CN117094171A - Numerical simulation method for solid-fluid conversion movement of rock debris - Google Patents

Abstract

The invention relates to the technical field of numerical simulation, and particularly discloses a numerical simulation method for solid-liquid conversion movement of rock fragments, which comprises the following steps: establishing a simulation model of the target research object based on an MPS method; calculating a particle count density based on all of the determined particle positions; determining yield stress of the chip body in different states based on the strain; calculating dynamic viscosity coefficients of the chip body in different states based on the obtained yield stress; discretizing a control equation by using a Laplace model and a gradient model based on the MPS, and calculating an external force and a viscosity term; calculating the pressure born by the particles by adopting a pressure poisson equation, and then dispersing pressure gradient items based on a gradient model; and correcting the speed and the position of the particles based on the obtained result to obtain a numerical simulation result of the solid-liquid conversion movement of the rock debris. The invention considers the solid-fluid conversion motion state of the ice-rock fragments, and the simulation result is more fit for the actual situation.

Description

A numerical simulation method for the solid-fluid transformation motion of ice-rock debris

Technical field

The present invention relates to the technical field of numerical simulation, and in particular to a numerical simulation method for the solid-fluid transformation motion of ice-rock debris.

Background technique

Ice-rock debris flow is a phenomenon in which a mixture of ice debris, rock blocks and soil particles flows at high speed after landslides, ice avalanches or rock avalanches in steep mountain slopes in alpine areas; due to the entrapped ice debris, ice-rock debris flow Flows are highly mobile and harmful, often causing catastrophic events that shock the world. They are also a hot and cutting-edge issue in the study of geological disasters under the background of global warming. Therefore, by studying the solid-flow transformation movement of ice and rock debris, we Simulation is of great significance for predicting and controlling related accident disasters.

In the existing technology, physical test devices can be used to simulate the solid-to-fluid transformation motion of ice and rock debris. For example, patent CN 116358828 A discloses a test system for simulating the solid-to-fluid transformation motion of high-speed ice and rock debris; However, physical test methods have problems such as long cycle time, high cost, and difficulty in sample preparation to ensure that the experimental results are consistent with the on-site fluid. The solid-fluid transformation movement of ice-rock debris is a complex multi-state transformation movement process, which requires a more refined method. way to truly simulate the solid-fluid transformation movement of ice and rock debris. In the traditional CFD (Computational Fluid Dynamics) method using meshes, generating an "optimal mesh" is very time-consuming, and it is difficult to simulate free surface flow or complex boundary geometry.

Therefore, in order to solve the above problems, a numerical simulation method for the solid-to-fluid transformation motion of ice and rock clasts is needed, which can more realistically simulate the solid-to-fluid transformation motion of ice and rock clasts, making the simulation results more consistent with the actual situation. .

Contents of the invention

In view of this, the purpose of the present invention is to provide a numerical simulation method for the solid-to-fluid transformation motion of ice and rock debris, which can more realistically simulate the solid-to-fluid transformation motion of ice and rock debris, so that the simulation results are more realistic. Condition.

In order to achieve the above purpose, the present invention provides a numerical simulation method for the solid-fluid transformation motion of ice and rock clasts. First, a simulation model of ice and rock clasts is established according to the MPS method. The simulation model of ice and rock clasts includes: The MPS fluid domain and the MPS particles located in the MPS fluid domain regard the solid particles in the MPS particles as fluid particles and perform numerical calculations together with the fluid particles; the numerical calculation includes the following steps:

S11: After starting and initializing, calculate the particle number density based on the determined positions of all particles;

S12: Determine the yield stress of the clastic body in different states based on strain;

S13: Based on the yield stress determined above, calculate the dynamic viscosity coefficient of the debris body in different states;

S14: Use the Laplace model and the gradient model to discretize the control equations and calculate the external force and viscosity terms;

S15: Update particle position;

S16: Calculate the particle number density after position update;

S17: Use the Laplace model to discretize the pressure Poisson equation;

S18: Calculate the pressure on particles based on the pressure Poisson equation, and then use the gradient model to calculate the pressure gradient term;

S19: Based on the above obtained results, the velocity and position of the particles are corrected, and the numerical simulation results of the solid-fluid transformation motion of the ice-rock debris are obtained.

As a further improvement to the above technical solution, in step S19, it is determined whether the number of simulation time steps reaches the preset value. If it does not reach the preset value, return to step S11, otherwise the simulation is stopped.

As a further improvement to the above technical solution, in step S11, the positions of all particles are obtained. The particle number density will be affected by adjacent particles within the effective radius and follow the weight function:

Among them, w _ij (r _ij ) is the weight function between particle i and particle j, r ^e is the effective radius;

Then based on the weights between all the particles, the particle number density can be obtained by adding them.

As a further improvement to the above technical solution, in step S12, the relative displacement equation of the particles is first discretized to obtain the strain;

The resulting strain is then compared with its plastic deviation strain in the peak state, residual state, and fluid state to determine whether the clastic body behaves in a solid state, a transition state, or a fluid state.

As a further improvement to the above technical solution, in step S13, the velocity gradient term is first discretized based on the MPS gradient model to obtain the velocity gradient tensor, and the shear rate is obtained based on the obtained result;

Then the shear rate obtained above is brought into the Bingham model to calculate the dynamic viscosity coefficient of the clastic body in different states;

The constitutive relation expression of the Bingham model is:

Among them, τ is shear stress, μ is viscosity coefficient, is the shear rate, τ _y is the yield shear stress.

As a further improvement to the above technical solution, in step S14, the minimum pressure of all particles in their adjacent areas is first calculated, and then based on the MPS method, the control equation is discretized by using the Laplace model and the gradient model to obtain the fluid the pressure on the particles;

The Laplacian model is:

in, is an arbitrary scalar quantity of particle i, d is the spatial dimension, and n ₀ is the initial particle number density;

The gradient model is:

Among them, p is the pressure.

As a further improvement to the above technical solution, in step S18, calculating the pressure on the particle based on the pressure Poisson equation includes: first discretizing the left side of the pressure Poisson equation using the Laplace model, etc. The right side of the formula represents the deviation of particle number density;

The pressure Poisson equation is:

Among them, ρ is the density and Δt is the size of the time step;

Then the simultaneous equations are represented by a linear symmetry matrix and solved using the incomplete Cholesky conjugate gradient method to obtain the pressure on the particles.

As a further improvement to the above technical solution, in step S18, the MPS gradient model is used to calculate the pressure gradient term.

As a further improvement to the above technical solution, in step S19, the formula for modifying the speed and position is as follows:

Among them, u is the speed and k is the current time step.

Compared with the existing technology, the present invention has the following beneficial technical effects:

The present invention provides a numerical simulation method for the solid-to-fluid transformation motion of ice and rock debris, which uses fluid control equations to calculate the speed and position of all particles, and after solving the pressure Poisson equation, corrects the speed and position; Since the solid-fluid transformation motion state of the ice-rock debris body is taken into account, the simulation results are more in line with the actual situation.

Additional advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.

Description of the drawings

The description and drawings that constitute a part of the present invention are used to provide a further understanding of the present invention. The illustrative embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute a limitation of the present invention.

Figure 1 is a schematic flow chart of the numerical calculation of the present invention;

Figure 2 is a schematic diagram showing the state of the debris body changing with plastic strain in the present invention.

Detailed ways

In order to enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

Example

As shown in Figures 1 and 2: This embodiment provides a numerical simulation method for the solid-fluid transformation motion of ice and rock debris.

As a background, first the Moving Particle Semi-implicit (MPS) method and the Bingham fluid model (Bingham fluid model) are explained.

The MPS (Moving Particle Semi-implicit) method is a numerical analysis method for incompressible fluids first proposed by Koshizuka S and Oka in 1996. It was initially mainly used in nuclear engineering and coastal engineering problems, focusing on fluid research; through The fluid control equation is used to calculate the displacement and velocity of the particles, and the Poisson equation is used to correct the velocity and position of the particles; the MPS method is gradually applied to the field of landslides in geotechnical engineering by using a semi-implicit time calculation algorithm. In each time step, the viscosity term in the momentum equation is first explicitly calculated to obtain the initial values of the velocity and position of the example, and then the Poisson equation is implicitly solved to obtain the correction value of the velocity and position; through the corresponding correction calculation, the particle's position in the next time step is obtained. The speed and position of each particle; by tracking the movement patterns of each particle at each time step, the flow information of the entire flow field fluid is obtained. The mesh-free MPS method is easy to model and can simulate surface changes and liquid splash phenomena without difficulty.

Bingham fluid (Bingham fluid) was first proposed as a viscoelastic non-Newtonian fluid with linear fluidity; in the Bingham fluid model, if the shear stress is lower than the threshold τ _y (yield shear stress), it will not occur Deformation; when the shear stress is greater than τ _y , deformation will occur; and the deformation is proportional to the degree to which the shear stress exceeds τ _y .

This embodiment provides a numerical simulation method for the solid-fluid transformation motion of ice and rock clasts. First, a simulation model of ice and rock clasts is established based on the MPS method (the actual ice and rock clasts can be used as the target research object, and the collection Modeling is performed after the relevant physical parameters). The ice-rock debris simulation model includes the MPS fluid domain and the MPS particles located in the MPS fluid domain. The solid particles in the MPS particles are regarded as fluid particles and numerical calculations are performed together with the fluid particles. .

As shown in Figure 1 (in Figure 1, u represents the rate, r represents the position, Δt: represents the time step, * represents the calculation time, and k represents the calculation step), the numerical calculation includes the following steps:

S11: After starting and initializing, calculate the particle number density based on the determined positions of all particles;

S12: Determine the yield stress of the clastic body (i.e. ice rock clastic body simulation model) in different states based on the strain ε;

S13: Based on the yield stress determined above, calculate the dynamic viscosity coefficient of the debris body in different states;

S14: Use the Laplace model and the gradient model to discretize the control equations and calculate the external force and viscosity terms;

S15: Update particle position;

S16: Calculate the particle number density after position update;

S17: Use the Laplace model to discretize the pressure Poisson equation;

S18: Calculate the pressure on particles based on the pressure Poisson equation, and then use the gradient model to calculate the pressure gradient term;

S19: Based on the above obtained results, correct the speed and position of the particles to obtain the numerical simulation results of the solid-flow transformation motion of the ice rock debris; determine whether the simulation time steps have reached the preset value. If it has not reached the preset value, value, return to step S11, otherwise stop the simulation.

In the MPS method, an implicit algorithm is used to calculate the pressure term, and an explicit algorithm is used to calculate the viscosity and external force terms. The mass conservation equation and momentum conservation equation of incompressible fluid are as follows:

Among them, ρ is the fluid density; u is the fluid velocity; p is the pressure; μ is the dynamic viscosity coefficient; f is the body force; the left side of the momentum conservation equation is the Lagrangian differential including the convection term, which is obtained by It is calculated directly by tracking the motion of particles; the right side consists of pressure gradient and external force terms; all terms expressed by differential operators should be replaced by the interaction of particles.

Among them, the discrete form of the momentum conservation equation can be written as:

Among them, k is the current time step, is the size of the time step.

The viscous term in the formula is discretized into the following form:

in, is the kinematic viscosity coefficient of particle i at time step k, dynamic viscosity coefficient/> is a variable parameter; the Laplace term on the left can be interpreted as the difference between the velocity of a point and the average velocity of a surrounding small volume, which means that viscosity is the diffusion of momentum.

In the MPS method, the number of particles will be affected by adjacent particles within the effective radius; the effective radius is represented by re; the weight function is expressed by the following formula:

Among them, w _ij (r _ij ) is the weight function between particle i and particle j, r ^e is the effective radius.

When all particle positions are obtained, the particle number density can also be obtained:

The strain tensor ε _d is represented by the relative displacement vector d:

Among them, x is the space vector coordinate, α and β are spatial indicators; the gradient model of the MPS method is suitable for each term on the right side of equation (1); the strain tensor ε _i of particle i is obtained; it can be summarized by the following formula:

The strain ε _d is obtained from the above formula. When the strain is less than When, the mechanical behavior of the solid represented by the clastic body; when the strain is greater than/> and less than/> When , the clastic body represents transition state mechanical behavior; when the plastic deviation strain of the fluid is greater than/> When , the clastic body shows perfect rheological characteristics; based on this, the yield stress is determined; the specific formula is as follows:

The dynamic viscosity coefficient of clastic bodies in different states (solid state, transition state, flow state) can be expressed as:

in, It is derived from the following formula:

Here, the MPS gradient model is introduced to discretize the velocity change rate in equation (11):

After obtaining the value of the velocity gradient tensor, replace it with equation (11) to obtain the value of the shear rate; the viscosity coefficient μ is obtained by substituting the known shear rate into equation (10).

The MPS method discretizes the governing equations by using the Laplace model and the gradient model:

in, is the minimum pressure in the adjacent area of particle i:

The Laplacian operator is discretized as:

In the formula:

Pressure is calculated using Poisson's equation for pressure:

The left side can be discretized by the MPS Laplace model [such as equation (15)]; the right side of the equation represents the deviation of the particle number density; on this basis, the simultaneous equations are expressed by linear symmetry matrices, and can be expressed by incomplete Cholesky conjugate gradient method (ICCG) solution.

Furthermore, using the MPS gradient model, the pressure gradient term can be calculated.

The final modifications to speed and position are as follows:

In order to maintain the stability of the simulation, the time step t needs to satisfy the following constraints:

Among them, l ₀ is the distance between adjacent particles, D is a value obtained based on experience, and should be less than 1.0; generally, D can be set equal to 0.2; under this constraint, when the kinematic viscosity is high, the time step will become smaller, resulting in a very long simulation time; too small a time step is disadvantageous.

To sum up, this embodiment divides a calculation step into two processes; in the first process, the acceleration of particles for all terms except the pressure term is calculated, and the time velocity and position are calculated; the pressure term is calculated in the second process. It is calculated during this process; after solving the Poisson equation for pressure, the velocity and position are corrected.

This embodiment uses the fluid control equation to calculate the velocity and position of all particles, and after solving the pressure Poisson equation, the velocity and position are corrected; since the solid-fluid transformation motion state of the ice-rock debris body is considered, its simulation The result is more in line with the actual situation.

Finally, this article uses specific examples to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the core idea of the present invention. Without departing from the principles of the present invention, other methods can also be used. Several improvements and modifications are made to the present invention, and these improvements and modifications also fall within the protection scope of the present invention.

Claims (9)

1. A numerical simulation method for the solid-to-fluid transformation motion of ice-rock clasts, which is characterized in that firstly, a simulation model of ice-rock clasts is established according to the MPS method. The simulation model of ice-rock clasts includes MPS fluid domain and MPS particles located in the MPS fluid domain regard the solid particles in the MPS particles as fluid particles and perform numerical calculations together with the fluid particles; the numerical calculation includes the following steps: S11: After starting and initializing, calculate the particle number density based on the determined positions of all particles; S12: Determine the yield stress of the clastic body in different states based on strain; S13: Based on the yield stress determined above, calculate the dynamic viscosity coefficient of the debris body in different states; S14: Use the Laplace model and the gradient model to discretize the control equations and calculate the external force and viscosity terms; S15: Update particle position; S16: Calculate the particle number density after position update; S17: Use the Laplace model to discretize the pressure Poisson equation; S18: Calculate the pressure on particles based on the pressure Poisson equation, and then use the gradient model to calculate the pressure gradient term; S19: Based on the above obtained results, the velocity and position of the particles are corrected, and the numerical simulation results of the solid-fluid transformation motion of the ice-rock debris are obtained. 2. A numerical simulation method for the solid-to-fluid transformation motion of ice and rock debris according to claim 1, characterized in that: In step S19, it is determined whether the number of simulation time steps reaches the preset value. If it does not reach the preset value, return to step S11. Otherwise, the simulation is stopped. 3. A numerical simulation method for the solid-to-fluid transformation motion of glacial rock debris according to claim 1 or 2, characterized in that: In step S11, the positions of all particles are obtained. The particle number density will be affected by adjacent particles within the effective radius and follow the weight function: Among them, w _ij (r _ij ) is the weight function between particle i and particle j, r ^e is the effective radius; Then based on the weights between all the particles, the particle number density can be obtained by adding them. 4. A numerical simulation method for the solid-to-fluid transformation motion of ice and rock debris according to claim 3, characterized in that: In step S12, first discretize the relative displacement equation of the particles to obtain the strain; The resulting strain is then compared with its plastic deviation strain in the peak state, residual state, and fluid state to determine whether the clastic body behaves in a solid state, a transition state, or a fluid state. 5. A numerical simulation method for the solid-to-fluid transformation motion of ice and rock debris according to claim 4, characterized in that: In step S13, first, the velocity gradient term is discretized based on the MPS gradient model to obtain the velocity gradient tensor, and the shear rate is obtained based on the obtained result; Then the shear rate obtained above is brought into the Bingham model to calculate the dynamic viscosity coefficient of the clastic body in different states; The constitutive relation expression of the Bingham model is: Among them, τ is shear stress, μ is viscosity coefficient, is the shear rate, τ _y is the yield shear stress. 6. A numerical simulation method for the solid-to-fluid transformation motion of ice and rock debris according to claim 5, characterized in that: In step S14, first calculate the minimum pressure of all particles in their adjacent areas, and then use the Laplace model and gradient model to discretize the control equation based on the MPS method to obtain the pressure experienced by the fluid particles; The Laplace model is: in, is an arbitrary scalar quantity of particle i, d is the spatial dimension, and n ₀ is the initial particle number density; The gradient model is: Among them, p is the pressure. 7. A numerical simulation method for the solid-to-fluid transformation motion of ice and rock debris according to claim 6, characterized in that: In step S18, calculating the pressure of particles based on the pressure Poisson equation includes: first discretizing the left side of the equation of the pressure Poisson equation using the Laplace model, and the right side of the equation represents the particle number density. deviation; The pressure Poisson equation is: Among them, ρ is the density and Δt is the size of the time step; Then the simultaneous equations are represented by a linear symmetry matrix and solved using the incomplete Cholesky conjugate gradient method to obtain the pressure on the particles. 8. A numerical simulation method for the solid-to-fluid transformation motion of ice and rock debris according to claim 7, characterized in that: In step S18, the pressure gradient term is calculated using the MPS gradient model. 9. A numerical simulation method for the solid-to-fluid transformation motion of ice and rock debris according to claim 8, characterized in that: In step S19, the formula for modifying the speed and position is as follows: Among them, u is the speed and k is the current time step.