56 results about "Governing equation" patented technology

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.

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 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 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.

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.

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 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.

This invention relates to the field of tunnel pipe roof deformation calculation technology, and discloses a method and system for predicting tunnel pipe roof deflection based on elastic constraint boundaries. The method includes treating the pipe roof at the tunnel entrance as an equivalent elastic foundation beam with translational and rotational springs at both ends, establishing a longitudinal segmented force model, determining the applied loads and governing equations, and obtaining the deflection values ​​at each node of the pipe roof. The specific mechanism is as follows: by introducing translational and rotational springs at the ends of the pipe roof at the tunnel entrance, this invention can more realistically simulate the actual constraint effect at the pipe roof ends. This invention establishes three types of analysis models: an entrance segment model, a finite-length pipe roof model, and an exit segment model. These models are applicable to the force and deformation analysis at different construction stages, such as when the pipe roof enters the tunnel, when excavation approaches the end of the pipe roof, and when it exits the tunnel. This improves the completeness, computational efficiency, and applicability of the pipe roof deflection prediction method.

This invention provides a numerical simulation method for magnetotellurics under the Lorentz specification. The Maxwell equations are transformed into a set of governing equations consisting only of vector potentials using the Lorentz specification. A two-dimensional Fourier transform is performed on the quadratic vector potential governing equations in the horizontal direction, converting the three-dimensional governing equations into one-dimensional governing equations, reducing computational load and storage requirements, and improving computational efficiency. The Fourier transform can employ the standard Fourier transform algorithm, the offset sampling Fourier transform algorithm, or the non-uniform sampling Fourier transform algorithm. Then, the one-dimensional equations are solved using the one-dimensional finite element method with quadratic interpolation shape functions, resulting in three pentagonal equation sets, which are then solved using the pursuit method. This invention offers fast computation speed and small memory footprint, providing a new method for efficient and high-precision numerical simulation of large-scale magnetotellurics.

This invention provides a method for calculating the horizontal nonlinear response of large-diameter piles in layered foundations considering end resistance, comprising: S1, establishing a calculation model for the horizontal nonlinear response of large-diameter piles in layered foundations considering end resistance; S2, dividing the pile-side soil into several layers along the depth direction, and equating each layer of pile-side soil with a nonlinear horizontal soil spring; S3, simplifying the pile-end soil into an end shear elastoplastic spring describing the shear force-displacement relationship and an end bending elastoplastic spring describing the bending moment-rotation relationship; S4, determining the secant stiffness of the pile-side soil spring at each depth; S5, discretizing the governing equations using the finite difference method; S6, establishing the horizontal load, vertical load, and bending moment constraints at the pile top, as well as the boundary conditions for shear force and bending moment at the pile end; S7, solving for the nonlinear responses such as horizontal displacement, bending moment, and shear force at each node of the pile body using an iterative calculation method. This invention can be used for pile-soil interaction analysis and design optimization of horizontally loaded large-diameter foundations.

This invention discloses a topology control method for pressure-regulated macroscopic heat transfer networks to achieve functional switching. Based on the governing equations of Keller's law, this invention regulates the heat flow transmission path in the macroscopic network by adjusting the pressure, i.e., adjusting the anisotropic thermal conductivity of the background and functional regions of the macroscopic heat transfer network. This enables functions such as thermal stealth and heat accumulation during heat transfer. Furthermore, combining the design concepts of thermal switches and variable thermal resistance, this invention presents a metamaterial model of a macroscopic heat transfer network with continuously adjustable stealth and heat accumulation functions. Through geometric control, different functions can be exhibited under different pressure differences, achieving adjustable heat flow and thermal function switching in the macroscopic heat transfer network. This method has potential applications in fields such as electronic chips, power devices, and wearable electronic devices.

This application discloses a method, equipment, medium, and product for establishing an analysis model of thaw settlement deformation of frozen soil subgrade, relating to the fields of geotechnical engineering and road engineering in cold regions. The method includes establishing a set of governing equations coupled with thermal, water, and mechanical fields, including temperature field governing equations, moisture field governing equations, and mechanical field governing equations; constructing a subgrade geometric model based on the governing equations; configuring initial and boundary conditions for the subgrade geometric model, including Dirichlet temperature boundary conditions for simulating environmental temperature changes and mechanical constraint boundary conditions for limiting displacement; and performing transient solutions on the subgrade geometric model under the constraints of the initial and boundary conditions to obtain evolution data of the subgrade during freeze-thaw cycles. This application fundamentally overcomes the shortcomings of existing technologies, such as simplified models and incomplete mechanism characterization, and significantly improves the prediction accuracy and long-term reliability of the spatiotemporal evolution law of differential settlement of subgrade.

The invention discloses a phase field control equation numerical solution method. The method comprises the following steps: S1, establishing a phase field control equation representing a basic physical process; s2, deducing a weak form of the phase field control equation; s3, dispersing a displacement field and a phase field in the phase field control equation by adopting a shape function to respectively obtain domain weak forms of a displacement field equation and a phase field equation; s4, creating a user phase field model through an interactive interface of the PDE module builder; s5, after vector function discretization is carried out on the displacement field equation and the phase field equation by adopting a PDE module, an associated coefficient field is specified in the module; and S6, solving the numerical model by strictly applying boundary conditions and initialization parameters. According to the numerical solution method for the phase field control equation, through innovative algorithm design, the calculation efficiency and the numerical stability are remarkably improved.

This invention relates to the field of geophysical exploration technology, specifically to a high-precision three-dimensional forward modeling method for airborne electromagnetic spectral elements considering induced polarization effects. Based on the Cole-Cole model, a complex conductivity expression considering induced polarization effects is established, and the frequency domain Helmholtz equation is introduced to construct the corresponding governing equations. A regular hexahedral mesh is generated, and reference domain vector basis functions are constructed using the Gauss-Lobatto-Legendre orthogonal polynomial method according to the spectral element method. The mapping relationship between these functions and physical mesh elements is established. The Galerkin weighted residual method is applied to discretize the governing equations into element system matrices, which are then assembled to form the overall system matrix and the corresponding linear equation set. A direct solver is used to obtain the frequency domain three-dimensional electromagnetic response, and the time domain three-dimensional forward modeling result of the computational region is obtained through Hankel transformation. This invention achieves rapid and high-precision three-dimensional forward modeling simulation of complex geological models containing induced polarization effects.

This invention discloses a method for calculating borehole grouting pressure and stability considering the seepage softening effect, comprising: S1. Parameter acquisition and problem definition; S2. Establishing governing equations considering the seepage effect; S3. Solving for displacement and stress field in the elastic zone; S4. Solving for displacement and stress field in the plastic zone; S5. Determining the borehole inner diameter, plastic radius, and ultimate grouting pressure. This invention, for the first time, fully couples seepage force and soil softening effect in a unified analytical model, more realistically reflecting the complex mechanical mechanism of the grouting process. Starting from basic mechanical principles, the derivation process is rigorous, providing a complete semi-analytical solution from stress to displacement with clear physical meaning. This method can be quickly applied to engineering calculations, parameter sensitivity analysis, and safety assessment. By adjusting parameters, it can flexibly degenerate into a specific case considering only a single effect, facilitating mechanism research and comparative analysis, and demonstrating strong universality.

This application provides a method, apparatus, and electronic device for determining the critical displacement in shale gas fracturing, relating to the field of hydraulic fracturing technology. The method for determining the critical displacement in shale gas fracturing includes: establishing a three-dimensional geomechanical model of the reservoir in the target area; obtaining the governing equations for solid deformation and fluid flow under the three-dimensional geomechanical model of the reservoir based on the principle of pore elastic dynamics; performing numerical simulation of the fracturing process according to the governing equations, with the simulated values ​​including geostress and fluid pressure; obtaining the injection parameters when the fault is activated based on the numerical simulation; and obtaining the critical displacement based on the injection parameters. The implementation method provided in this application improves the accuracy of critical displacement determination and provides guidance for safe construction of shale gas hydraulic fracturing.

This invention discloses a method for environmental assessment in aquaculture, relating to the field of aquaculture environmental monitoring technology. The method includes: acquiring multi-source data and performing time-resolution normalization on the data, wherein the multi-source data includes hydrological data, meteorological data, marine data, and water depth and topographic data; and constructing a three-dimensional hydrodynamic model and a temperature-salinity model of the aquaculture area based on the multi-source data. This invention, by establishing a three-dimensional hydrodynamic model and a temperature-salinity model of the aquaculture area, systematically describes the water movement, heat exchange, and salinity diffusion processes based on a complete set of governing equations and boundary conditions conforming to physical mechanisms. By introducing key parameters such as horizontal and vertical turbulence coefficients, bottom roughness, and surface heat flux, and combining model calibration and verification, the model possesses strong environmental response realism and simulation reliability, effectively reflecting the spatiotemporal variation characteristics of salinity under different external driving conditions.

This invention discloses a numerical analysis method for quantifying differential diffusion in coal / ammonia co-combustion, belonging to the field of numerical simulation technology for coal / ammonia co-combustion. The steps include: establishing gas-solid two-phase governing equations and a general transport equation for the total mixture fraction based on element conservation; defining specific differential diffusion quantification parameters; calculating mass diffusion using a non-unity constant Lewis number; discretizing the model using the PIMPLE algorithm and coupling it with a velocity-pressure field; obtaining combustion characteristic data through CP-DNS solution; and comparing and analyzing the influence of differential diffusion on component distribution and temperature field. This invention solves the problem of incomplete physical process characterization caused by traditional models neglecting differential diffusion, and can systematically quantify the diffusion differences of heavy / light components and their effects on the combustion process, providing a reliable numerical tool for the optimized design of coal / ammonia co-combustion systems.

The invention belongs to the technical field of hydrogen-oxygen combustion mixed emission, and discloses a closed container transient high-temperature pressure hydrogen-oxygen premixed combustion numerical model construction method, which comprises the following steps: establishing a geometric model in simulation software according to the actual structure size of a closed container, and then establishing a transient high-temperature pressure hydrogen-oxygen premixed combustion numerical model on the basis of the constructed physical model. Setting a control equation, a turbulence model, a combustion model, a solver algorithm and initial conditions, finally operating the models to carry out transient calculation, evaluating the mixing uniformity of the hydrogen-oxygen mixed gas by utilizing spatial mixing unevenness SMD, and evaluating the filling accuracy by utilizing a filling quality error. According to the method, by constructing the high-precision numerical model, the mixing and combustion mechanism can be deeply explored, and a theoretical basis and method support are provided for optimization design, DDT inhibition and realization of accurate injection and safe and efficient combustion of oxyhydrogen gas.

This application discloses a method for constructing a numerical model to simulate the combustion of remains using the decomposition of organic matter, relating to the field of computer simulation technology. The method includes obtaining the proportions of biological components and hydrocarbon substitute components input by the user through an interface. These proportions are determined by heterogeneous combustion reaction experiments, thermal decomposition experiments, and oxygen bomb calorimetry experiments of organic matter. The biological components include total moisture, volatile matter, and ash, while hydrocarbon substitutes are used to replace the volatile matter. A cremation model is established based on these proportions. After dividing the cremation model into a grid, the grid area is discretized and combustion simulation is performed using governing equations to obtain the temperature field data corresponding to the cremation model. The numerical model construction method of this application can simulate the combustion process of remains, facilitating subsequent upgrades and optimization designs of crematoriums.

This invention relates to a method and system for constructing an explicit unstructured two-dimensional hydrodynamic model. The method includes constructing an unstructured mesh and identifying wet and dry states based on critical water depths, adapting to complex boundaries; discretizing the governing equations using the finite volume method based on conserved two-dimensional shallow water equations, and simultaneously solving the pressure and velocity terms through an explicit pressure-velocity coupling mechanism to achieve flow field prediction and correction and water depth updates; and combining optimization techniques such as adaptive time stepping and vectorization acceleration to perform time-iterative calculations and output visualized results. Its advantages include: effectively suppressing numerical oscillations under explicit in-situ meshes without requiring implicit or iterative algorithms, thus improving simulation accuracy and stability; improving computational efficiency through algorithm optimization, supporting large-scale mesh simulations; and adapting to complex boundaries such as estuaries and coastlines, providing a scientific basis for integrated estuarine and coastal management and intertidal ecological protection and restoration.

This invention relates to the field of geophysical exploration technology, specifically to a well-to-surface electromagnetic forward modeling method, apparatus, and storage medium. The method includes: S1, modeling based on an octree mesh; S2, constructing vector Nédélec basis functions on the elements based on Gauss integration points and Gauss-Legendre-Lobatto (GLL) integration points set in the elements; S3, deriving the governing equations of the well-to-surface electromagnetic finite element method starting from Maxwell's equations; S4, constructing block diagonal preconditions and solving using an iterative method; S5, after exiting the iteration, calculating the electromagnetic response using the iterative model. This invention significantly reduces the number of elements in the mesh while maintaining model accuracy, thereby reducing computational costs. Higher-order shape functions are constructed and used in the forward modeling calculation to improve the accuracy of the numerical solution.