85 results about "Governing equation" patented technology

The present invention relates to the technical field of heat sink structure design, and in particular to a micro-channel heat sink structure design method based on a multi-objective function. The method comprises the following specific steps: S1, constructing a general mathematical description of a topology optimization problem; S2, acquiring input conditions for a specific design scenario, and dividing a topology optimization design domain; S3, establishing a governing equation for a topology optimization model; S4, on the basis of an adjoint method, performing sensitivity analysis of a multi-objective function with respect to design variables; S5, solving the topology optimization model by means of a method of moving asymptotes (MMA); S6, obtaining a two-dimensional flow channel configuration of a heat sink on the basis of contour reconstruction, carrying out finite element analysis of a two-dimensional flow channel structure, and narrowing down the selection range of constraint conditions; and S7, on the basis of a two-dimensional finite element analysis result, constructing a corresponding pseudo-three-dimensional model, carrying out finite element analysis, and determining optimal constraint conditions to obtain a final topology-optimized heat sink configuration. Compared with traditional methods, the present invention can more efficiently solve the problem in respect of heat sink structure optimization under different scenarios.

The invention provides a method and equipment for predicting the heat exchange performance of a buried pipe ground source heat pump thermal camouflage system. The method comprises the steps that S1, a multi-physics field coupling heat exchange mathematical model of a buried pipe heat exchange system is established; s2, based on the multi-physics field coupling heat exchange mathematical model, a control equation and boundary conditions are constructed; s3, on the basis of the control equation and the boundary conditions, a multi-physics field numerical model is constructed, and simulation and calibration are carried out; and S4, based on the calibrated numerical model, designing a simulation test and carrying out main control factor analysis to obtain a prediction effect of the heat exchange performance. By establishing a rock-soil body-fluid multi-physical field coupling model, the interaction mechanism of underground heat conduction, working medium flow and ground surface heat radiation is completely represented, and the hiding efficiency of the thermal camouflage system is remarkably improved.

The invention discloses a simulation method, device and equipment for predicting flow and deformation of a porous medium and the medium. The method comprises the steps that a computational domain is selected, a corresponding computational grid is generated, and porosity initialization is conducted on the computational domain; determining a time step length and a discrete format, and setting a non-uniform factor to solve a control equation set which comprises a continuity equation, a fluid dynamics equation, a skeleton mechanics equation and a porosity updating equation; and analyzing and displaying a solving result. According to the porous medium flow and deformation simulation method independent of hypothesis and empirical parameters, the method is based on the basic principle of the microcosmic fluid-solid coupling effect, a porous medium fluid-solid coupling body kinetic equation is adopted, the situation that a traditional modeling method depends on volume averaging hypothesis and depends on a multi-phase interaction model is avoided, and the modeling efficiency is improved. The method has cross-scale applicability, and provides a new theoretical basis and prediction means for the development of technologies related to porous medium multiphase dynamics and multi-field coupling problems.

The invention discloses a storm surge artificial intelligence forecasting method based on physical equation constraints, and relates to the technical field of artificial intelligence storm surge forecasting. Comprising the following steps: step 1, collecting multi-source data; step 2, assimilating and preprocessing the data; step 3, realizing a machine learning calculation method of physical loss; step 4, constructing a physical and data co-constrained artificial intelligence model; 5, performing hyper-parameter adjustment by using a random search algorithm, and further optimizing the model; and step 6, carrying out interpretability analysis on the forecasting process and result. According to the invention, three control equations for storm surge calculation are introduced into the machine learning model, so that the dependence on the training data volume is greatly reduced compared with a traditional data-driven intelligent forecasting model; and analyzing the change trend of the physical variables in the forecasting process, carrying out visual display and uncertainty analysis, and solving the problem of uninterpretability of an artificial intelligence forecasting model.

The invention provides a frequency dispersion curve calculation method based on a decoupling type Legendre-Gauss-Labatto spectral element method, and belongs to the technical field of discrete solution of guided wave propagation in a thin plate, and the method comprises the following steps: S1, constructing a wave equation which comprises a Cartesian space coordinate system based on an orthotropic plate, and combining a constitutive equation, a geometrical relationship under the coordinate system and guided wave displacement to obtain a wave dispersion curve; substituting into a control equation when the volume force is zero to obtain an improved three-dimensional elastic wave equation; s2, a differential matrix is constructed, wherein discretization and decoupling are carried out on a wave equation on the basis of a Lagrange interpolation basis function of a Legendre-Gauss-Labatto node; s3, explicitly embedding the stress free boundary condition into the solving process through matrix line transformation, and solving to obtain a frequency dispersion curve, the derivation process is simplified, the boundary and the interior of the material are decoupled, and the physical significance is clearer. And meanwhile, the high-precision advantage of the spectrum method is maintained, and the calculation rate is remarkably improved.

The invention discloses a cooperative regulation and control method for seepage and heat transfer in a heterogeneous medium, and relates to the technical field of heterogeneous media, and the method comprises the following steps: S1, through a logging technology, a seismic exploration technology and a drilling sampling experiment, obtaining spatial distribution parameters of a target heterogeneous medium, constructing a heterogeneous parameter field, and obtaining a heterogeneous parameter field; the spatial distribution parameters comprise permeability distribution data, heat conductivity coefficient distribution data and medium deformation data; and S2, based on the permeability distribution data, the heat conductivity coefficient distribution data and the medium deformation data, establishing a seepage, heat transfer and medium deformation three-field coupling model. Three fields of seepage, heat transfer and medium deformation are coupled and incorporated into a regulation and control system, a mathematical model containing seepage and heat transfer control equations is established, the multi-field interaction process is accurately simulated, the limitation of isolated regulation and control of a traditional method is avoided, and a quantitative theoretical basis is provided for coordinated regulation and control.

The invention discloses a non-coal measure stratum natural gas displacement mathematical model construction method. The method comprises the following steps that gas migration equations are established, wherein the gas migration equations comprise the step of establishing a rock mass pore gas diffusion motion control equation and the step of establishing a stratum fracture gas seepage equation; establishing a stratum rock mass deformation control equation; establishing a dynamic porosity and permeability change control equation: establishing a rock mass porosity dynamic change equation, establishing a stratum fracture rate dynamic change equation and establishing a permeability dynamic change equation; and establishing a non-coal measure stratum natural gas displacement mathematical model based on the above steps. The non-coal measure stratum natural gas displacement mathematical model is established by combining the non-coal measure stratum natural gas displacement characteristics, and a scheme which is good in treatment effect, low in cost and high in efficiency is provided for non-coal measure stratum natural gas emission.

The phase structure evolution phase field analysis method in the annealing and crystallization process of the amorphous hafnium oxide-based ferroelectric film comprises the following steps: S1, setting a sequence parameter xi according to the evolution process from an amorphous phase to a crystal phase in the annealing process, and setting a sequence parameter eta according to the process of the crystal phase and the crystal phase; s2, a phase field theoretical model is established, the total free energy is the sum of the free energy of the sequence parameter xi and the free energy of the sequence parameter eta, and the free density in the free energy of the sequence parameter eta is obtained through coupling of the sequence parameter xi and the sequence parameter eta; s3, deducing a weak form of the control equation; and S4, compiling the weak form equation into COMSOL finite element software, solving and analyzing the phase structure in the annealing crystallization process of the thin film. According to the method, the sequence parameter xi representing the transformation process from the amorphous phase to the crystalline phase is introduced and coupled with the sequence parameter eta to construct a new free energy equation and a new control equation, the weak form of the control equation is deduced, and the phase structure and the evolution rule of the hafnium oxide-based ferroelectric film at different annealing moments can be dynamically reproduced.

A method for calculating the in-plane nonlinear deformation of an arch structure with axial defects in a Cartesian coordinate system is presented. This method is based on two states of the arch structure's curve element in the Cartesian coordinate system: an ideal axis and an actual axial defect. It derives the changes in the arc length and curvature of the curve element before and after deformation, obtaining expressions for the nonlinear compressive and bending strains in the in-plane of the arch structure with axial defects in the Cartesian coordinate system. The method also derives the nonlinear equilibrium differential equations in the in-plane of the arch structure with axial defects in the Cartesian coordinate system, obtaining solutions that satisfy the mechanical and geometric boundaries of the arch structure with axial defects. Finally, the method derives the nonlinear equilibrium governing equations in the in-plane of the arch structure with axial defects, ultimately obtaining the solution to the nonlinear mechanical problem in the in-plane of the arch structure with axial defects in the Cartesian coordinate system. This method can obtain the essence of the nonlinear mechanical problem of the arch structure with axial defects in the Cartesian coordinate system, filling the gap in the nonlinear strain-displacement expression for the in-plane of the arch structure with axial defects in the Cartesian coordinate system.

This invention discloses a method for calculating the deformation of adjacent pile foundations considering the spatial effect of foundation pit excavation. The method comprises the following steps: First, determining the spatial distribution curve of the lateral deformation of the retaining wall; second, determining the free displacement field of the soil outside the pit induced by the spatial deformation of the foundation pit; and finally, determining the governing equations for the deformation of adjacent pile foundations using the Pasternak foundation and Euler-Bernoulli beam models. This invention takes into account the significant spatial effect of the surrounding soil deformation at different spatial locations of the pile foundation. When the pile foundation is near the center of the foundation pit, the surrounding soil deformation is often large. Therefore, considering the spatial shape of the soil deformation and the spatial distribution of the pile foundation can better reproduce the actual situation of foundation pit excavation and the response of the pile foundation.

This invention belongs to the field of artificial intelligence and system response calculation technology, and provides a method and system for calculating system response based on a generalizable physical information neural network. The technical solution involves establishing a family of differential equations consisting of multiple governing equations based on the physical characteristics of the system to be analyzed, and obtaining the corresponding dataset; constructing a neural network model consisting of a main network and multiple channel networks, where the main network learns the basis functions representing the system response and shares them with all channel networks; each channel network processes a specific differential equation task within the task family and learns the basis function coefficients corresponding to that task; inputting the dataset into the neural network model, training the model by minimizing a loss function containing multiple constraints, and obtaining the optimal solution for the system response under different stimuli based on the trained model. This method can solve complex differential equations more accurately and improve the model's generalization performance on unseen tasks.

This invention discloses a chemical nonequilibrium partitioning method based on local Damcole numbers, comprising: S1. Selecting a characteristic length according to the flow field characteristics; S2. Calculating the chemical reaction rate; S3. Calculating the equilibrium components of each component under isochoric and adiabatic reaction conditions using the local thermodynamic physical density and static enthalpy of the flow field; S4. Establishing a local Damcole number that quantifies the relative size of chemical reactions and flow scales; S5. Quantifying the degree of chemical nonequilibrium at different locations in the flow field based on the local Damcole number, thereby establishing a partitioning criterion to divide the flow field into equilibrium, freezing, and nonequilibrium regions; S6. Obtaining a unified dimensionless governing equation system that includes the degree of chemical nonequilibrium based on the local Damcole number.

This disclosure relates generally to high resolution simulation prediction for Computational Fluid Dynamics (CFD). CFD plays a crucial role in comprehending intricate physical phenomena spanning across scientific and engineering domains, hence it is essential to conduct simulations at high mesh resolutions for the governing equation of fluid flow. The current state-of-the-art super-resolution techniques involve reconstructing high-resolution data from down sampled low-resolution is limited to single scenario and does not accurately reflect real-world scenarios. The disclosed techniques enable prediction of fine-resolution data from low-resolution inputs from a variety of real-world CFD scenarios. Further the disclosed technique also identifies the most relevant network architecture for any CFD scenario and enabling accurate prediction of high-resolution data from low-resolution inputs by training the network architecture. Furthermore, the disclosure ensures also the robustness of the disclosed system through uncertainty analysis, encompassing both aleatoric and epistemic uncertainty analyses.

This invention provides a method and device for predicting temperature changes in electronic components based on pentahedral elements. The method includes: meshing the electronic component into pentahedral elements based on its structural parameters; determining the three-dimensional transient heat conduction governing equation and initial algebraic equation for the target region; determining correction terms based on the virtual node domain defined for the pentahedral elements, the Galerkin weight function, the three-dimensional transient heat conduction governing equation, and the initial algebraic equation; correcting the initial algebraic equation based on the correction terms to obtain the target algebraic equation; determining the final algebraic equation based on the target algebraic equation and a preset time interval; solving the final algebraic equation to obtain the transient heat conduction temperature simulation result; adjusting design parameters based on the transient heat conduction temperature simulation result; and implementing optimized design of the electronic component based on the adjusted design parameters.

The invention relates to the technical field of computational fluid mechanics, and discloses a transonic flow numerical simulation method, system and device and a medium, and the method comprises the steps: judging whether a flow field has an area of which the Mach number is greater than a preset value or not; if not, indicating that the whole flow field is a subsonic velocity region and belongs to a shock-wave-free region; if yes, determining that a supersonic speed region exists; judging whether shock waves exist between adjacent grid points or unstructured grid units or not, and if so, dividing a shock wave region and a shock-wave-free region; for the shock wave region, discretizing a space item of the control equation by adopting a TVD format to obtain a TVD format discretization result of the shock wave region; for the shock-wave-free region, discretizing a space item of the control equation by adopting a linear numerical format to obtain a linear format discretization result of the shock-wave-free region; updating the flow field by adopting a time marching method; and if the residual error converges, outputting a simulation result of the transonic flow numerical value. According to the invention, efficient, high-precision and robust transonic flow simulation can be realized.

This invention discloses a PINN flow field modeling method based on wall vortex-triggered sampling, belonging to the field of numerical modeling in fluid mechanics. The method includes the following steps: constructing the flow field solution domain, governing equations, and boundary conditions; establishing a physical information neural network with spatial and temporal coordinates as inputs and velocity and pressure fields as outputs; constructing wall vortex structure quantities based on the wall tangential velocity gradient and local positive Q-vortex structure intensity; converting the wall vortex structure quantities into sampling activation factors using a trigger gate function, and performing adaptive densification sampling in highly sensitive regions using physical residuals; jointly training the network using boundary condition loss, initial condition loss, and equation residual loss; and outputting flow parameters such as velocity, pressure, and wall shear stress. This invention addresses the problem of insufficient prediction accuracy of traditional PINN in the boundary layer, separation region, and wake region, improving the stability and sample utilization efficiency of complex wall flow modeling.

This invention discloses an efficient transient analysis method for electromagnetic-thermal-fluid multiphysics fields on integrated chips. Focusing on electromagnetic, thermal, and fluid fields as core research objects, and centering on typical scenarios of full electromagnetic-thermal-fluid coupling, it systematically integrates the governing equations, boundary conditions, and constitutive relations of each physical field to construct a unified set of coupled partial differential equations. Under the premise of verifying and satisfying the stability conditions of all physical field discretization schemes, simultaneous numerical solutions for the multiphysics fields are achieved through FDTD. This invention, through multi-faceted synergistic optimization, achieves comprehensive adaptation to complex structures, providing reliable technical support for solving various complex engineering multiphysics coupling problems.

The invention discloses a method for calculating the inherent frequency of a porous two-dimensional functionally graded material framework, and belongs to the technical field of structural design, the framework is simplified into a beam model with two clamped ends, a motion control equation of a porous two-dimensional functionally graded material beam in a humid and hot environment is deduced through a Hamilton principle based on a Timoshenko beam theory, and the inherent frequency of the porous two-dimensional functionally graded material beam is calculated. Simplifying the equation by using a variable separation method; the inherent frequency of the beam is solved by adopting a differential quadrature method; a motion control equation is discretized by utilizing a differential quadrature method discretization principle, then the equation is converted into a matrix form, the problem of solving the motion equation is converted into the problem of solving a matrix eigenvalue by adopting a matrix transformation method, and finally solving is carried out by writing a corresponding program. The corresponding solving program is clear in logic and high in uniformity, the calculation efficiency and precision are greatly improved, and a theoretical reference can be provided for the design of the functional gradient skeleton in the later period.

This invention discloses a method and system for calculating the lateral displacement of an adjacent tunnel caused by bottom heave during foundation pit excavation. The method first calculates the lateral displacement of the soil at any depth at the retaining structure caused by the unloading of the bottom heave, and then, based on the deformation coordination between the soil and the retaining structure, converts it into an equivalent displacement S of the retaining structure. z (z); then, based on the displacement S of the enclosure structure z (z) and the maximum displacement value S reached in the active state a The ratio η is used to obtain the cohesion utilization value, and from this, the non-limit active earth pressure p is obtained based on the theory of non-limit active earth pressure. a Thus, the horizontal unloading stress p1 is obtained, and finally, the additional horizontal stress σ in the tunnel direction is obtained. y Ultimately, the additional horizontal stress σ in the tunnel is... y The load P(x) is obtained, and the governing equation for the tunnel's lateral displacement ω(x) is derived based on the coordination between soil and tunnel displacement. This equation is then expressed in matrix form to calculate the tunnel's lateral displacement ω(x). This calculation method allows for a more accurate assessment of the impact of foundation pit construction on the tunnel structure in practice, providing guidance for foundation pit design and construction.

This invention discloses a numerical calculation method and system for the interaction between a hydrogen-ammonia blended combustion flame and the wall, belonging to the field of energy and combustion engineering. Addressing the problem that existing models struggle to simultaneously capture differential diffusion effects and wall heat loss, this invention achieves this through the following steps: Solving the governing equations including wall boundary conditions based on direct numerical simulation (DNS) to generate a high-precision dataset; constructing a small flame database containing one-dimensional free-propagating flames (FPP) and head-on quenched flames (HOQ), embedding the wall heat loss effect; mapping the database to a three-dimensional parameter space of mixing fraction, reaction process variables, and normalized enthalpy to form a small flame lookup table; solving the governing parameter equations and outputting the field variables from the lookup table; and verifying the model accuracy by comparing with DNS data. This method significantly improves near-wall flame quenching and NO reduction. x The accuracy of predictions for key processes such as generation provides technical support for the optimized design of hydrogen-ammonia burners.

This invention discloses a method and apparatus for constructing an equivalent conduit flow model for solute transport in intersecting fractured groundwater, belonging to the field of groundwater pollution prevention and risk management technology. The method for constructing the equivalent conduit flow model includes: selecting relevant characteristic variables related to the spatiotemporal evolution of groundwater solutes; determining a conceptual model for groundwater solute migration in intersecting fractures under typical conditions; selecting relevant characteristic variables for the spatiotemporal evolution of groundwater solute transport; obtaining the mathematical governing equations for groundwater solute transport; obtaining a numerical simulation system for the spatiotemporal evolution of groundwater solute transport; obtaining a quantitative model of equivalent dispersion of groundwater solute transport in fractured fractures, as well as corresponding quantitative models of equivalent permeability and equivalent circular pipe seepage cross-sections, thereby establishing an equivalent conduit flow model for groundwater solute transport. This invention can provide strong support for rapid prediction, early warning, and effective risk management of groundwater pollution in large-scale complex media.

This simulation device updates a governing equation and performs a simulation. The simulation device comprises a processor and a memory that stores a program to be executed by the processor. The processor acquires an event flag that stores events included in a target to be analyzed by the governing equation. The processor generates data in which coefficients of respective terms of the governing equation are stored, for each event stored in the event flag. The processor updates the coefficients of respective terms of the governing equation to coefficients of the corresponding event in the data, on the basis of the event that is a target of the simulation based on the governing equation.

The present invention relates to a method for topological optimization design of a dual-fluid heat exchanger structure based on a multi-material model, comprising: defining a topological optimization design domain and design variables of the heat exchanger including the flow areas of the hot and cold fluids; establishing an objective function and setting constraints, with the optimization objectives of maximizing the heat transfer within the design domain and minimizing the inlet and outlet pressure drops, and constructing a topological optimization model; solving the governing equations for the flow problems of the cold and hot fluids respectively, solving the corresponding topological optimization models, and obtaining the corresponding velocity fields; solving the heat transfer problem using the heat conduction equation based on the combined velocity field obtained by superimposing the two velocity fields; performing a sensitivity analysis based on the solution to the heat transfer problem, and updating the design variables using a topological optimization algorithm based on the results of the sensitivity analysis; and iterating and updating the design variables multiple times until the objective function converges and meets the predetermined design requirements. The present invention efficiently solves the problem of heat exchanger structure optimization in different scenarios.

The invention discloses a high-pressure thin-walled tube heat exchange and thermal stress adjustment method for an energy storage system, and relates to the technical field related to underground energy storage, and the method comprises the following steps: constructing a heat-fluid-solid coupling mathematical model based on the working parameters of a high-pressure thin-walled tube of a compressed gas energy storage system, and calculating the heat-fluid-solid coupling mathematical model by solving a fluid and solid domain control equation; calculating a stress distribution nephogram of the thin-walled tube under stable and transient working conditions, and identifying a maximum stress concentration area; according to the maximum stress concentration area, functionally graded material design is conducted on the thin-walled pipe, so that the physical property of the material changes in a gradient mode in the pipe wall thickness direction or the pipeline axial direction; a distributed phase-change heat exchange device is arranged in a maximum stress concentration area, temperature and stress data monitored in real time are combined, the flow and temperature of a temperature adjusting medium are controlled according to a preset stress threshold value, and active adjustment of thermal stress is achieved. The invention provides a closed-loop logic of stress monitoring, feedback control, local temperature regulation and stress counteracting, and dynamic management of thermal stress is realized.

This invention belongs to the field of aero-engine cooling design and flow heat transfer optimization technology. It provides a method, system, configuration, and blade for constructing turbine blade cooling fringe based on level set topology optimization. The method includes: constructing a fluid-structure interaction (FSI) computational model encompassing the fluid domain of the cooling channel and the solid domain of the blade wall; defining a level set function to implicitly represent the two-phase region; establishing a unified set of governing equations covering the entire computational domain based on this function; introducing a velocity suppression mechanism in the solid domain to perform single-domain coupling solution of fluid flow and solid heat conduction; constructing an optimization model based on the physical field solution, with cooling performance as the objective function and fringe volume fraction as the constraint; calculating the sensitivity of the objective function to the level set function; using this sensitivity to drive the level set function update to evolve the fringe boundary; iterating until convergence to output the final fringe geometry. This invention does not require pre-setting the fringe type and can automatically generate irregular fringe structures with high heat transfer efficiency and low flow resistance.

This invention discloses a method and processor for predicting overpressure in a square confined space flammable gas explosion, relating to the field of flammable gas explosion overpressure prediction technology. The method includes: first, assuming relevant parameters during the explosion process in a square confined space; establishing a simplified physical model based on the flame development characteristics of flammable gas explosions in experiments; then, deriving a mathematical model for predicting explosion pressure based on the simplified physical model and the governing equations; finally, substituting the actual initial parameters from engineering predictions into the mathematical model for calculating explosion pressure, thus obtaining the predicted values ​​of overpressure at different stages of the explosion in the square confined space. The explosion overpressure prediction model established by this invention using a segmented method shows high agreement with experimental results; it can quickly predict the overpressure in a square confined space explosion, providing a reliable reference for assessing the hazard effects and consequences of flammable gas explosions.

This invention discloses a method and system for simulating ground fissures under pre-existing fracture geological conditions using a coupled FEM-PD model, relating to the field of numerical simulation technology for ground subsidence and ground fissures. The method includes the following steps: constructing a finite element-peripheral dynamics model and initializing its parameters; statically dividing the geological computational domain into a finite element region, a periphery dynamics region, and a coupling transition region; applying pore water pressure changes as an external load to the finite element region; obtaining the global displacement field and stress field by solving the finite element governing equations; applying the global displacement field as a displacement boundary condition unidirectionally to the boundary of the periphery dynamics region; simulating the motion process of material points using an adaptive dynamic relaxation method; and calculating local damage by using the Mohr-Coulomb failure criterion to determine the bond fracture between two material points. This invention innovatively couples the finite element model with the periphery dynamics model, accurately simulating both regional continuity and local discontinuity deformation targets.

This invention relates to a time-domain calculation method for the dynamic response of suspended tunnels under multi-load coupling, belonging to the field of dynamic response analysis of suspended tunnels. Addressing the problems of poor versatility and difficulty in handling multi-load coupling and structural variations caused by inconsistent governing equations in traditional methods, this invention proposes establishing a unified equation of motion for the tunnel body. This equation is decomposed into a system of generalized coordinate ordinary differential equations using the modal superposition method. An implicit Newmark-β method is employed for solving the equations, and a sub-loop iteration mechanism is embedded to achieve dynamic coupling between loads and tunnel motion. By independently modeling anchor cable constraint reactions and using a modular environmental load interface, the method is compatible with complex terrain and various load coupling effects. This invention improves the versatility and computational efficiency of dynamic response analysis of suspended tunnels, solves the accuracy and stability challenges under multi-load interaction, and provides a reliable basis for engineering design.

The invention discloses a subsurface erosion simulation numerical method based on a semi-implicit two-phase substance point method, and relates to the technical field of geotechnical engineering numerical simulation, and the method comprises the following steps: generalizing unsaturated easily subsurface-eroded accumulated soil into a two-phase multi-component medium based on a mixture theory; establishing a solid-liquid double-phase double-layer grid system; establishing a core control equation of seepage subsurface erosion in the soil body; transferring the material point information of the solid phase and the liquid phase to corresponding background grid nodes in the double-layer grid system; applying a boundary condition on a background grid of the double-layer grid system, and carrying out semi-implicit solution on the core control equation; mapping the obtained node speed to a substance point; judging whether the relative velocity of the solid phase and the liquid phase exceeds a seepage velocity threshold value or not; state variable information carried by the two-phase substance points is updated; correcting permeability and saturation; and judging and calculating whether the specified time is up or whether the soil body reaches the yield limit. The method provided by the invention has important theoretical and engineering practical values for solving the difficulty in simulating the subsurface erosion disaster of the accumulated soil.

This invention provides a method for predicting landslide surge wave height based on the Transformer-PINN model, comprising the following steps: S1, data acquisition and preprocessing; S2, Transformer-PINN model construction and configuration; S3, loss function definition and training; S4, model inference and prediction. This invention addresses the problem of pure data-driven model predictions violating physical laws. By introducing physical governing equations as constraints into the model, it ensures the physical consistency of the prediction results, improves the model's generalization ability and robustness in data-scarce or unknown scenarios, enabling it to adapt to different boundary conditions and landslide parameters. Leveraging the advantages of the Transformer architecture, it effectively captures the long-range spatiotemporal dependence characteristics of landslide surge generation and propagation, improving prediction accuracy. It provides a hybrid modeling framework that is faster than traditional numerical simulations and more reliable than pure deep learning models, providing technical support for achieving real-time or near-real-time prediction of landslide surges.