An underwater explosion fluid numerical simulation method, device, equipment, medium and product

Abstract

The application discloses a kind of underwater explosion fluid numerical simulation method, device, equipment, medium and product, it is related to fluid mechanics numerical simulation technical field.The method comprises: the preset underwater explosion calculation region is divided into grid, and based on the given underwater explosion simulation working condition, the fluid physical parameter of the flow field in grid is initialized;High-order space reconstruction is carried out to fluid physical parameter using finite volume ALW-MR-WENO method;Based on UPP positive limit, the modified reconstruction polynomial is constructed according to initial reconstruction polynomial;Based on the numerical flux of the reconstruction polynomial after modification, time advancing is solved until the time step reaches the set explosion simulation termination time, and the real-time evolution data of underwater explosion flow field is obtained.The application can efficiently improve the accuracy and robustness of underwater explosion fluid numerical simulation, to solve the problem of calculation interruption caused by negative density or negative pressure that easily occurs when simulating underwater near-field explosion.

Description

Technical Field

[0001] This application relates to the field of numerical simulation technology in fluid mechanics, and in particular to a method, apparatus, equipment, medium, and product for numerical simulation of underwater explosion fluids. Background Technology

[0002] Underwater explosions involve complex hydrodynamic processes, including the propagation of strong shock waves, bubble pulsation, and accompanying jet phenomena. Numerical simulations of underwater explosions typically require solving the compressible Euler equations. Because the shock waves generated by the explosion have extremely high pressure gradients, and low-pressure, low-density regions that approach vacuum may appear during bubble expansion, this places extremely high demands on the robustness of numerical algorithms.

[0003] Current high-precision numerical simulation methods (such as the traditional WENO (Weighted Essentially Non-Oscillatory) scheme) often face the following challenges when dealing with extreme problems such as underwater explosions: The problem of non-positive physical quantities: Traditional high-order schemes cannot guarantee that density and pressure will always be positive during the calculation. Once negative values ​​appear, the equation of state will fail, leading to calculation crashes.

[0004] Computational efficiency and stability: In order to maintain stability, traditional positive-preservation methods often need to limit the CFL (Courant-Friedrichs-Lewy) number, resulting in low computational efficiency.

[0005] Adaptability to complex meshes: When dealing with complex underwater explosion geometry boundaries, higher-order reconstructions in control volume elements often face the problem of negative or non-existent linear weights.

[0006] Therefore, there is an urgent need for a numerical simulation algorithm that can balance high accuracy, high robustness, and adaptability to complex underwater environments, in order to solve the problem of computational interruption caused by negative density or negative pressure when traditional simulation methods simulate near-field underwater explosions. Summary of the Invention

[0007] The purpose of this application is to provide a method, apparatus, equipment, medium, and product for numerical simulation of underwater explosive fluids, which can effectively improve the accuracy and robustness of numerical simulation of underwater explosive fluids, and address the calculation interruption problem caused by negative density or negative pressure that is prone to occur when simulating underwater near-field explosions.

[0008] To achieve the above objectives, this application provides the following solution: Firstly, this application provides a numerical simulation method for underwater explosion fluids, including: The preset underwater explosion calculation region is divided into grids, and the fluid physical parameters of the calculation flow field within the grid are initialized based on the given underwater explosion simulation conditions; the fluid physical parameters include: fluid density, fluid mass, and fluid energy; The finite volume ALW-MR-WENO method is used to reconstruct the fluid physical parameters in a higher-order space to obtain the initial reconstruction polynomial. Based on the UPP positive limiter, a modified reconstructed polynomial is constructed according to the initial reconstructed polynomial; The numerical flux of the underwater explosion flow field is calculated based on the modified reconstructed polynomial computation grid boundary and time-progressed solution is performed until the time step reaches the set explosion simulation termination time to obtain real-time evolution data. The real-time evolution data is used to subsequently assess the dynamic response and damage level of offshore facility structures under explosion loads.

[0009] Secondly, this application provides an underwater explosion fluid numerical simulation device, comprising: The mesh generation and parameter initialization module is used to generate a mesh for the preset underwater explosion calculation region and initialize the fluid physical parameters of the calculation flow field within the mesh based on the given underwater explosion simulation conditions. The fluid physical parameters include fluid density, fluid mass, and fluid energy. The spatial reconstruction module is used to perform high-order spatial reconstruction of fluid physical parameters using the finite volume ALW-MR-WENO method to obtain the initial reconstruction polynomial. The correction module is used to construct a corrected reconstructed polynomial based on the initial reconstructed polynomial using the UPP correction limiter. The solver module is used to calculate the numerical flux of the grid boundary based on the corrected reconstructed polynomial and perform time-progression solving until the time step reaches the set explosion simulation termination time to obtain real-time evolution data of the underwater explosion flow field; the real-time evolution data is used to subsequently assess the dynamic response and damage level of offshore facility structures under explosion loads.

[0010] Thirdly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described underwater explosion fluid numerical simulation method.

[0011] Fourthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described underwater explosion fluid numerical simulation method.

[0012] Fifthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the above-described underwater explosion fluid numerical simulation method.

[0013] According to the specific embodiments provided in this application, the following technical effects are disclosed: This application provides a method, apparatus, equipment, medium, and product for numerical simulation of underwater explosion fluids. It involves meshing a pre-defined underwater explosion computational domain and initializing the fluid physical parameters of the computational flow field within the mesh based on given underwater explosion simulation conditions. The finite volume ALW-MR-WENO method is used to reconstruct the fluid physical parameters in a high-order spatial manner, capturing strong shock waves while accurately simulating the fine structure of bubble pulsations. A corrected reconstruction polynomial is constructed based on the initial reconstruction polynomial using a UPP (Ultra-Pure Pressure) correction limiter. The numerical flux at the mesh boundary is calculated based on the corrected reconstruction polynomial, and a time-progressed solution is performed until the time step reaches the set explosion simulation termination time, obtaining real-time evolution data of the underwater explosion flow field. By introducing the UPP correction limiter, this application can handle near-vacuum conditions in underwater explosions, avoiding computational crashes caused by negative values ​​of physical quantities in traditional methods, thus improving robustness. Therefore, this application can efficiently improve the accuracy and robustness of underwater explosion fluid numerical simulation, addressing the computational interruption problem caused by negative density or negative pressure that easily occurs when simulating near-field underwater explosions. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 A flowchart of a numerical simulation method for underwater explosion fluids; Figure 2 A flowchart illustrating the design of an underwater explosion numerical simulation method for practical applications; Figure 3 A schematic diagram of the density distribution of the underwater explosion flow field; Figure 4 This is a schematic diagram of the velocity distribution in the underwater explosion flow field. Figure 5 This is a schematic diagram of the pressure distribution in the underwater explosion flow field. Figure 6 Spatiotemporal point diagram of the UPP positive limiter triggered by the underwater explosion flow field; Figure 7 A schematic diagram of the functional modules of an underwater explosion fluid numerical simulation device; Figure 8 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0016] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0017] This application designs a numerical simulation scheme for underwater explosion fluid based on the Multi-Resolution Weighted Essentially Non-Oscillatory with Adaptive Linear Weight (ALW-MR-WENO) algorithm and Uniform-Positivity-Presreving (UPP) technology. Specifically: the underwater explosion computational domain is determined and divided into structured or unstructured meshes; based on the given underwater explosion simulation conditions, the corresponding physical parameters such as density, mass, and energy within the mesh are initialized; at each time step, the finite volume ALW-MR-WENO method is used to reconstruct the conserved variables of the current flow field in a higher-order spatial manner, obtaining an initial reconstruction polynomial; the finite volume ALW-MR-WENO method only requires a small template containing the target element and a large template containing the target element and its neighboring elements, and adaptively adjusts the linear and nonlinear weights corresponding to the two templates through a single judgment condition to construct the higher-order reconstruction polynomial.

[0018] Apply a positive constraint to the initial reconstructed polynomial, calculate the minimum value of the polynomial within the computational cell, and impose a constraint that the density and pressure are always greater than 0 to obtain the corrected reconstructed polynomial.

[0019] The numerical flux of the underwater explosion flow field is obtained by calculating the boundary of the grid using the corrected reconstructed polynomial and performing time-progression solution until the preset simulation termination time is reached.

[0020] This application aims to solve the problems of low computational efficiency and easy interruption caused by negative pressure and negative density in existing underwater explosion simulations.

[0021] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0022] In one exemplary embodiment, such as Figure 1 As shown, a numerical simulation method for underwater explosion fluids is provided, including: Step 100: Mesh the preset underwater explosion calculation region and initialize the fluid physics parameters of the computational flow field within the mesh based on the given underwater explosion simulation conditions. The fluid physics parameters include: fluid density, fluid mass, and fluid energy.

[0023] Model the devices involved in the explosion scenario, such as constructing a model that includes explosives, seawater, a spherical protective net, and the target to be protected; set the observation area as the computational area, and divide the computational area into several control volume units using structured or unstructured meshes.

[0024] Based on the set underwater explosion simulation conditions such as explosive equivalent, detonation point location, and water depth, the physical parameters such as fluid density, fluid mass, and fluid energy, as well as the corresponding boundary conditions, are initialized in each control volume unit within the calculation area.

[0025] Step 200: Use the finite volume ALW-MR-WENO method to reconstruct the fluid physical parameters in a higher-order space to obtain the initial reconstruction polynomial.

[0026] The finite volume ALW-MR-WENO method is used to reconstruct the higher-order space of each control volume element in sequence. The reconstructed control volume element is called the target element. Using the geometric information and internal fluid information in the target element, a first-order algebraic polynomial is reconstructed on a small template, and a second-order or higher-order algebraic polynomial is reconstructed on a large template according to the actual accuracy requirements.

[0027] Based on first-order algebraic polynomials and second-order or higher-order algebraic polynomials, the corresponding smoothing factors, linear weights, and nonlinear weights are calculated. Then, through a simple judgment criterion, the linear and nonlinear weights are automatically adjusted to determine the initial reconstruction polynomial.

[0028] Among them, the finite-volume ALW-MR-WENO method is used to reconstruct the fluid physical parameters in a higher-order spatial manner, resulting in an initial reconstruction polynomial, which specifically includes: Step 201: Determine the fluid control equations corresponding to the underwater explosion simulation process based on the fluid physics parameters to obtain the Euler equations; the expressions corresponding to the Euler equations are: .

[0029] .

[0030] .

[0031] in, The first time derivative of the conserved variable; The first spatial derivative of the flux function; For time; The horizontal direction of the coordinate axes; It is a conserved variable; It is the flux function; For fluid density; For fluid momentum; For fluid energy; For fluid velocity; For fluid pressure; Momentum flux is used to describe the transport of momentum; Energy flux is used to describe the transfer of total energy, including kinetic and internal energy. This is the vector transpose symbol.

[0032] Step 202: Spatial discretization of the Euler equations is performed based on the control volume element, and high-order spatial reconstruction is performed using the finite volume ALW-MR-WENO method to obtain the initial reconstruction polynomial; the control volume element is the mesh element obtained after meshing the preset underwater explosion calculation area.

[0033] In one embodiment, the Euler equations are spatially discretized based on control volume elements, and a higher-order spatial reconstruction is performed using the finite-volume ALW-MR-WENO method to obtain an initial reconstructed polynomial, specifically including: Two unequally spaced hierarchical central space templates are selected and reconstructed to obtain two interpolation polynomials of unequal degree; the hierarchical central space templates include: a central space template. and central space template .

[0034] Construct first-order algebraic polynomial vectors on the hierarchical central space template. and octet polynomial vectors .

[0035] Calculate a smoothing factor that measures the smoothness of a polynomial vector on a control volume unit; the polynomial vector includes: a first-order algebraic polynomial vector. and octet polynomial vectors .

[0036] Determine the equivalent expression of the polynomial vector, and determine the preliminary reconstructed polynomial based on the equivalent expression.

[0037] The corresponding nonlinear weights are obtained by solving based on the smoothness factor; the corresponding nonlinear weights are: .

[0038] .

[0039] An adaptive linear weight adjustment strategy is used to update the initial reconstructed polynomial to ensure the positivity of the linear weights; where, when When the corresponding nonlinear weights are substituted into the initial reconstruction polynomial, the initial reconstruction polynomial is obtained; if: ; but, The algorithm returns the step of "determining the equivalent expression of the polynomial vector and determining the preliminary reconstructed polynomial based on the equivalent expression"; otherwise, it substitutes the adaptively adjusted and recalculated nonlinear weights into the preliminary reconstructed polynomial to obtain the initial reconstructed polynomial.

[0040] in, template The corresponding nonlinear weights; ; template The corresponding initial nonlinear weights; The initial nonlinear weights are for the small template; The initial nonlinear weights are for the large template. template The corresponding linear weights; A parameter related to the absolute consistency among smoothing factors; For algebraic polynomials The corresponding smoothing factor; For positive numbers that are close to zero; For serial numbers; is the smoothing factor corresponding to the vector of a first-order algebraic polynomial; The smoothing factor corresponding to the eighth-degree polynomial vector; The initial linear weights are for the large template. The initial linear weights are for the small template; For the initial reconstruction polynomial; For control unit The right endpoint; For control unit The unit mean vector; The grid length; For control unit The unit mean vector; For control unit The unit mean vector; template The corresponding initial linear weights; To be The corresponding linear weights after adjustment.

[0041] Step 300: Construct the corrected reconstructed polynomial based on the initial reconstructed polynomial using the UPP positive constraint.

[0042] The design concept for applying the UPP correction limiter to the initial reconstructed polynomial is as follows: Calculate the element mean of the initial reconstruction polynomial in each control element of the large template; construct a series of auxiliary polynomials by interpolation on the large template based on the element mean; calculate the exact minimum of the initial reconstruction polynomial and the auxiliary polynomials in the target element using the nested bisection method, and take the minimum value as the reference minimum value.

[0043] If the reference minimum value is less than the set threshold, a nonlinear positive constraint is introduced to correct the reconstructed polynomial; the corrected reconstructed polynomial satisfies positiveness throughout the entire target cell. The numerical flux at the mesh boundary is calculated based on the corrected reconstructed polynomial. The left and right state values ​​at the Gaussian integration points on the grid boundary are calculated using the modified reconstructed polynomial; based on the left and right state values, the numerical flux at the boundary is calculated using the Riemann solver.

[0044] Specifically, the process of constructing the corrected reconstructed polynomial based on the initial reconstructed polynomial using the UPP correction limiter includes: The new element mean vector on the control volume element is determined based on the initial reconstruction polynomial. .

[0045] .

[0046] Construct an auxiliary polynomial vector based on the new unit mean. : .

[0047] The minimum function value at the midpoint of the control volume element is determined based on the auxiliary polynomial vector. : .

[0048] like Then there is no need to perform density correction; simply set the scaling factor directly. Otherwise, apply a UPP correction limiter to perform density correction to obtain a density-corrected reconstructed polynomial vector.

[0049] Density-corrected reconstructed polynomial vector for: .

[0050] .

[0051] Based on the pressure values ​​at the equal division points of the control unit The pressure polynomial after density correction is constructed through interpolation; the minimum value of the pressure polynomial on the control volume element is calculated, and the function value of the auxiliary pressure polynomial at the midpoint of the control volume element is determined. .

[0052] .

[0053] like Then there is no need for pressure correction; simply set the scaling factor directly. Otherwise, reconstruct the polynomial vector after density correction. Applying a UPP correction limiter for pressure correction yields the corrected reconstructed polynomial; the expression corresponding to the corrected reconstructed polynomial is: .

[0054] in, The final density reconstruction polynomial of ALW-MR-WENO in the control volume unit The unit mean on; The final momentum reconstruction polynomial for ALW-MR-WENO in the control volume unit The unit mean on; The final energy reconstruction polynomial for ALW-MR-WENO in the control volume unit The unit mean on; The grid length; Reconstruct the final density polynomial for ALW-MR-WENO; The final momentum reconstruction polynomial for ALW-MR-WENO; The final energy reconstruction polynomial for ALW-MR-WENO; For a series of initial auxiliary density polynomials; Reconstruct the polynomial for the initial auxiliary momentum; Reconstruct the polynomial for the initial auxiliary energy; The symbol for vector transpose; An eighth-degree polynomial In the control unit The minimum value on; The function value of the initial auxiliary sixth-order density polynomial at the center of the control volume element; The function value of the initial auxiliary quartic density polynomial at the center of the control volume element; The function value of the initial auxiliary quadratic density polynomial at the center of the control volume element; These are a series of auxiliary density polynomials after density correction; For control unit The average density of the cells; This is the specific heat rate, which is typically taken as 1.4 for ideal gases; The function values ​​of a series of initial auxiliary energy polynomials at the center of the control volume unit; It is the square of the function values ​​of a series of initial auxiliary momentum polynomials at the center of the control volume element; These are the function values ​​of a series of auxiliary density polynomials after density correction at the center of the control volume element; For control unit The unit mean vector on; , , All are serial numbers.

[0055] Step 400: Calculate the numerical flux of the grid boundary based on the corrected reconstructed polynomial and perform time-progressed solving until the time step reaches the set explosion simulation termination time, obtaining real-time evolution data of the underwater explosion flow field. This real-time evolution data is used to subsequently assess the dynamic response and damage level of offshore facilities under explosion loads. In other words, the real-time evolution data can be further used to evaluate the performance of specific explosives or for the protection of various equipment around the explosion site.

[0056] The numerical flux of the grid boundary is calculated based on the corrected reconstructed polynomial, and a time-progressed solution is performed until the time step reaches the set termination time of the explosion simulation, thus obtaining real-time evolution data of the underwater explosion flow field, including: Step 401: Calculate the numerical flux of the grid boundary based on the modified reconstructed polynomial; wherein, the function value of the modified reconstructed polynomial at the boundary of the control volume element is used as the numerical flux.

[0057] Step 402: Using the third-order strongly stable Runge-Kutta method, the solution is obtained by time-progression based on numerical flux until the time step reaches the set explosion simulation termination time, thus obtaining the real-time evolution data of the underwater explosion flow field.

[0058] The calculation formula corresponding to the time-progression solution is: .

[0059] in, , All are intermediate temporary solutions; For the first The unit mean value corresponding to each time step; For time step; For the discretization operator of spatial variables, ALW-MR-WENO spatial discretization is used here; For the first The unit mean value corresponding to each time step; For serial numbers.

[0060] This application first defines the underwater explosion computational domain and performs mesh generation. Then, it sets initial fluid physics parameters based on the predetermined explosive equivalent and water depth. The ALW-MR-WENO method is used to reconstruct the fluid physics parameters in a high-order spatial manner, and a modified reconstruction polynomial is constructed using a UPP correction limiter. The numerical flux and time step are calculated based on the modified reconstruction polynomial until the predetermined explosion simulation termination time is reached. This application utilizes the adaptive linear weighting technique of the ALW-MR-WENO algorithm, combined with UPP correction processing for extreme underwater explosion conditions, to capture the strong shock waves, bubble pulsations, and fluid dynamic responses generated by underwater explosions with high accuracy and robustness. While avoiding costly and difficult-to-measure full-scale physical explosion experiments, it effectively solves the problem of computational interruption caused by negative density or negative pressure when simulating near-field underwater explosions using traditional simulation methods.

[0061] Specifically, such as Figure 2 As shown, the operation process corresponding to the method mentioned in this application includes the following steps: Discretization and initialization of the computational domain: The computational domain is determined based on the actual underwater explosion scenario, a spatial rectangular coordinate system is established, and the computational domain is meshed. For example... Figure 2 S1 in the equation: Determines the underwater computational domain and mesh generation.

[0062] Specifically, regarding geometric modeling and mesh generation, a computational domain containing the explosive sphere and the water medium is constructed. The computational domain is divided using a uniform grid with a grid length of [value missing]. , grid cell (control volume cell) Control unit center .

[0063] in, For control unit The left endpoint; For control unit The right endpoint; For serial numbers.

[0064] like Figure 2 S2: Sets the initial physical parameters of the explosive and water medium. Specifically, based on the explosive equivalent, detonation point location, and water depth and static pressure, initializes the density, momentum, and total energy of the fluid within the grid. The physical parameter initialization includes: Assuming TNT explosives are placed at a point in the calculation area, the explosive units are set according to detonation physics. The initial total energy, i.e., fluid energy For the remaining water-medium units, the initial total energy, i.e., the fluid energy, is set. Set the initial fluid density of all units to 1 and the initial fluid velocity to 0.

[0065] S3: High-order spatial reconstruction based on the finite-volume ALW-MR-WENO algorithm: At each time step, the conserved variables of the Euler equations are spatially discretized using the finite-volume ALW-MR-WENO algorithm. This algorithm constructs polynomials using two central templates of different sizes (a small template and a large template). Through a simple criterion, the corresponding linear and nonlinear weights are adaptively adjusted, ensuring that the numerical solution obtained by the algorithm maintains high-order accuracy in smooth regions while automatically switching to a low-order non-oscillatory scheme at discontinuities of equal strength, such as those caused by shock waves.

[0066] That is: considering the underwater explosion simulation process, the fluid control equations are the Euler equations: .

[0067] Among them, the conserved variables Flux function , , , Indicates fluid density, It represents fluid momentum. Represents fluid energy. Indicates fluid velocity. Indicates fluid pressure. This represents the specific heat rate, which is typically taken as 1.4.

[0068] In the control unit Spatial discretization of the above Euler equations yields the following semi-discrete numerical scheme: .

[0069] in, These are monotonic numerical fluxes with positive property, such as the Lax-Friedrichs flux. It is a vector of unit mean functions that are spatially discretized and only related to time. For the discretization operator of spatial variables, ALW-MR-WENO spatial discretization is used here; For control unit The vector of function values ​​at the right endpoint of the reconstructed polynomial obtained by spatial discretization of the central element; For control unit The vector of function values ​​at the left endpoint of the reconstructed polynomial obtained by spatial discretization of the central element; For control unit The vector of function values ​​at the right endpoint of the reconstructed polynomial obtained by spatial discretization of the central element; For control unit The vector of function values ​​at the left endpoint of the reconstructed polynomial obtained by spatial discretization of the central element; This is a numerical flux vector; here, the Lax-Friedrichs flux is used.

[0070] It can be obtained through finite-volume ALW-MR-WENO higher-order space reconstruction. The point-by-point numerical approximation is as follows.

[0071] Two unequally spaced hierarchical central space templates are selected and reconstructed to obtain two interpolation polynomials of unequal order.

[0072] For the ninth-order spatial approximation, the central space template is chosen. and Construct linear algebraic polynomial vectors on these two central space templates respectively. and octet polynomial vector ,satisfy: .

[0073] .

[0074] in, These represent the corresponding control unit; It is a first-order interpolation density polynomial; It is a first-order interpolation momentum polynomial; It is a first-order interpolation energy polynomial; It is an octet interpolation density polynomial; It is an eighth-order interpolation momentum polynomial; It is an octet interpolation energy polynomial.

[0075] Calculate the measure polynomial in the control unit The smoothness factor determines the smoothness of the surface.

[0076] Specifically, for each component of a first-order polynomial vector (in... For example, its corresponding smoothing factor The calculation process is as follows: .

[0077] .

[0078] .

[0079] .

[0080] .

[0081] in, , All are squared deviations from the mean; For control unit Upper density cell mean; For control unit Upper density cell mean; For control unit Upper density cell mean; The initial linear weights are the linear weights of the first-order polynomial vector corresponding to the small template on the left. The initial linear weights are the linear weights of the first-order polynomial vector corresponding to the small template on the right. The linear weights are the linear weights of the first-order polynomial vector corresponding to the small template on the left. The linear weights are the linear weights of the first-order polynomial vector corresponding to the small template on the right. The initial nonlinear weights are the first-order polynomial vectors corresponding to the small template on the left. The initial nonlinear weights are the first-order polynomial vectors corresponding to the small template on the right. This is an intermediate parameter for nonlinear weight normalization.

[0082] It is a positive number approaching zero, and in this embodiment, it is taken as... .

[0083] For each component of the octet polynomial vector (with... For example, its corresponding smoothing factor : .

[0084] in, For serial numbers.

[0085] Obtain the equivalent expression for a polynomial vector: Linear algebraic polynomial vector and octet polynomial vectors The equivalent expressions are as follows: .

[0086] .

[0087] Among them, linear weights and satisfy Considering the balance between the inherently non-oscillating shock wave transitions in non-smooth regions and the accuracy in smooth regions, the following settings are adopted: , . , These are the equivalent polynomial vectors corresponding to the small template and the large template, respectively; All of these are the three components of the equivalent polynomial vector corresponding to the small template. These are the three components of the equivalent polynomial vector corresponding to the large template.

[0088] The linear weights are adaptively adjusted, and the corresponding nonlinear weights are solved based on the smoothing factor obtained above.

[0089] Specifically, we first define parameters related to the absolute consistency among smoothing factors. : .

[0090] And the corresponding nonlinear weights are defined as follows: .

[0091] At this point, the polynomial vector can be initially reconstructed. Represented as: .

[0092] Next, the reconstructed polynomial is updated according to the following adaptive linear weight adjustment strategy to ensure the positivity of the linear weights. To reduce computational cost, when If so, jump directly to the step corresponding to the reconstructed polynomial after adjusting the linear weights. If: , ,but The process jumps to the equivalent expression for determining the polynomial vector and, based on the equivalent expression, determines the initial reconstructed polynomial and re-executes the subsequent process; otherwise, the reconstructed polynomial with adjusted linear weights is obtained.

[0093] Substitute the recalculated nonlinear weights after adaptive adjustment into We obtain the reconstructed polynomial after adjusting the linear weights.

[0094] S4: UPP positive limiter correction, that is: applying the UPP positive limiter to correct and reconstruct the polynomial.

[0095] To ensure computational stability of the bubble expansion region in underwater explosion simulations, a novel UPP (Using a nested bisection method) correction limiter is introduced. This limiter constructs a series of auxiliary polynomials, calculates the minimum values ​​of the auxiliary and reconstructed polynomials within the element (using a nested bisection method), and applies nonlinear compression constraints to force the density and pressure of the modified polynomial at any point within the element to be greater than zero.

[0096] In numerical simulations of underwater explosions, bubble expansion leads to a sharp drop in density and pressure, resulting in numerical collapse. To further improve the stability of numerical schemes simulating extreme cases (such as underwater explosion simulations), this embodiment employs a UPP positive limiting device to ensure the positiveness of fluid density and fluid pressure during the numerical simulation, which is also the core idea of ​​this application. The specific process is as follows.

[0097] Construct a series of auxiliary polynomials of different degrees.

[0098] Based on the reconstructed polynomial vector after adjusting the linear weights, the new unit mean values ​​on the five control volume units of the large template are obtained: .

[0099] Obviously Using these new unit means, we construct a series of auxiliary polynomial vectors of different degrees (where the superscript represents the polynomial degree). They satisfy: .

[0100] According to the ALW-MR-WENO reconstruction process, it is easy to obtain . for A series of auxiliary polynomial vectors corresponding to the value of 4.

[0101] The positivity of the density polynomial is detected, and the UPP technique is applied to ensure its positivity across the entire control volume unit.

[0102] Accurately calculate the precise minimum value of the density polynomial after adjusting the linear weights on the control volume element, and then take the minimum value together with the function value of the auxiliary density polynomial at the midpoint of the element. .like Then there is no need to perform density correction; simply set the scaling factor directly. Otherwise, apply a UPP correction limiter to the density polynomial for density correction. The corrected density polynomial and the auxiliary density polynomial are: .

[0103] .

[0104] .

[0105] .

[0106] .

[0107] .

[0108] .

[0109] .

[0110] The reconstructed polynomial vector after density correction is: .

[0111] in, The nonlinear weights are for the octet density polynomial; The linear weights are the corresponding to the octet density polynomial; The initial nonlinear weights are for the eighth-order density polynomial; The initial nonlinear weights are the values ​​corresponding to the density mean. The parameter is related to the absolute consistency of the smoothness factor corresponding to the octet density polynomial; and These are the smoothing factors corresponding to the eighth-order density polynomial and the density mean, respectively; The density mean; The coefficient is constant. To ensure the correct threshold. The nonlinear weights are those corresponding to the octet density polynomial.

[0112] The positivity of the pressure polynomial after density correction is constructed and tested, and the UPP technique is applied to ensure its positivity across the entire control volume unit.

[0113] Specifically, firstly, based on the pressure values ​​at the equal division points of the control unit... : .

[0114] Interpolation constructs the pressure polynomial after density correction: .

[0115] in, The energy function value at the division points of the control volume unit; These are the equal division points of the control unit; The momentum function values ​​at the division points of the control volume element; This represents the density function value at the division points of the control volume element after density correction. This is the midpoint of the control unit.

[0116] Then, the exact minimum value of the pressure polynomial on the control volume element is precisely calculated. And calculate the function values ​​of a series of auxiliary pressure polynomials of different degrees (the superscripts indicate the degree of the polynomials) at the midpoints of the elements. : .

[0117] Take the minimum of the above four values: .

[0118] in, for Midpoint of the unit The function value at that location; for Midpoint of the unit The function value at that location.

[0119] like Then there is no need for pressure correction; simply set the scaling factor directly. Otherwise, for this polynomial vector Applying a UPP correction limiter for pressure correction, the corrected polynomial vector is: .

[0120] .

[0121] .

[0122] .

[0123] .

[0124] 。

[0125] .

[0126] .

[0127] S5: Calculate numerical flux and time progression, that is, calculate numerical flux based on the corrected reconstructed polynomial vector.

[0128] The function values ​​of the modified polynomial vector at the cell boundary are used as numerical flux. , .in, and These are the corrected polynomial vectors. The function values ​​at the left and right endpoints of the unit.

[0129] Based on the numerical flux at the interface of the modified polynomial computational grid, the Runge-Kutta time discretization method is used for time progression until the preset explosion simulation termination time is reached. The output includes density, velocity, and pressure distribution maps of the flow field. Figure 6 The diagram shows the spatiotemporal point of the triggering UPP positivity limiter. Among them, Figure 3A schematic diagram of the density distribution of the underwater explosion flow field; Figure 4 This is a schematic diagram of the velocity distribution in the underwater explosion flow field. Figure 5 This is a schematic diagram of the pressure distribution in the underwater explosion flow field.

[0130] Specifically, the third-order strong stability (SSP) Runge-Kutta method is used for time advancement (advancing from the k-th time step to the (k+1)-th time step), and its calculation formula is as follows.

[0131] .

[0132] in, For time step, . For the first One time step; For the first Each time step.

[0133] In each time step, the higher-order approximation of the numerical flux of the modified polynomial at the cell boundary is calculated and substituted into the time-progression formula above. This process is iterated until the simulation time reaches the preset underwater explosion bubble pulsation period. As... Figure 2 S6: Determine if the termination time has been reached. If so, output the process data. Otherwise, use the unit mean value obtained by the polynomial calculation after the time step correction as the initial value to iteratively calculate the numerical flux and numerical solution of the next time step.

[0134] The benefits of this application are: High robustness: By introducing the UPP positive limiter, this application can handle the near-vacuum state in underwater explosions, avoiding the computational collapse caused by negative values ​​of physical quantities in traditional methods.

[0135] High precision: Based on the finite volume ALW-MR-WENO algorithm, this application can accurately simulate the fine structure of bubble pulsation while capturing strong shock waves.

[0136] Efficiency: This algorithm allows for the use of a large number of CFLs, which significantly improves computational efficiency compared to traditional positive-preserving methods.

[0137] This application also provides an application scenario in which the above-mentioned underwater explosion fluid numerical simulation method is applied. Specifically, the underwater explosion fluid numerical simulation method provided in this embodiment can be applied to the safety assessment of offshore platforms and cross-sea bridge pile foundations. Offshore oil drilling platforms, wind power foundations, and cross-sea bridge piers are constantly in complex marine environments. If an accidental underwater explosion occurs nearby (such as a passing ship accident or illegal operation), the huge shock wave and bubble pulsation will pose a serious threat to these infrastructures. Using the underwater explosion fluid numerical simulation method in this application, the dynamic response and damage level of these structures under explosive loads can be assessed in advance, providing theoretical support for protective design.

[0138] In one exemplary embodiment, such as Figure 7 As shown, an underwater explosion fluid numerical simulation device is provided, comprising: The mesh generation and parameter initialization module is used to generate a mesh for the preset underwater explosion calculation region and initialize the fluid physical parameters of the calculation flow field within the mesh based on the given underwater explosion simulation conditions. The fluid physical parameters include fluid density, fluid mass, and fluid energy.

[0139] The spatial reconstruction module is used to perform high-order spatial reconstruction of fluid physical parameters using the finite volume ALW-MR-WENO method to obtain the initial reconstruction polynomial.

[0140] The correction module is used to construct a corrected reconstruction polynomial based on the initial reconstruction polynomial using the UPP correction limiter.

[0141] The solver module is used to calculate the numerical flux of the grid boundary based on the corrected reconstructed polynomial and perform time-progression solving until the time step reaches the set explosion simulation termination time to obtain real-time evolution data of the underwater explosion flow field; the real-time evolution data is used to subsequently assess the dynamic response and damage level of offshore facility structures under explosion loads.

[0142] Real-time evolution data can include the density, pressure, and velocity distribution of the underwater explosion flow field.

[0143] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 8As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The database stores numerical simulation data of underwater explosive fluids. The I / O interfaces are used for information exchange between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements the numerical simulation method for underwater explosive fluids.

[0144] Those skilled in the art will understand that Figure 8 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0145] In one exemplary embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0146] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0147] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0148] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0149] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0150] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, data processing logic devices, etc., and are not limited to these.

[0151] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0152] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A numerical simulation method for underwater explosion fluids, characterized in that, include: The preset underwater explosion calculation region is meshed, and the fluid physical parameters of the calculation flow field within the mesh are initialized based on the given underwater explosion simulation conditions. The fluid physical parameters include: fluid density, fluid mass, and fluid energy; The finite volume ALW-MR-WENO method is used to reconstruct the fluid physical parameters in a higher-order space to obtain the initial reconstruction polynomial. Based on the UPP positive limiter, a modified reconstructed polynomial is constructed according to the initial reconstructed polynomial; The numerical flux of the underwater explosion flow field is calculated based on the modified reconstructed polynomial computation grid boundary and time-progressed solution is performed until the time step reaches the set explosion simulation termination time to obtain real-time evolution data. The real-time evolution data is used to subsequently assess the dynamic response and damage level of offshore facility structures under explosion loads.

2. The underwater explosion fluid numerical simulation method according to claim 1, characterized in that, The finite volume ALW-MR-WENO method is used to reconstruct the high-order spatial parameters of the fluid physics, resulting in the initial reconstruction polynomial, which includes: The fluid control equations corresponding to the underwater explosion simulation process are determined based on fluid physics parameters to obtain the Euler equations; the expressions corresponding to the Euler equations are: ； ； ； in, The first time derivative of the conserved variable; The first spatial derivative of the flux function; For time; The horizontal direction of the coordinate axes; It is a conserved variable; It is the flux function; For fluid density; For fluid momentum; For fluid energy; For fluid velocity; For fluid pressure; Momentum flux is used to describe the transport of momentum; Energy flux is used to describe the transfer of total energy, including kinetic and internal energy. The symbol for vector transpose; The Euler equations are spatially discretized based on the control volume element, and a higher-order spatial reconstruction is performed using the finite volume ALW-MR-WENO method to obtain the initial reconstruction polynomial; the control volume element is the mesh element obtained after meshing the preset underwater explosion calculation region.

3. The underwater explosion fluid numerical simulation method according to claim 2, characterized in that, The Euler equations are spatially discretized based on control volume elements, and a higher-order spatial reconstruction is performed using the finite-volume ALW-MR-WENO method to obtain the initial reconstructed polynomials, specifically including: Two unequally spaced hierarchical central space templates are selected and reconstructed to obtain two interpolation polynomials of unequal degree; the hierarchical central space templates include: a central space template. and central space template ; Construct first-order algebraic polynomial vectors on the hierarchical central space template. and octet polynomial vectors ; Calculate a smoothing factor that measures the smoothness of a polynomial vector on a control volume unit; the polynomial vector includes: a first-order algebraic polynomial vector. and octet polynomial vectors ; Determine the equivalent expression of the polynomial vector, and determine the preliminary reconstructed polynomial based on the equivalent expression; The corresponding nonlinear weights are calculated based on the smoothness factor; the corresponding nonlinear weights are: ； ； An adaptive linear weight adjustment strategy is used to update the initial reconstructed polynomial to ensure the positivity of the linear weights; where, when When the corresponding nonlinear weights are substituted into the initial reconstruction polynomial, the initial reconstruction polynomial is obtained; if: ； but, The algorithm returns the step of "determining the equivalent expression of the polynomial vector and determining the preliminary reconstructed polynomial based on the equivalent expression"; otherwise, it substitutes the adaptively adjusted and recalculated nonlinear weights into the preliminary reconstructed polynomial to obtain the initial reconstructed polynomial. in, template The corresponding nonlinear weights; ; template The corresponding initial nonlinear weights; The initial nonlinear weights are for the small template; The initial nonlinear weights are for the large template. template The corresponding linear weights; A parameter related to the absolute consistency among smoothing factors; For algebraic polynomials The corresponding smoothing factor; For positive numbers that are close to zero; For serial numbers; is the smoothing factor corresponding to the vector of a first-order algebraic polynomial; The smoothing factor corresponding to the eighth-degree polynomial vector; The initial linear weights are for the large template. The initial linear weights are for the small template; For the initial reconstruction polynomial; For control unit The right endpoint; For control unit The unit mean vector; The grid length; For control unit The unit mean vector; For control unit The unit mean vector; template The corresponding initial linear weights; To be The corresponding linear weights after adjustment.

4. The underwater explosion fluid numerical simulation method according to claim 1, characterized in that, Based on the UPP positive constraint, a modified reconstructed polynomial is constructed according to the initial reconstructed polynomial, specifically including: The new unit mean vector on the control volume unit is determined based on the initial reconstruction polynomial. ; Construct an auxiliary polynomial vector based on the new unit mean. ; ； The minimum function value at the midpoint of the control volume unit is determined based on the auxiliary polynomial vector. : ; like Then there is no need to perform density correction; simply set the scaling factor directly. Otherwise, apply a UPP correction limiter to perform density correction to obtain a density-corrected reconstructed polynomial vector. Density-corrected reconstructed polynomial vector for: ； ； Based on the pressure values ​​at the equal division points of the control unit The pressure polynomial after density correction is constructed through interpolation; the minimum value of the pressure polynomial on the control volume element is calculated, and the function value of the auxiliary pressure polynomial at the midpoint of the control volume element is determined. ; ； like Then there is no need for pressure correction; simply set the scaling factor directly. Otherwise, reconstruct the polynomial vector after density correction. Applying a UPP correction limiter for pressure correction yields the corrected reconstructed polynomial; the corrected reconstructed polynomial... The corresponding expression is: ； in, The final density reconstruction polynomial of ALW-MR-WENO in the control volume unit The unit mean on; The final momentum reconstruction polynomial for ALW-MR-WENO in the control volume unit The unit mean on; The final energy reconstruction polynomial for ALW-MR-WENO in the control volume unit The unit mean on; The grid length; Reconstruct the final density polynomial for ALW-MR-WENO; The final momentum reconstruction polynomial for ALW-MR-WENO; The final energy reconstruction polynomial for ALW-MR-WENO; For a series of initial auxiliary density polynomials; Reconstruct the polynomial for the initial auxiliary momentum; Reconstruct the polynomial for the initial auxiliary energy; The symbol for vector transpose; An eighth-degree polynomial In the control unit The minimum value on; The function value of the initial auxiliary sixth-order density polynomial at the center of the control volume element; The function value of the initial auxiliary quartic density polynomial at the center of the control volume element; The function value of the initial auxiliary quadratic density polynomial at the center of the control volume element; These are a series of auxiliary density polynomials after density correction; For control unit The average density of the cells; Specific heat rate; The function values ​​of a series of initial auxiliary energy polynomials at the center of the control volume unit; It is the square of the function values ​​of a series of initial auxiliary momentum polynomials at the center of the control volume element; These are the function values ​​of a series of auxiliary density polynomials after density correction at the center of the control volume element; For control unit The unit mean vector on; , , All are serial numbers.

5. The underwater explosion fluid numerical simulation method according to claim 1, characterized in that, The numerical flux of the underwater explosion flow field is calculated based on the corrected reconstructed polynomial calculation grid boundary, and a time-progressed solution is performed until the time step reaches the set explosion simulation termination time, obtaining real-time evolution data of the underwater explosion flow field, including: The numerical flux of the grid boundary is calculated based on the modified reconstructed polynomial; wherein the function value of the modified reconstructed polynomial at the boundary of the control volume element is used as the numerical flux. The third-order strongly stable Runge-Kutta method is adopted to solve the problem by time stepping based on numerical flux until the time step reaches the set explosion simulation termination time, so as to obtain the real-time evolution data of the underwater explosion flow field.

6. The underwater explosion fluid numerical simulation method according to claim 5, characterized in that, The calculation formula corresponding to the time-progression solution is: ； in, , All are intermediate temporary solutions; For the first The unit mean value corresponding to each time step; For time step; For discrete operators on spatial variables; For the first The unit mean value corresponding to each time step; For serial numbers.

7. A numerical simulation device for underwater explosion fluids, characterized in that, include: The mesh generation and parameter initialization module is used to generate a mesh for the preset underwater explosion calculation area and initialize the fluid physics parameters of the calculation flow field within the mesh based on the given underwater explosion simulation conditions. The fluid physical parameters include: fluid density, fluid mass, and fluid energy; The spatial reconstruction module is used to perform high-order spatial reconstruction of fluid physical parameters using the finite volume ALW-MR-WENO method to obtain the initial reconstruction polynomial. The correction module is used to construct a corrected reconstructed polynomial based on the initial reconstructed polynomial using the UPP correction limiter. The solver module is used to calculate the numerical flux of the grid boundary based on the corrected reconstructed polynomial and perform time-progression solving until the time step reaches the set explosion simulation termination time to obtain real-time evolution data of the underwater explosion flow field; the real-time evolution data is used to subsequently assess the dynamic response and damage level of offshore facility structures under explosion loads.

8. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the underwater explosion fluid numerical simulation method according to any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the underwater explosion fluid numerical simulation method as described in any one of claims 1-6.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the underwater explosion fluid numerical simulation method as described in any one of claims 1-6.

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