SPH Injection Boundary Method for Multi-Scale Analysis of Debris Flow Dynamics

Abstract

This invention discloses a SPH injection boundary method for cross-scale analysis of debris flow dynamic processes, belonging to the fields of computational fluid dynamics and disaster prevention and mitigation engineering technology. The method includes the following steps: First, a dataset is constructed by extracting hydraulic time-series parameters of discrete nodes at the inflow section based on shallow water equations. Then, a mapping operator is built using nonlinear spatial interpolation to establish a three-dimensional inflow boundary nonlinear parameter field mapping model. After initializing the SPH particle system, the instantaneous target boundary parameters of the particles are analyzed using spatiotemporal dual interpolation. A bilateral truncation activation function is then used to achieve precise control of the particle's three-dimensional state. Finally, a particle reset mechanism is used to maintain the mass flux closed loop. Using this method, accurate mapping of cross-scale data is achieved, ensuring the stability and continuity of the debris flow SPH simulation inflow boundary, and improving simulation accuracy and numerical stability.

Description

Technical Field

[0001] This invention relates to the fields of computational fluid dynamics and disaster prevention and mitigation engineering technology, and in particular to the SPH injection boundary method for cross-scale analysis of debris flow dynamic processes. Background Technology

[0002] Currently, numerical simulation of debris flow dynamics mainly adopts two types of technical solutions: one is a macroscopic calculation method based on shallow water equations (SW) oriented towards the watershed scale, and the other is a refined simulation method based on smoothed particle hydrodynamics (SPH) oriented towards the local region. The two types of methods undertake the simulation tasks of debris flow motion at different scales, and constitute the conventional technical system for debris flow dynamic process analysis.

[0003] When performing cross-scale coupling analysis between macroscopic shallow water equation simulation results and microscopic SPH fine simulation, existing SPH inflow boundary techniques have significant shortcomings, including: the boundary driving method only supports steady flow or simple function forms, and cannot directly use the complex time-series hydraulic data output by the shallow water equation as inflow conditions; at the same time, the particle emitter height is fixed, which cannot simulate the dynamic water depth changes in the actual debris flow process, nor can it reproduce the non-uniform distribution characteristics of lateral velocity and water depth in the river cross section. Ultimately, it is difficult to accurately reproduce the real three-dimensional dynamic process of unsteady debris flow, and the accuracy and realism of cross-scale coupling simulation cannot be guaranteed. Summary of the Invention

[0004] The purpose of this invention is to provide an SPH injection boundary method for cross-scale analysis of debris flow dynamic processes, thereby solving the aforementioned technical problems.

[0005] To achieve the above objectives, this invention provides an SPH injection boundary method for cross-scale analysis of debris flow dynamic processes, comprising the following steps: S1. Based on the macroscopic simulation of debris flow, the hydraulic time series parameters of discrete nodes at the inflow section are extracted by simulating the shallow water equation SW to obtain a discrete hydrodynamic dataset. S2. Based on the discrete hydrodynamic dataset of S1 and the differences between macro and micro scales, a mapping operator is constructed through nonlinear spatial interpolation to obtain a three-dimensional inflow boundary nonlinear parameter field mapping model. S3. Based on the three-dimensional inflow boundary nonlinear parameter field mapping model of S2, the SPH particle system is initialized by dividing the active region and the buffer zone and generating a particle set. S4. Based on the SPH particle system initialized in S3 and the three-dimensional inflow boundary nonlinear parameter field mapping model in S2, the instantaneous target boundary parameters of the particles are obtained through spatiotemporal dual interpolation analysis. S5. Based on the instantaneous target boundary parameters of particles and local riverbed topography of S4, the state of particles in the buffer is determined and synchronized through a bilateral truncation activation function to obtain the three-dimensional running state of the precisely activated particles. S6, based on the precise activation of the particle's three-dimensional running state in S5, obtains a continuous and stable mass flux closed loop through particle reset and cyclic injection mechanisms.

[0006] Preferably, the specific steps of S1 include: S1.1 Based on the requirement of macroscopic simulation of debris flow, the macroscopic movement process of debris flow on real terrain is simulated by SW model; S1.2 Select an inflow section that matches the location of the SPH transmitter, and deploy discrete monitoring nodes covering the entire boundary from the left bank to the right bank of the river in the transverse direction of the section. S1.3 Extract the flow velocity vector and hydraulic parameters of water depth for each discrete node step by step, and record the simulation time corresponding to each time step simultaneously. S1.4 Integrate the extracted time series parameters and time data to construct a discrete hydrodynamic time series dataset. Complete the preparation of basic data.

[0007] Preferably, hydraulic parameters of m discrete nodes at the inflow cross-section of the study area are extracted over N time steps to construct a discrete hydrodynamic time series dataset. The formula is: ; in, , And respectively the first The velocity vector and water depth at each node at each time step; The time corresponding to each time step; Preferably, the specific steps of S2 include: S2.1, based on the discrete hydrodynamic time series dataset of S1, compares the resolution differences between macroscopic discrete nodes and microscopic SPH particles, defining the SPH inflow boundary as the domain. ,in, for particles and The distance of the particle in the Y direction, For discrete monitoring nodes; for , The maximum value in the range is used to obtain the computational domain for the three-dimensional SPH inflow boundary parameter mapping. S2.2, Based on the inflow boundary domain Based on the fluid viscosity distribution pattern, through the left bank of the cross-section and the right bank Introduce no-slip boundary constraints and set and In order to obtain flow velocity boundary constraints that fit the river channel boundary; S2.3. Based on the node parameters and no-slip boundary constraints of the discrete hydrodynamic time series dataset, a piecewise cubic polynomial function corresponding to the flow velocity and water depth is constructed. and The spatial interpolation fundamental polynomial of the coefficients to be solved is obtained as follows: ; ; in, is the flow velocity interpolation function at the transverse position y of the cross section; is the water depth interpolation function at the transverse position y of the cross section; , They are respectively and The coefficient of the constant term; , They are respectively and The coefficients of the first-order term; , They are respectively and The coefficients of the second-order terms; , They are respectively and The coefficients of the third-order terms; S2.4. Based on the piecewise cubic polynomial function, by solving the polynomial coefficients, ... and The first and second derivatives are continuous at all nodes to obtain a cubic spline space interpolation function with a smooth transition. S2.5. Based on the resolution difference between macroscopic discrete nodes and microscopic SPH particles, by integrating the cubic spline space interpolation function and the discrete hydrodynamic time series dataset, a mapping operator that can convert discrete data into a continuous spatiotemporal parameter field is obtained: ; in, and These are continuous functions of velocity and depth, respectively. It is a nonlinear mapping operator used to transform discrete node data into a continuous parameter field; S2.6, based on the mapping operator of S2.5, maps the time-varying hydraulic parameters of discrete nodes to a value covering the entire computational domain. The continuous spatiotemporal function is used to obtain a three-dimensional inflow boundary nonlinear parameter field mapping model that can analyze the hydraulic parameters at any position and time of the inflow section.

[0008] Preferably, the specific steps of S3 include: S3.1, a three-dimensional inflow boundary nonlinear parameter field mapping model based on S2.6, establishes a three-dimensional emitter region upstream of the SPH computational domain for particle generation and inflow control. ; S3.2, Three-dimensional emitter region based on S3.1 The flow is divided into emitter partitions along the debris flow direction, including an active region adjacent to the main computational domain and a buffer zone upstream of the active region. The active region consists of a single or multiple layers of particles, and the buffer zone is used to provide kernel function support for SPH calculations. S3.3, based on the emitter partitioning structure of S3.2, generates a particle set within the three-dimensional emitter region. This yields the initial SPH particle set covering the entire area of ​​the emitter. S3.4, the initial particle set of SPH based on S3.3, through each particle Initialize state vector ,in, For position coordinates, To initialize as a zero vector, For density, The pressure is then used to obtain the initialized SPH particle system.

[0009] Preferably, the specific steps of S4 include: S4.1, the SPH particle system initialized based on S3.4 and the three-dimensional inflow boundary nonlinear parameter field mapping model based on S2.6, by entering the SPH time integration step and selecting only particles in the active region for calculation, the active region particle calculation objects participating in the instantaneous parameter analysis are obtained. S4.2, based on the active zone particle computational object of S4.1 and the discrete hydrodynamic time series dataset of S1, performs time-dimensional linear interpolation on the hydraulic parameters of discrete nodes and calculates the time weight coefficients. The instantaneous hydraulic parameters of the discrete nodes at the current SPH time are obtained by the following calculation formula: ; in, This is the current moment of the SPH time integration step; , The first , The corresponding time for each time step; The formula for the instantaneous variables of discrete nodes is: ; in, For instantaneous variables of velocity or depth; S4.3, based on the discrete node instantaneous hydraulic parameters at the current SPH time in S4.2 and the cubic spline space interpolation function in S2.4, by performing spatial nonlinear mapping analysis using the instantaneous node values ​​as input control points, the instantaneous target boundary parameters of the active zone particles are obtained, including the flow velocity target parameters. and water depth target parameters .

[0010] Preferably, the specific steps of S5 include: The SPH particle system, based on the instantaneous target boundary parameters of particles in S4.3 and the initialization in S3.4, determines the local riverbed bottom elevation corresponding to the lateral position of each particle by acquiring the instantaneous position vector of each particle within the active zone. Local instantaneous inflow depth This yields a particle position-terrain-hydraulic parameter matching dataset; S5.2, based on the particle position-terrain-hydraulic parameter matching dataset of S5.1, constructs a bilateral truncated activation function for each active region particle. The validity is determined, and then the particle activation determination result is obtained; S5.3 Based on the particle activation state determination result of S5.2, by assigning instantaneous inflow target velocity to effective particles and forcing invalid particles to zero velocity, the particle velocity vector in the active zone is dynamically updated to obtain the precise velocity assignment state of the particles in the active zone, so as to achieve dynamic and precise injection in non-uniform water depth. S5.4, Based on the particle activation determination result of S5.2, the static pressure initialization formula is used. Dynamically corrected particle pressure, wherein... Particle pressure; For reference density; This refers to the elevation of the riverbed bottom. The instantaneous target water depth; The vertical coordinates of the particle are used to obtain the particle pressure state that matches the free liquid surface. S5.5 Based on the updated three-dimensional state of the active region particles, by synchronizing the particle state in the buffer with the particle state in the active region at the same time, the three-dimensional running state of the particles with precise activation of the entire emitter region is obtained, so as to provide the neighbor kernel function support required for SPH calculation to the active region particles.

[0011] Preferably, in S5.2, the bilateral truncation activation function is the Heaviside step function, with the following formula: ; in, This is the result of the activation status determination; For the first The three-dimensional position vector of each particle; For the inflow section in the lateral position The elevation function of the riverbed topography at the location; The instantaneous water depth at this location is calculated using nonlinear interpolation. It is the Heaviside step function; For the first The instantaneous free surface elevation of each particle; Bilateral cutoff includes: via Implement lower boundary truncation, and when At that time, the function value is 1 to ensure that the particle is located on the riverbed; pass Implement upper boundary truncation, and when When the function value is 1, it ensures that the particle is below the free surface. This is used to ensure that the particle is considered a valid water flow particle only when it is simultaneously above the local riverbed surface and below the local free surface.

[0012] Preferably, the specific steps of S6 include: S6.1, based on the precisely activated three-dimensional particle running state of S5.5 and the three-dimensional emitter region defined in S3.1, obtains the flow length threshold for particle escape determination by setting the flow length of the emitter region. ; S6.2, based on the flow length threshold and particle three-dimensional running state of S6.1, through the particle set Each particle in the process is examined individually to determine its flow direction and position. The particle escape boundary check results are obtained, which are used to distinguish between escaped particles that have entered the main computational domain and those that have not escaped. S6.3, based on the particle escape boundary check results of S6.2, by satisfying... Particles that escape the condition perform a particle reset operation, resetting the particle position coordinates to the initial generated grid point coordinates within the emitter buffer, thus obtaining the spatial position of the escaped particle after reset. S6.4. Based on the spatial position of the escaped particles after S6.3, by resetting the particle velocity, density and pressure to the initial zero state, the initial state of the particles to be activated is obtained, so that the particles wait to enter the active area to receive the next round of state control. S6.5 By continuously stabilizing the number of particles entering the flow and the injection flux, a continuous and stable mass flux closed loop is obtained, thereby realizing the continuous and conserved injection of debris flow mass.

[0013] Therefore, the SPH injection boundary method for cross-scale analysis of debris flow dynamic processes, as described above, has the following beneficial effects: 1. Based on the shallow water equation, macroscopic discrete hydraulic time-series parameters are extracted. A cubic spline space interpolation mapping operator is constructed by combining the differences between macro and micro scales, forming a three-dimensional inflow boundary nonlinear parameter field mapping model. This solves the problems of scale mismatch between macroscopic shallow water simulation and microscopic SPH particle simulation, and the inability of sparse discrete monitoring data to be directly adapted to the fine analysis of microscopic particles. It realizes the continuous and smooth mapping of macroscopic inflow hydraulic parameters to the microscopic SPH computational domain, and can accurately analyze the instantaneous inflow parameters of SPH particles at any location, ensuring the consistency and accuracy of cross-scale debris flow dynamic transmission.

[0014] 2. The SPH inflow emitter region is divided into an active region and a buffer region to complete the generation of particle sets and the initialization of multi-physical quantity state vectors. The partition structure clarifies the functional division of particle inflow control and kernel function support. The active region focuses on assigning values ​​to the inflow parameters of the main computational domain, while the buffer region provides stable neighbor particles to support the SPH kernel function calculation. This avoids the calculation distortion problem caused by the lack of neighbors for inflow boundary particles. At the same time, the particle initialization process is standardized, which builds a stable particle system foundation for the accurate injection of subsequent boundary parameters.

[0015] 3. By employing a dual interpolation method combining linear interpolation in the time dimension and cubic spline interpolation in the spatial dimension, the instantaneous target boundary parameters of particles in the active zone are analyzed. This method takes into account both the temporal dynamic changes and spatial non-uniform distribution characteristics of the hydraulic parameters of the debris inflow. It overcomes the limitation that discrete time series data can only match fixed time steps and fixed monitoring nodes, making the solution of instantaneous particle parameters within the SPH time integration step more closely match the actual dynamic process, and significantly improving the spatiotemporal adaptability and dynamic accuracy of the inflow boundary parameter analysis.

[0016] 4. Based on the Heaviside bilateral truncation activation function combined with local riverbed topography to determine particle validity, the particle pressure is simultaneously corrected and the buffer zone particle state is matched. Through double truncation at the upper and lower boundaries, effective water flow particles are accurately screened, eliminating invalid particles from interfering with the inflow state. At the same time, coupled with riverbed topography, dynamic and accurate injection of non-uniform water depth is achieved. Combined with static pressure correction to match the free liquid surface pressure distribution, this not only ensures the continuity of SPH kernel function calculation, but also improves the physical rationality and accuracy of the particle state assignment at the inflow boundary.

[0017] 5. By resetting the position and physical state of escaping particles through the particle reset operator, a particle cyclic injection mechanism is constructed. The cyclic reuse of particles replaces the continuous addition of new particles, avoiding the computational redundancy and efficiency loss caused by the infinite growth of the number of particles. At the same time, the rhythm of particle escape and reset is precisely controlled to achieve continuous and conserved injection of debris flow inflow mass. This solves the problem of mass leakage and flux fluctuation that easily occur at the inflow boundary of traditional SPH, and constructs a stable mass flux closed loop to ensure the continuity and conservation of debris flow dynamic process across scales.

[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0019] Figure 1 A flowchart of the SPH injection boundary method for cross-scale analysis of debris flow dynamic processes provided by the present invention. Figure 2 The diagram showing the simulated debris flow motion and data injection boundary location in SW provided by this invention; Figure 3 This invention provides a diagram showing the position of the injection boundary and the particle arrangement in a three-dimensional SPH. Figure 4 This is a cross-sectional view of the injection boundary at a certain moment in the three-dimensional SPH provided by the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the embodiments of the present invention and are not intended to limit the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout.

[0021] It should be noted that the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion, such as a process, method, system, product, or server that includes a series of steps or units, not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such process, method, product, or device.

[0022] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0023] In the cross-scale simulation of debris flow dynamics, existing technologies have significant shortcomings when coupling macroscopic shallow water equation (SW) simulation with microscopic smooth particle hydrodynamic (SPH) simulation. Existing SPH inflow boundaries mostly use steady flow or simple function driving, which cannot directly utilize the complex hydraulic time series data output by SW. In addition, the transmitter height is fixed, making it difficult to simulate the dynamic water depth changes of real debris flows and the non-uniform distribution of lateral velocity and water depth in the river cross section. As a result, it is impossible to accurately reproduce the real three-dimensional dynamic process of unsteady debris flow.

[0024] Based on the above analysis, this invention is designed, see appendix. Figures 1-4The SPH injection boundary method for cross-scale analysis of debris flow dynamic processes includes the following steps: S1. Based on the macroscopic simulation of debris flow, the hydraulic time series parameters of discrete nodes at the inflow section are extracted by simulating the shallow water equation SW to obtain a discrete hydrodynamic dataset. The specific steps of S1 include: S1.1 Based on the requirement of macroscopic simulation of debris flow, the macroscopic movement process of debris flow on real terrain is simulated by SW model; S1.2 Select an inflow section that matches the location of the SPH transmitter, and deploy discrete monitoring nodes covering the entire boundary from the left bank to the right bank of the river in the transverse direction of the section. S1.3 Extract the flow velocity vector and hydraulic parameters of water depth for each discrete node step by step, and record the simulation time corresponding to each time step simultaneously. S1.4 Integrate the extracted time series parameters and time data to construct a discrete hydrodynamic time series dataset. Complete the preparation of basic data; Hydraulic parameters of m discrete nodes at the inflow cross-section of the study area within N time steps are extracted to construct a discrete hydrodynamic time series dataset. The formula is: ; in, , And respectively the first The velocity vector and water depth at each node at each time step; The time corresponding to each time step; S2. Based on the discrete hydrodynamic dataset of S1 and the differences between macro and micro scales, a mapping operator is constructed through nonlinear spatial interpolation to obtain a three-dimensional inflow boundary nonlinear parameter field mapping model. The specific steps of S2 include: S2.1, based on the discrete hydrodynamic time series dataset of S1, compares the resolution differences between macroscopic discrete nodes and microscopic SPH particles, defining the SPH inflow boundary as the domain. ,in, for particles and The distance of the particle in the Y direction, For discrete monitoring nodes; for , The maximum value in the range is used to obtain the computational domain for the three-dimensional SPH inflow boundary parameter mapping. S2.2, Based on the inflow boundary domain Based on the fluid viscosity distribution pattern, through the left bank of the cross-section and the right bank Introduce no-slip boundary constraints and set and In order to obtain flow velocity boundary constraints that fit the river channel boundary; S2.3. Based on the node parameters and no-slip boundary constraints of the discrete hydrodynamic time series dataset, a piecewise cubic polynomial function corresponding to the flow velocity and water depth is constructed. and The spatial interpolation fundamental polynomial of the coefficients to be solved is obtained as follows: ; ; in, y is the velocity interpolation function at the transverse position y of the cross section, used to characterize the velocity value corresponding to any transverse position on the inflow cross section; is the water depth interpolation function at the transverse position y of the cross section, used to characterize the water depth value corresponding to any transverse position on the inflow cross section; , They are respectively and The coefficient of the constant term; , They are respectively and The coefficients of the first-order term; , They are respectively and The coefficients of the second-order terms; , They are respectively and The coefficients of the third-order terms; S2.4. Based on the piecewise cubic polynomial function, by solving the polynomial coefficients, ... and The first and second derivatives are continuous at all nodes to obtain a cubic spline space interpolation function with a smooth transition. S2.5. Based on the resolution difference between macroscopic discrete nodes and microscopic SPH particles, by integrating the cubic spline space interpolation function and the discrete hydrodynamic time series dataset, a mapping operator that can convert discrete data into a continuous spatiotemporal parameter field is obtained: in, and These are continuous functions of velocity and depth, respectively. It is a nonlinear mapping operator used to transform discrete node data into a continuous parameter field; S2.6, based on the mapping operator of S2.5, maps the time-varying hydraulic parameters of discrete nodes to a value covering the entire computational domain. The continuous spatiotemporal function is used to obtain a three-dimensional inflow boundary nonlinear parameter field mapping model that can analyze the hydraulic parameters at any position and time of the inflow section.

[0025] S3. Based on the three-dimensional inflow boundary nonlinear parameter field mapping model of S2, the SPH particle system is initialized by dividing the active region and the buffer zone and generating a particle set. The specific steps of S3 include: S3.1, a three-dimensional inflow boundary nonlinear parameter field mapping model based on S2.6, establishes a three-dimensional emitter region upstream of the SPH computational domain for particle generation and inflow control. To provide a carrier for the spatial arrangement and state control of particles; S3.2, Three-dimensional emitter region based on S3.1 The flow is divided into emitter partitions along the debris flow direction, including an active region adjacent to the main computational domain and a buffer zone upstream of the active region. The active region consists of a single or multiple layers of particles, and the buffer zone is used to provide kernel function support for SPH calculations. S3.3, based on the emitter partitioning structure of S3.2, generates a particle set within the three-dimensional emitter region. This yields the initial SPH particle set covering the entire area of ​​the emitter. S3.4, the initial particle set of SPH based on S3.3, through each particle Initialize state vector ,in, For position coordinates, To initialize as a zero vector, For density, The pressure is then used to obtain the initialized SPH particle system.

[0026] S4. Based on the SPH particle system initialized in S3 and the three-dimensional inflow boundary nonlinear parameter field mapping model in S2, the instantaneous target boundary parameters of the particles are obtained through spatiotemporal dual interpolation analysis. The specific steps of S4 include: S4.1, the SPH particle system initialized based on S3.4 and the three-dimensional inflow boundary nonlinear parameter field mapping model based on S2.6, by entering the SPH time integration step and selecting only particles in the active region for calculation, obtain the active region particle calculation objects that participate in the instantaneous parameter analysis, providing an execution carrier for spatiotemporal dual interpolation; S4.2, based on the active zone particle computational object of S4.1 and the discrete hydrodynamic time series dataset of S1, performs time-dimensional linear interpolation on the hydraulic parameters of discrete nodes and calculates the time weight coefficients. The instantaneous hydraulic parameters of the discrete nodes at the current SPH time are obtained by the following calculation formula: ; in, This is the current moment of the SPH time integration step; , The first , The corresponding time for each time step; The formula for the instantaneous variables of discrete nodes is: ; in, For instantaneous variables of velocity or depth; S4.3, based on the discrete node instantaneous hydraulic parameters at the current SPH time in S4.2 and the cubic spline space interpolation function in S2.4, by performing spatial nonlinear mapping analysis using the instantaneous node values ​​as input control points, the instantaneous target boundary parameters of the active zone particles are obtained, including the flow velocity target parameters. and water depth target parameters .

[0027] S5. Based on the instantaneous target boundary parameters of particles and local riverbed topography of S4, the state of particles in the buffer is determined and synchronized through a bilateral truncation activation function to obtain the three-dimensional running state of the precisely activated particles. The specific steps of S5 include: The SPH particle system, based on the instantaneous target boundary parameters of particles in S4.3 and the initialization in S3.4, determines the local riverbed bottom elevation corresponding to the lateral position of each particle by acquiring the instantaneous position vector of each particle within the active zone. Local instantaneous inflow depth This yields a particle position-terrain-hydraulic parameter matching dataset; S5.2, based on the particle position-terrain-hydraulic parameter matching dataset of S5.1, constructs a bilateral truncated activation function for each active region particle. The validity is determined, and then the particle activation determination result is obtained; In S5.2, the bilaterally truncated activation function is the Heaviside step function, and the formula is: ; in, This is the result of the activation status determination; For the first The three-dimensional position vector of each particle; For the inflow section in the lateral position The elevation function of the riverbed topography at the location; The instantaneous water depth at this location is calculated using nonlinear interpolation. It is the Heaviside step function; For the first The instantaneous free surface elevation of each particle; Bilateral cutoff includes: via Implement lower boundary truncation, and when At that time, the function value is 1 to ensure that the particle is located on the riverbed; pass Implement upper boundary truncation, and when When the function value is 1, it ensures that the particle is below the free surface. This is used to ensure that the particle is considered a valid water flow particle only when it is simultaneously above the local riverbed surface and below the local free surface.

[0028] S5.3 Based on the particle activation state determination result of S5.2, by assigning instantaneous inflow target velocity to effective particles and forcing invalid particles to zero velocity, the particle velocity vector in the active zone is dynamically updated to obtain the precise velocity assignment state of the particles in the active zone, so as to achieve dynamic and precise injection in non-uniform water depth. Specifically, the particle velocity vector within the active region is dynamically updated based on the judgment result. The formula is: ; in, The instantaneous inflow target velocity, and At that time, the particle is given the target inflow velocity; when At that time, the particle velocity is forced to zero in order to achieve dynamic and precise injection of non-uniform water depth on a three-dimensional complex cross-section. S5.4, Based on the particle activation determination result of S5.2, the static pressure initialization formula is used. Dynamically corrected particle pressure, wherein... Particle pressure; For reference density; This refers to the elevation of the riverbed bottom. The instantaneous target water depth; The vertical coordinates of the particle are used to obtain the particle pressure state that matches the free liquid surface. S5.5 Based on the updated three-dimensional state of the active region particles, by synchronizing the particle state in the buffer with the particle state in the active region at the same time, the three-dimensional running state of the particles with precise activation of the entire emitter region is obtained, so as to provide the neighbor kernel function support required for SPH calculation to the active region particles.

[0029] S6. Based on the precise activation of the particle three-dimensional running state of S5, a continuous and stable mass flux closed loop is obtained through particle reset and cyclic injection mechanism. The specific steps of S6 include: S6.1, based on the precisely activated three-dimensional particle running state of S5.5 and the three-dimensional emitter region defined in S3.1, obtains the flow length threshold for particle escape determination by setting the flow length of the emitter region. ; S6.2, based on the flow length threshold and particle three-dimensional running state of S6.1, through the particle set Each particle in the process is examined individually to determine its flow direction and position. The particle escape boundary check results are obtained, which are used to distinguish between escaped particles that have entered the main computational domain and those that have not escaped. S6.3, based on the particle escape boundary check results of S6.2, by satisfying... Particles escaping the condition perform a particle reset operation, where the particle reset operator is defined as follows: And perform a state update, the formula is: ; in, This is the reset state vector; This is the initial state vector for S3.4; The rules for the particle reset operator include resetting the particle position coordinates to the coordinates of the initial generated grid points within the emitter buffer, thus obtaining the spatial position of the escaped particles after reset. S6.4. Based on the spatial position of the escaped particles after S6.3, by resetting the particle velocity, density and pressure to the initial zero state, the initial state of the particles to be activated is obtained, so that the particles wait to enter the active area to receive the next round of state control. S6.5 By continuously stabilizing the number of particles entering the flow and the injection flux, a continuous and stable mass flux closed loop is obtained, thereby realizing the continuous and conserved injection of debris flow mass.

[0030] In one embodiment of the present invention, specifically, a case study of a mudslide impacting a house is simulated: The macroscopic motion characteristics of debris flow were obtained using the SW method. Hydraulic parameters at m=5 discrete nodes with N=10 time steps were extracted at the inflow section of the study area. and Corresponding to the left and right bank boundaries of the river channel, respectively, parameters including flow velocity and water depth were extracted to construct a discrete hydrodynamic time series dataset. : ; in, , , , These are the velocity vector and water depth vector for each node in the first and second time steps, respectively. The time corresponding to each time step, and , This is used to complete the discretization of basic hydrodynamic data.

[0031] Define the inflow boundary of SPH as the domain. ,in for and The distance between particles in the y-direction, for The maximum value in the range is 0.5m. A cubic spline interpolation method is used to... Time nodes The distance is 0.5m and Taking the velocity interpolation between particles with a distance of 1m as an example, according to , and boundary conditions and Based on discrete node data and boundary constraints, substituting the equations into a cubic polynomial function yields the following system of equations: ; ; ; ; Solving for the coefficients , , , This function is used to calculate the lateral position y of each particle. i The velocity at that point, and when y = 0.6m, Similarly, the depth can be calculated to generate a parabolic velocity profile with smooth transition characteristics and conforming to the fluid viscosity distribution law; The discrete hydrodynamic time series dataset is obtained through interpolation. The mapping to a continuous spatiotemporal parameter field is given by the following formula: ; This ensures that every transverse position y at the inflow cross section corresponds to a unique instantaneous velocity. and instantaneous water depth .

[0032] Then, a three-dimensional emitter region is set up upstream of the SPH computational domain. The region is divided along the flow direction into an active region adjacent to the main computational domain and a buffer zone upstream of the active region; the active region consists of a single or multiple layers of particles, and the buffer zone provides computational support; particle sets are generated within the region. For each particle i, initialize the state vector; Integrating step at SPH time For each particle i within the active region, taking velocity as an example, first, linear interpolation along the time dimension is performed. The current SPH time has a time weighting coefficient of... : ; Next, calculate the instantaneous values ​​of the second and third discrete nodes at the current time: ; in, This represents the velocity of the second particle in the first second. This represents the velocity of the second particle at the second second. The velocity of the second particle at 1.5s; Then the instantaneous value node As input control points, their corresponding local boundary condition parameters are analyzed using a nonlinear mapping operator. Taking particles as an example, and in At that time, we obtained: ; .

[0033] For each particle within the active region ,by Taking two particles as an example, one of them is , particles and The position vector is The other is , and The position vector is Determine the local riverbed bottom elevation based on the lateral position of the particles. , and local instantaneous inflow depth , Introducing a bilateral truncation activation function : ; ; Dynamically update the particle velocity vector based on the determination result: ; ; For the active state The particle pressure is dynamically corrected, and the static pressure of the particles is initialized based on an instantaneous local depth of 0.2m. ; in, For reference density, and ; Define the particle reset operator Set the flow length of the transmitter area For sets Each particle in If its flow direction is location This indicates that the particle has entered the main computational domain, triggering a reset operation: Execute This process resets the particle position coordinates to the initial generated grid point coordinates within the emitter buffer, while simultaneously resetting the particle velocity, density, and pressure to their initial zero state. This allows the particles to return to the buffer and await the next round of state control, achieving continuous and stable injection of debris flow mass flux and forming a closed-loop control of the inflow process.

[0034] In summary, by constructing a discrete hydrodynamic time series dataset, establishing a three-dimensional inflow boundary nonlinear parameter field mapping model, analyzing instantaneous target parameters of particles through spatiotemporal dual interpolation, implementing fine control of particle three-dimensional state in the emitter region, and maintaining mass flux through a closed-loop particle reset operator, a precise mapping from macroscopic discrete hydrodynamic data to a microscopic continuous spatiotemporal parameter field of SPH can be achieved. Smooth velocity and depth profiles conforming to fluid viscosity distribution are generated through cubic spline interpolation, accurately analyzing the instantaneous hydraulic parameters of SPH particles at any lateral position and at any time in the inflow section. Simultaneously, dynamic determination and control of particle three-dimensional state are achieved through a bilateral truncation activation function, combined with static pressure correction to ensure consistency between the inflow pressure field and the dynamic free surface. Furthermore, continuous and conserved injection of inflow mass flux is achieved through a particle cyclic reuse reset operator, ensuring the stability and continuity of the inflow boundary in debris flow SPH simulations, and improving simulation accuracy and numerical stability.

[0035] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. The SPH injection boundary method for multi-scale analysis of debris flow dynamic processes, characterized in that, Includes the following steps: S1. Based on the macroscopic simulation of debris flow, the hydraulic time series parameters of discrete nodes at the inflow section are extracted by simulating the shallow water equation SW to obtain a discrete hydrodynamic dataset. S2. Based on the discrete hydrodynamic dataset of S1 and the differences between macro and micro scales, a mapping operator is constructed through nonlinear spatial interpolation to obtain a three-dimensional inflow boundary nonlinear parameter field mapping model. S3. Based on the three-dimensional inflow boundary nonlinear parameter field mapping model of S2, the SPH particle system is initialized by dividing the active region and the buffer zone and generating a particle set. S4. Based on the SPH particle system initialized in S3 and the three-dimensional inflow boundary nonlinear parameter field mapping model in S2, the instantaneous target boundary parameters of the particles are obtained through spatiotemporal dual interpolation analysis. S5. Based on the instantaneous target boundary parameters of particles and local riverbed topography of S4, the state of particles in the buffer is determined and synchronized through a bilateral truncation activation function to obtain the three-dimensional running state of the precisely activated particles. S6, based on the precise activation of the particle's three-dimensional running state in S5, obtains a continuous and stable mass flux closed loop through particle reset and cyclic injection mechanisms.

2. The SPH injection boundary method for multi-scale analysis of debris flow dynamic processes according to claim 1, characterized in that: The specific steps of S1 include: S1.1 Based on the requirement of macroscopic simulation of debris flow, the macroscopic movement process of debris flow on real terrain is simulated by SW model; S1.2 Select an inflow section that matches the location of the SPH transmitter, and deploy discrete monitoring nodes covering the entire boundary from the left bank to the right bank of the river in the transverse direction of the section. S1.3 Extract the flow velocity vector and hydraulic parameters of water depth for each discrete node step by step, and record the simulation time corresponding to each time step simultaneously. S1.4 Integrate the extracted time series parameters and time data to construct a discrete hydrodynamic time series dataset. Complete the preparation of basic data.

3. The SPH injection boundary method for cross-scale analysis of debris flow dynamic processes according to claim 2, characterized in that: Hydraulic parameters of m discrete nodes at the inflow cross-section of the study area within N time steps are extracted to construct a discrete hydrodynamic time series dataset. The formula is: ； in, , And respectively the first The velocity vector and water depth at each node at each time step; The time corresponding to each time step.

4. The SPH injection boundary method for cross-scale analysis of debris flow dynamic processes according to claim 3, characterized in that: The specific steps of S2 include: S2.1, based on the discrete hydrodynamic time series dataset of S1, compares the resolution differences between macroscopic discrete nodes and microscopic SPH particles, defining the SPH inflow boundary as the domain. ,in, for particles and The distance of the particle in the Y direction, For discrete monitoring nodes; for , The maximum value in the range is used to obtain the computational domain for the three-dimensional SPH inflow boundary parameter mapping. S2.2, Based on the inflow boundary domain Based on the fluid viscosity distribution pattern, through the left bank of the cross-section and the right bank Introduce no-slip boundary constraints and set and In order to obtain flow velocity boundary constraints that fit the river channel boundary; S2.

3. Based on the node parameters and no-slip boundary constraints of the discrete hydrodynamic time series dataset, a piecewise cubic polynomial function corresponding to the flow velocity and water depth is constructed. and The spatial interpolation fundamental polynomial of the coefficients to be solved is obtained as follows: ； ； in, is the flow velocity interpolation function at the transverse position y of the cross section; is the water depth interpolation function at the transverse position y of the cross section; , They are respectively and The coefficient of the constant term; , They are respectively and The coefficients of the first-order terms; , They are respectively and The coefficients of the second-order terms; , They are respectively and The coefficients of the third-order terms; S2.

4. Based on the piecewise cubic polynomial function, by solving the polynomial coefficients, ... and The first and second derivatives are continuous at all nodes to obtain a cubic spline space interpolation function with a smooth transition. S2.

5. Based on the resolution difference between macroscopic discrete nodes and microscopic SPH particles, by integrating the cubic spline space interpolation function and the discrete hydrodynamic time series dataset, a mapping operator that can convert discrete data into a continuous spatiotemporal parameter field is obtained: in, and These are continuous functions of velocity and depth, respectively. It is a nonlinear mapping operator used to transform discrete node data into a continuous parameter field; S2.6, based on the mapping operator of S2.5, maps the time-varying hydraulic parameters of discrete nodes to a value covering the entire computational domain. The continuous spatiotemporal function is used to obtain a three-dimensional inflow boundary nonlinear parameter field mapping model that can analyze the hydraulic parameters at any position and time of the inflow section.

5. The SPH injection boundary method for cross-scale analysis of debris flow dynamic processes according to claim 4, characterized in that: The specific steps of S3 include: S3.1, a three-dimensional inflow boundary nonlinear parameter field mapping model based on S2.6, establishes a three-dimensional emitter region upstream of the SPH computational domain for particle generation and inflow control. ; S3.2, Three-dimensional emitter region based on S3.1 The flow is divided into emitter partitions along the debris flow direction, including an active region adjacent to the main computational domain and a buffer zone upstream of the active region. The active region consists of a single or multiple layers of particles, and the buffer zone is used to provide kernel function support for SPH calculations. S3.3, based on the emitter partitioning structure of S3.2, generates a particle set within the three-dimensional emitter region. This yields the initial SPH particle set covering the entire area of ​​the emitter. S3.4, the initial particle set of SPH based on S3.3, through each particle Initialize state vector ,in, For position coordinates, To initialize as a zero vector, For density, The pressure is then used to obtain the initialized SPH particle system.

6. The SPH injection boundary method for cross-scale analysis of debris flow dynamic processes according to claim 5, characterized in that: The specific steps of S4 include: S4.1, the SPH particle system initialized based on S3.4 and the three-dimensional inflow boundary nonlinear parameter field mapping model based on S2.6, by entering the SPH time integration step and selecting only particles in the active region for calculation, the active region particle calculation objects participating in the instantaneous parameter analysis are obtained. S4.2, based on the active zone particle computational object of S4.1 and the discrete hydrodynamic time series dataset of S1, performs time-dimensional linear interpolation on the hydraulic parameters of discrete nodes and calculates the time weight coefficients. The instantaneous hydraulic parameters of the discrete nodes at the current SPH time are obtained by the following calculation formula: ； in, This is the current moment of the SPH time integration step; , The first , The corresponding time for each time step; The formula for the instantaneous variables of discrete nodes is: ； in, For instantaneous variables of velocity or depth; S4.3, based on the discrete node instantaneous hydraulic parameters at the current SPH time in S4.2 and the cubic spline space interpolation function in S2.4, by performing spatial nonlinear mapping analysis using the instantaneous node values ​​as input control points, the instantaneous target boundary parameters of the active zone particles are obtained, including the flow velocity target parameters. and water depth target parameters .

7. The SPH injection boundary method for cross-scale analysis of debris flow dynamic processes according to claim 6, characterized in that: The specific steps of S5 include: The SPH particle system, based on the instantaneous target boundary parameters of particles in S4.3 and the initialization in S3.4, determines the local riverbed bottom elevation corresponding to the lateral position of each particle by acquiring the instantaneous position vector of each particle within the active zone. Local instantaneous inflow depth This yields a particle position-terrain-hydraulic parameter matching dataset; S5.2, based on the particle position-terrain-hydraulic parameter matching dataset of S5.1, constructs a bilateral truncated activation function for each active region particle. The validity is determined, and then the particle activation determination result is obtained; S5.3 Based on the particle activation state determination result of S5.2, by assigning instantaneous inflow target velocity to effective particles and forcing invalid particles to zero velocity, the particle velocity vector in the active zone is dynamically updated to obtain the precise velocity assignment state of the particles in the active zone, so as to achieve dynamic and precise injection in non-uniform water depth. S5.4, Based on the particle activation determination result of S5.2, the static pressure initialization formula is used. Dynamically corrected particle pressure, wherein... Particle pressure; For reference density; This refers to the elevation of the riverbed bottom. The instantaneous target water depth; The vertical coordinates of the particle are used to obtain the particle pressure state that matches the free liquid surface. S5.5 Based on the updated three-dimensional state of the active region particles, by synchronizing the particle state in the buffer with the particle state in the active region at the same time, the three-dimensional running state of the particles with precise activation of the entire emitter region is obtained, so as to provide the neighbor kernel function support required for SPH calculation to the active region particles.

8. The SPH injection boundary method for cross-scale analysis of debris flow dynamic processes according to claim 7, characterized in that: In S5.2, the bilaterally truncated activation function is the Heaviside step function, and the formula is: ； in, This is the result of the activation status determination; For the first The three-dimensional position vector of each particle; For the inflow section in the lateral position Elevation function of riverbed topography at the location; The instantaneous water depth at this location is calculated using nonlinear interpolation. It is the Heaviside step function; For the first The instantaneous free surface elevation of each particle; Bilateral cutoff includes: via Implement lower boundary truncation, and when At that time, the function value is 1 to ensure that the particle is located on the riverbed; pass Implement upper boundary truncation, and when When the function value is 1, it ensures that the particle is below the free surface. This is used to ensure that the particle is considered a valid water flow particle only when it is simultaneously above the local riverbed surface and below the local free surface.

9. The SPH injection boundary method for multi-scale analysis of debris flow dynamic processes according to claim 8, characterized in that: The specific steps of S6 include: S6.1, based on the precisely activated three-dimensional particle running state of S5.5 and the three-dimensional emitter region defined in S3.1, obtains the flow length threshold for particle escape determination by setting the flow length of the emitter region. ; S6.2, based on the flow length threshold and particle three-dimensional running state of S6.1, through the particle set Each particle in the process is examined individually to determine its flow direction and position. The particle escape boundary check results are obtained, which are used to distinguish between escaped particles that have entered the main computational domain and those that have not escaped. S6.3, based on the particle escape boundary check results of S6.2, by satisfying... Particles that escape the condition perform a particle reset operation, resetting the particle position coordinates to the initial generated grid point coordinates within the emitter buffer, thus obtaining the spatial position of the escaped particle after reset. S6.

4. Based on the spatial position of the escaped particles after S6.3, by resetting the particle velocity, density and pressure to the initial zero state, the initial state of the particles to be activated is obtained, so that the particles wait to enter the active area to receive the next round of state control. S6.5 By continuously stabilizing the number of particles entering the flow and the injection flux, a continuous and stable mass flux closed loop is obtained, thereby realizing the continuous and conserved injection of debris flow mass.

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