic crystal growth and motion simulation method and system based on Euler-Lagrangian method

Abstract

The invention discloses a dendritic crystal growth and motion simulation method and system based on an Euler-Lagrangian method.The method comprises the steps that firstly, a phase field model is constructed based on convection flux in a solute field; solving liquid convection on an Euler background grid, and solving solid motion through a Lagrange grid; and updating the moved solid boundary through the conservative phase field model. According to the method, on the basis of simulation of the growth condition of the dendritic crystal, the Lagrange grid is introduced into the discrete interface to simulate the motion behavior of the dendritic crystal, the alloy growth morphology and convection motion are simulated at the same time, the problem that the speed between the grid and the fluid is not matched is solved, and the problem of topological change of a complex interface is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of material processing, and more specifically, to a method and system for simulating dendrite growth and movement based on the Euler-Lagrange method. Background Art

[0002] As one of the most typical and important phase change processes, alloy solidification has always attracted the attention of researchers. For a long time, people have attached great importance to the research on the formation process of dendritic structures, hoping to adjust the solidification structure of alloys by reasonably designing the solidification process. With the development of simulation technology, the phase field method (PFM) has become an effective means for the microstructure evolution during solidification. By introducing phase field variables, the phase field method performs a smearing treatment on the interface, avoiding the complex tracking of the evolution process of sharp interfaces. At the same time, the phase field method can couple multiple physical fields and various random influencing factors, making it an ideal means for dealing with tissue evolution.

[0003] Existing phase field models for simulating dendrite growth are all based on the assumption that dendrites are stationary. For example, the invention with the publication number CN116994683A discloses a method for simulating the microstructure morphology of magnesium alloys under forced convection based on the phase field method-lattice Boltzmann method and its application. A lattice Boltzmann model is constructed to calculate the movement of the fluid in the liquid-solid two-phase region, the phase field model is discretely solved by the finite difference method, and the distribution function of the lattice Boltzmann model is solved by the D2Q9 model to simulate the change in dendrite morphology caused by solute flow. However, during the simulation of material tissue growth, there is always a density difference between the solid phase and the liquid phase, and the relative flow behavior between the solid and liquid phases is inevitable. The relative movement between the solid and liquid phases can change the heat / solute transport throughout the entire scale range during solidification, resulting in morphological asymmetry. Therefore, it is necessary to deal with the complex interactions between dendrite growth, solute transport, and the relative movement between the solid and liquid phases.

[0004] Current phase field model simulation methods do not simultaneously address the issues of dendrite growth and movement, and the simulation of dendrite growth is not rigorous in terms of physical mechanisms. Because whether the solid-liquid density is unequal or there is external force interference, it will drive the movement of the solid phase. Therefore, how to solve the problem of topological changes in complex interfaces is an urgent problem to be solved. Summary of the Invention

[0005] In view of this, the present invention provides a method and system for simulating dendrite growth and movement based on the Euler-Lagrange method, which is used to solve the problem that existing phase field model simulation methods do not simultaneously involve dendrite growth and movement.

[0006] To achieve the above object, the following solutions are proposed:

[0007] A method for simulating dendrite growth and movement based on the Euler-Lagrange method, comprising:

[0008] Construct a phase-field model based on the convective flux in the solute field;

[0009] Solve the liquid convection on the Eulerian background grid and solve the solid motion through the Lagrangian grid;

[0010] Update the solid boundary after motion through the conservative phase-field model.

[0011] Preferably, the process of constructing the phase-field model based on the convective flux in the solute field includes:

[0012] Expand the phase-field equation based on the convective flux in the solute field to couple the phase field, solute field, and flow field;

[0013] Process the expanded phase-field equation through a non-linear preconditioning transformation to obtain the phase-field model.

[0014] Preferably, the process of solving the liquid convection on the Eulerian background grid and solving the solid motion through the Lagrangian grid includes:

[0015] Calculate the liquid convection on the Eulerian background grid by the lattice Boltzmann method;

[0016] Solve the solid motion on the Lagrangian grid through Newton's laws of motion and update the Lagrangian grid.

[0017] Preferably, the process of solving the solid motion on the Lagrangian grid through Newton's laws of motion includes:

[0018] Solve for the position of the centroid of the target dendrite based on Newton's laws of motion:

[0019] r0 = ∑rρ s f s ΔV / M s ,

[0020] where r0 is the centroid of the target dendrite, r is the centroid of the original dendrite, ρ s is the solid density, f s is the solid fraction, M is the mass of the dendrite, and ΔV is the volume of the Lagrangian grid;

[0021] Calculate the total force and total torque acting on the dendrite:

[0022] F s = M s (dv st / dt),

[0023] T s = I s (dω s / dt),

[0024] Among them, F s is the total force, T s is the total torque, v st is the translational velocity, ω s is the angular velocity, I s is the moment of inertia, and t is time;

[0025] Based on the centroid position, total force, and total torque, the motion velocity of the solid is obtained:

[0026] v s = v st + ω s (r - r0),

[0027] where v s is the motion velocity of the solid.

[0028] Preferably, the process of updating the solid boundary after motion by the conservative phase field model includes:

[0029] Balancing the phase separation flux, diffusion flux, and convective flux to obtain the updated solid boundary:

[0030]

[0031] where φ is, M is the mobility, and W is the interface thickness.

[0032] Preferably, the simulation method further includes

[0033] Obtaining a set of experimental parameters, which includes the actual interface width, chemical capillary length, computational domain, seed initial position, and degree of supercooling, as well as the zero Neumann boundary conditions for the solute field and temperature field at the wall, and the no-slip boundary condition for the flow field.

[0034] Preferably, the simulation method further includes:

[0035] Generating a phase field distribution map of dendrite evolution over time.

[0036] A dendrite growth and motion simulation system based on the Euler-Lagrange method includes:

[0037] A model construction module for constructing a phase field model based on the convective flux in the solute field;

[0038] A model solving module for solving liquid convection on the Euler background grid and solving solid motion through the Lagrangian grid;

[0039] A boundary update module for updating the solid boundary after motion by the conservative phase field model.

[0040] According to the specific embodiments provided by the present invention, the following technical effects are disclosed by the present invention:

[0041] The dendrite growth motion simulation method based on Euler-Lagrange provided by the present invention first constructs a phase field model based on the convective flux in the solute field; solves the liquid convection on the Euler background grid and solves the solid motion through the Lagrangian grid; updates the solid boundary after motion through the conservative phase field model. In the simulation of the growth of dendrites, the present invention also introduces Lagrangian grids at the discrete interface to simulate the motion behavior of dendrites, realizing the simultaneous simulation of the growth morphology and convective motion of alloys, avoiding the problem of velocity mismatch between solids and liquids, and solving the problem of topological changes of complex interfaces. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained according to the provided drawings without creative efforts.

[0043] Figure 1 It is a flowchart of a dendrite growth and motion simulation method based on the Euler-Lagrange method provided by an embodiment of the present invention;

[0044] Figure 2 It is a schematic diagram of a transition grid of a Lagrangian grid provided by an embodiment of the present invention;

[0045] Figure 3 It is a phase field distribution diagram of the dendrites of Mg-6wt% Gd alloy evolving with time provided by an embodiment of the present invention;

[0046] Figure 4 It is a schematic diagram of the structure of a dendrite growth and motion simulation system based on the Euler-Lagrange method provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0047] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0048] First, in combination with Figure 1An introduction is given to the dendrite growth and motion simulation method based on the Euler - Lagrange method provided by the embodiments of the present invention. To simulate the growth and motion behavior of dendrites, the numerical simulation scheme of the embodiments of the present invention includes two parts: First, dealing with the growth behavior of dendrites; Second, solving the solid - liquid two - phase flow behavior (including liquid convection and solid kinematics). At the same time, by introducing a set of spatio - temporal varying Lagrangian grids defined within the diffuse interface, these two parts are coupled. As Figure 1 shown, the simulation method includes:

[0049] Step S01, construct a phase - field model based on the convective flux in the solute field.

[0050] Specifically, consider the convective flux in the solute field, and expand the phase - field equation based on the convective flux in the solute field to couple the phase - field, solute field, and flow field, etc. Then, the governing equations include the phase - field equation and the solute - field equation, etc. Since the phase - field variable varies in the form of hyperbolic tangent at the diffuse interface, therefore, through a non - linear pre - treatment transformation process the expanded phase - field equation to relax the strict restrictions on the grid size. Thus, the governing equations can be obtained as follows:

[0051]

[0052]

[0053] Among them, is an anisotropy function with k f -fold symmetry. For example: when k f = 4, it represents a cubic crystal structure (such as Al), and when k f = 6, it represents a hexagonal crystal structure (such as Mg). is the unit vector in the direction of the interface normal, ε is the anisotropy strength, is the initial orientation angle, is the current orientation angle, φ is the phase - field variable, represents the angle between the main arm and the x - axis, Le, k, λ, D, and f l =(1 - φ) / 2, and each parameter in turn is the Lewis coefficient, equilibrium distribution coefficient, coupling parameter, dimensionless solute diffusion coefficient in the liquid, and liquid - phase fraction. U=(2C / C ∞ / (1 + k-(1 - k)φ)-1) / (1 - k) represents the dimensionless solute concentration, θ=(T - T M -mC ∞ ) / ΔT0 represents the dimensionless temperature, where C ∞ , T M, the parameters m and ΔT0 are the far-field solute concentration, the melting point of the pure solvent, the liquidus slope, and the equilibrium solidification temperature range, respectively. The dimensionless supercooling is defined as -θ.

[0054] Step S02: Solve the liquid convection on the Eulerian background grid and solve the solid motion through the Lagrangian grid.

[0055] Specifically, the solid-liquid two-phase flow is solved based on the developed Euler-Lagrange calculation framework. Among them, the liquid convection is solved on the fixed Eulerian background grid for solving the phase-field model. The liquid convection is calculated by the lattice Boltzmann method (LBM) on the Eulerian background grid. LBM is a method for calculating liquid convection based on mesoscopic dynamics, which has the characteristics of convenient boundary setting and good numerical stability, and can effectively handle the velocity discontinuity at the dendrite interface.

[0056] The solid motion is processed according to the Lagrangian method. The solid motion is solved by Newton's laws of motion on the Lagrangian grid, and the Lagrangian grid is updated. It is assumed that the region is filled with liquid, and the solid-liquid interaction is abstracted as a specific force applied to the liquid. This assumption conforms to the global characteristics in the Eulerian scheme. The solid motion is modeled by Newton's laws of motion, indicating that the grid representing the solid boundary changes with time, which conforms to the Lagrangian characteristics with moving elements as the core.

[0057] (1) Solving liquid convection

[0058] To characterize the liquid flow, it is assumed that particles repeatedly collide and migrate, and the evolution of the particle distribution function f i is controlled by the following factors:

[0059] f i (r + δr, t + δt) = f i (r, t) - (f i (r, t) - f i eq (r,t)) / τ f + δtF i (3)

[0060] where δr and δt are the lattice spacing and time step in LBM respectively, τ f is the relaxation time, f i eq is the equilibrium distribution function, F i is the melt flow driving force, and δ is the Dirac δ function.

[0061] The relaxation time τ f : τ f = 3v k (c 2 δt) + 0.5 (4)

[0062] Among them, \(c = \delta r / \delta t\) represents the lattice movement velocity, and the relaxation time is proportional to the kinematic viscosity \(v\). k Proportional to.

[0063] The equilibrium distribution function \(f\) i eq : Among them, \(\rho=\sum\) i \(f\) i is the particle density, \(e\) i and \(w\) i are the specific velocity and the corresponding weight coefficient along the \(i\)-direction respectively. The two-dimensional nine-velocity (D2Q9) model can be used to discretize the particle velocity, and \(v\) is the liquid flow velocity.

[0064] The melt flow driving force \(F\) i is:

[0065] Among them, \(F\) b is the buoyancy force, \(F\) eul is an abstract specific force describing the solid-liquid interaction, which depends on the velocity difference between the moving dendrite and the surrounding liquid.

[0066] \(F\) b =-\(\rho f\) l \(g\beta\) C (\(C - C\) ∞ ) (7)

[0067] Among them, \(g\) and \(\beta\) C are the gravitational acceleration and the solute expansion coefficient respectively, and \(C\) is the alloy solute concentration.

[0068] Introduce the Dirac \(\delta\) function, and assume that the force density per unit area acting on the fluid is known, then:

[0069] \(F\) eul =\(\sum F\) lag \(\delta(r - r\) lag )\(\Delta S\) (8)

[0070] Among them, the subscript with "lag" represents the value at the Lagrangian grid, \(\Delta S\) is the area segment, and the \(\delta\) function is defined as \(\delta(r - r\) lag )=\(\delta\) h ((x - x\) lag ) / \(\Delta x\)\(\delta_h((y - y\) lag ) / \(\Delta y\)).

[0071]

[0072] \(F\) eul comes from the difference between the solid velocity \(v\) s and the Lagrangian grid velocity \(v\) lag .

[0073] F lag = ρ(v s - v icg ) / Δt (10)

[0074] where v s is the solid velocity at the same grid as v lag .

[0075] The grid velocity is affected by liquid convection and solid motion. The Dirac delta function is also used to update v lag (r, t) from v(r, t):

[0076] v lag = ∑vδ(r - r lag )ΔV (11)

[0077] where ΔV is the Lagrangian grid volume.

[0078] Equations (9) and (11) are similar to the force interpolation and velocity extension operations in the immersed boundary method. However, the Euler - Lagrangian framework proposed in the embodiments of the present invention avoids the approximate treatment of the boundary by introducing off - grid marker points in the immersed boundary method. The layout of the Lagrangian grid depends on the contour of the growing dendrite, and the number of Lagrangian grids increases as the dendrite grows. Therefore, the liquid flow velocity is calculated as follows:

[0079]

[0080] where ci is the lattice motion velocity in the i - direction.

[0081] (2) Solving for solid motion

[0082] The solid motion follows Newton's laws of motion. The prerequisite for solving the kinematics of the dendrite is to update the position of the centroid. Therefore, the position of the centroid of the target dendrite can be solved based on Newton's laws of motion:

[0083] r0 = ∑rρ s f s ΔV / M s (13)

[0084] where r0 is the centroid of the target dendrite, r is the centroid of the original dendrite, r is a vector, ρ s is the solid density, f s is the solid fraction, M s is the dendrite mass, and ΔV is the volume of the Lagrangian grid.

[0085] The dendrite mass M s is: M s = ∑ρ s f sΔV (14).

[0086] Calculate the total force and total torque acting on the dendrite

[0087] F s = M s (dv st / dt) (15)

[0088] T s = I s (dω s / dt) (16)

[0089] where F s is the total force, T s is the total torque, v st is the translational velocity, ω s is the angular velocity, I s is the moment of inertia, and t is time.

[0090] The moment of inertia I s is: I s = ∑ρ s f s |r - r0| 2 ΔV (17).

[0091] The total force F s and the total torque T s satisfy:

[0092] F s = -∑(F eul + (ρ s - ρ l )f s g)ΔV (18)

[0093] T s = -∑(r - r0) × (F eul + (ρ s - ρ l )f s g)ΔV (19)

[0094] where F eul is equivalent to the drag force and is positively correlated with the velocity difference between the solid and the liquid.

[0095] Based on the centroid position, total force, and total torque, the translation and rotation of the dendrite solid can be obtained. Combining with the rotation, the motion velocity of the solid can be obtained:

[0096] v s = v st + ω s × (r - r0) (20)

[0097] where vs is the solid movement speed.

[0098] The layout of the Lagrangian grid needs to satisfy two constraints: one is to be able to characterize the interface shape, and the other is to conform to solid kinematics. Since the solid-liquid interface is a diffuse interface spanning multiple grids, defining the Lagrangian grid within the diffuse interface can naturally satisfy the first constraint. As Figure 2 shown, the phase field variable that varies smoothly on the diffuse interface generates at least one layer of transition grids that vary within a narrow range. The selected transition grids can specify the shape of the dendrite profile. The distribution of the specified discrete grids is synchronized with the interface evolution. Therefore, these transition grids are used to introduce the Lagrangian description in computational fluid dynamics. To comply with the kinematic law, that is, the second constraint, grids with specific phase field values are specified through numerical experiments. Integrating the diffuse boundary concept into the LBM to solve dendrite motion avoids the non-physical growth fluctuations caused by gradually creating new Lagrangian nodes during surface subdivision and recalibration, thereby improving the numerical accuracy and simplifying the solution process. In particular, the interface decomposition or separation caused by remelting can be handled without additional intervention, which lays a foundation for further predicting dendrite separation and fragment motion.

[0099] Step S03, update the solid boundary after movement through the conservative phase field model.

[0100] Specifically, in order to maintain the solid shape during movement, the conservative phase field model is used to update the solid boundary, and this formula is an extension of the convection-diffusion equation. By balancing the phase separation flux, diffusion flux, and convection flux, the updated solid boundary is obtained:

[0101]

[0102] where φ is the phase field variable, M is the mobility, and W is the interface thickness.

[0103] The dendrite growth in the embodiments of the present invention, including interface advancement and solute transport, is solved based on the Eulerian scheme. The solid movement and the update of the Lagrangian grid are determined based on the Lagrangian description. The Lagrangian grid is defined by specific phase field values in the diffuse interface to specify the unique position of the dendrite profile and conform to solid kinematics. The Lagrangian grid is synchronized with the movement of the dendrite centroid.

[0104] The dendritic growth motion simulation method based on Euler - Lagrange provided by the embodiments of the present invention first constructs a phase - field model based on the convective flux in the solute field; solves liquid convection on the Eulerian background grid and solves solid motion through the Lagrangian grid; updates the solid boundary after motion through the conservative phase - field model. In the simulation of the growth of dendrites, the embodiments of the present invention also introduce Lagrangian grids at the discrete interface to simulate the motion behavior of dendrites, realizing the simulation of both the growth morphology of alloys and convective motion, avoiding the problem of velocity mismatch between the grid and the fluid, and solving the problem of topological changes of complex interfaces. It lays a theoretical foundation for developing a high - fidelity model to clarify the growth and motion mechanisms of dendrites.

[0105] Based on the Euler - Lagrange calculation framework, the embodiments of the present invention introduce Lagrangian grids at the discrete interface, simulate the motion behavior of dendrites according to Newton's laws of motion and solid kinematics, and realize the simulation of the growth and relative motion of alloy morphology based on the set alloy physical property parameters, providing guidance for the further improvement of the phase - field model.

[0106] Considering that the model simulation process needs to build the model based on experimental parameters, before constructing the phase - field model, it is also possible to obtain the required set of experimental parameters, such as: the actual cross - section width, chemical capillary length, computational domain, initial position of the seed, and undercooling degree, as well as the zero Neumann boundary conditions of the solute field and temperature field at the wall, the no - slip boundary condition of the convection field, etc. For example: the actual cross - section width W0 and the chemical capillary length d0 are respectively set to 5.43×10 -8 m and 4.80×10 -9 m. The size of the computational domain X×Y is 512×512, the initial position of the seed is initialized to (0.5X, 0.75Y), and the relative undercooling degree is 0.2.

[0107] In addition, in order to better observe the growth and motion behavior of dendrites, a visual phase - field distribution map of dendrites evolving with time can be generated. For example: based on the Euler - Lagrange phase - field model, simulations are carried out using Mg - 6wt% Gd alloy to obtain the dendrite interface contour. The phase - field distribution map of alloy dendrites evolving with time is as Figure 3 shown, and the time steps of (a) - (c) are in sequence: 0.200 0.500 0. It can be seen that under the action of convection, the dendrites grow and move downward while growing, and have deviated from the starting position. At the same time, with the progress of solidification, secondary dendrite arms gradually grow on the main dendrite arms.

[0108] The PFM reproduces solidification kinetics with thermodynamically accurate metrics, and the LBM effectively handles complex boundaries and dynamic interfaces. Combining the LBM and PFM methods ensures the rigor of mathematical and physical mechanisms, the convenience of boundary settings, and good numerical stability. It can efficiently solve the velocity discontinuity on the dendritic interface, effectively handle the growth and movement behaviors of dendrites, accurately depict the interface evolution behavior, avoid problems such as large interface deformation, morphology distortion, and data divergence, and realize the simulation of alloy growth morphology and convective motion, enabling it to simulate and predict the solidification behavior of dendrites under complex conditions such as solid-liquid two-phase flow.

[0109] The following describes the dendritic growth and motion simulation system based on Euler-Lagrange provided by the embodiments of the present invention. The dendritic growth and motion simulation system based on Euler-Lagrange described below can be correspondingly referred to the dendritic growth and motion simulation method based on Euler-Lagrange described above.

[0110] First, in combination with Figure 4 , an introduction to the dendritic growth and motion simulation system based on Euler-Lagrange is given. As Figure 4 shown, the dendritic growth and motion simulation system based on Euler-Lagrange may include:

[0111] A model construction module for constructing a phase field model based on the convective flux in the solute field;

[0112] A model solving module for solving liquid convection on the Euler background grid and solving solid motion through the Lagrangian grid;

[0113] A boundary update module for updating the solid boundary after motion through the conservative phase field model.

[0114] Furthermore, the dendritic growth and motion simulation system based on Euler-Lagrange may further include:

[0115] A parameter acquisition module for acquiring an experimental parameter set, where the experimental parameter set includes the actual interface width, chemical capillary length, computational domain, seed initial position, and supercooling degree, as well as the zero Neumann boundary conditions of the solute field and temperature field at the wall, and the no-slip boundary condition of the convective field.

[0116] Furthermore, the dendritic growth and motion simulation system based on Euler-Lagrange may further include:

[0117] A visualization module for generating a phase field distribution map of dendrite evolution over time.

[0118] Finally, it should also be noted that in this text, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, such that a process, method, article or device comprising a series of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising an..." does not exclude the presence of additional identical elements in the process, method, article or device comprising the element.

[0119] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. For the same and similar parts among the various embodiments, reference may be made to each other.

[0120] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but will be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for simulating dendrite growth and movement based on the Euler-Lagrange method, characterized in that, Comprising: Construct a phase field model based on the convective flux in the solute field; Solve the liquid convection on the Eulerian background grid and solve the solid motion through the Lagrangian grid; Update the solid boundary after motion through the conservative phase field model.

2. The dendritic growth and movement simulation method based on the Euler-Lagrange method according to claim 1, wherein The process of constructing the phase field model based on the convective flux in the solute field includes: Expand the phase field equation based on the convective flux in the solute field to couple the phase field, solute field and flow field; Process the expanded phase field equation through a non-linear preconditioning transformation to obtain the phase field model.

3. The dendritic growth and movement simulation method based on the Euler-Lagrange method according to claim 1, characterized in that The process of solving the liquid convection on the Eulerian background grid and solving the solid motion through the Lagrangian grid includes: Calculate the liquid convection on the Eulerian background grid by the lattice Boltzmann method; Solve the solid motion on the Lagrangian grid by Newton's laws of motion and update the Lagrangian grid.

4. The dendritic growth and movement simulation method based on the Euler-Lagrange method according to claim 3, characterized in that, The process of solving the solid motion on the Lagrangian grid by Newton's laws of motion includes: Solve for the position of the centroid of the target dendrite based on Newton's laws of motion: r0 = ∑rρ s f s ΔV / M s , where r0 is the centroid of the target dendrite, r is the centroid of the original dendrite, ρ s is the solid density, f s is the solid fraction, M is the dendrite mass, and ΔV is the volume of the Lagrangian mesh; Calculate the total force and total torque acting on the dendrite: F s = M s (dv st / dt), T s = I s (dω s / dt), Among them, F s is the total force, T s is the total torque, v st is the translational velocity, ω s is the angular velocity, I s is the moment of inertia, and t is the time; Obtain the motion velocity of the solid based on the centroid position, total force and total torque: v s = v st + ω s (r - r0), Among them, v s is the solid motion speed.

5. The dendritic growth and movement simulation method based on the Euler-Lagrange method according to claim 4, characterized in that The process of updating the solid boundary after motion through the conservative phase field model includes: Balance the phase separation flux, diffusion flux and convective flux to obtain the updated solid boundary: where φ is, M is the mobility, and W is the interface thickness.

6. The dendritic growth and movement simulation method based on the Euler-Lagrange method according to claim 1, characterized in that Also comprising Obtain a set of experimental parameters, the set of experimental parameters including the actual interface width, chemical capillary length, computational domain, seed initial position and undercooling, as well as the zero Neumann boundary conditions of the solute field and temperature field at the wall, and the no-slip boundary condition of the flow field.

7. The dendritic growth and motion simulation method based on the Euler-Lagrange method according to any one of claims 1-6, characterized in that, Also comprising: Generate a phase field distribution map of the dendrite evolving over time.

8. A dendritic growth and movement simulation system based on the Euler-Lagrange method, characterized in that Comprising: A model construction module for constructing a phase field model based on the convective flux in the solute field; A model solving module for solving the liquid convection on the Eulerian background grid and solving the solid motion through the Lagrangian grid; A boundary update module for updating the solid boundary after motion through the conservative phase field model.

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