Multi-component gas progressive hold random particle bgk solving method and related device

Abstract

The application discloses a multi-component gas gradual holding random particle BGK solving method and a related device, relates to the technical field of gas dynamics numerical calculation and particle simulation, and comprises the following steps: acquiring initialization particle data of a multi-component gas random particle system; updating position information of each particle corresponding to different time steps in a free transport process; statistically calculating component macro-quantities and mixture macro-quantities of all particles in each calculation unit in a calculation domain; calculating a mixture relaxation time, and constructing a target distribution function for each component particle; adopting a Crank-Nicolson format time discretization for a multi-component BGK equation and updating particle velocity; performing translation-rotation energy exchange and full-mode energy exchange on each particle, and performing momentum conservation correction and energy conservation correction on particle velocity after collision. The application can realize unified description of multi-component and multi-energy mode in complex flow, and improves the accuracy of numerical simulation under complex flow conditions.

Description

Technical Field

[0001] This application relates to the fields of numerical calculation of gas dynamics and particle simulation technology, and in particular to a method and related apparatus for solving BGK asymptotically maintained random particles in multi-component gases. Background Technology

[0002] In the simulation of rarefied gases and hypersonic flows across watersheds, stochastic particle numerical methods are the mainstream approach for characterizing nonequilibrium effects. Direct Monte Carlo simulation (DSMC) offers high accuracy, but requires finer meshing and smaller time steps in the near-continuous flow region, resulting in high computational costs. In recent years, the stochastic particle BGK method (SPBGK) combined with the BGK (Bhatnagar-Gross-Krook) model has been developed, and further, the Crank-Nicolson (CN) scheme stochastic particle BGK method (CN-SPBGK) has been introduced. This gives the BGK method asymptotic preservation capability, effectively reducing the dependence of the near-continuous flow region on mesh size and time step, and improving computational efficiency. However, the CN-SPBGK method is mainly designed for monatomic gases and only considers translational degrees of freedom. It cannot handle the mixing process of multi-component gases, nor does it consider the momentum and energy exchange between different components. It is not capable of describing gases with internal degrees of freedom such as rotation and vibration. It is difficult to accurately describe the evolution of multimodal energy in strongly nonequilibrium flows, and the accuracy of numerical simulation under complex flow conditions is low.

[0003] Therefore, there is an urgent need for an asymptotically maintained random particle BGK solution method applicable to multi-component gases, so as to achieve a unified description of multi-component and multi-energy modes in complex flows and improve the accuracy of numerical simulation under complex flow conditions. Summary of the Invention

[0004] The purpose of this application is to provide a method and related apparatus for solving multi-component gas asymptotically maintained random particle BGK, which can realize a unified description of multi-component and multi-energy modes in complex flows and improve the accuracy of numerical simulation under complex flow conditions.

[0005] To achieve the above objectives, this application provides the following solution: In a first aspect, this application provides a method for solving the BGK problem of asymptotically maintained random particles in a multi-component gas, comprising the following steps: S1: Construct a multi-component gas random particle system based on the computational domain, and obtain the initial particle data of the multi-component gas random particle system; the initial particle data includes: component information, position information, velocity information and energy information of each particle, and the energy information includes: translational energy, rotational energy and vibrational energy.

[0006] S2: Based on the velocity information and the position information, update the position information of each particle at different time steps during free transport to obtain the updated position information.

[0007] S3: Based on the updated position information, the component information, and the energy information, respectively calculate the macroscopic quantities of the components and the macroscopic quantities of the mixture of all particles in each computing unit in the computing domain.

[0008] S4: Calculate the relaxation time of the mixture based on the macroscopic quantities of the mixture, and construct the corresponding target distribution function for each component particle by combining the macroscopic quantities of the components.

[0009] S5: Based on the relaxation time of the mixture and the target distribution function, the multi-component BGK equation is discretized in time using the Crank-Nicolson scheme and the particle velocity is updated to obtain the particle velocity after the collision.

[0010] S6: Based on the energy information and the macroscopic quantities of the components, perform translational-rotational energy exchange and full-modal energy exchange on each particle in sequence to obtain new translational energy, rotational energy and vibrational energy.

[0011] S7: Based on the new translational energy, rotational energy and vibrational energy, the velocity of each particle after the collision is corrected for momentum conservation and energy conservation in sequence to obtain the corrected velocity of each particle.

[0012] S8: Use the corrected velocity of each particle as the velocity information, and repeat the process from step S2 to step S7 until the full-time flow simulation of the computational domain is completed.

[0013] In a second aspect, 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 steps of the multi-component gas asymptotically maintained random particle BGK solution method described in the first aspect.

[0014] Thirdly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the multi-component gas asymptotically maintained random particle BGK solution method described in the first aspect.

[0015] Fourthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the multi-component gas asymptotically maintained random particle BGK solution method described in the first aspect.

[0016] According to the specific embodiments provided in this application, this application has the following technical effects: This application provides a method and related apparatus for solving the BGK (Browser-Gas Kernel) problem of asymptotically maintained random particles in multi-component gases. First, by constructing a multi-component random particle system within the computational domain, incorporating information on composition, position, velocity, and various energy types including translational, rotational, and vibrational energy, the system can completely retain multi-dimensional fundamental data of multi-component gas particles, providing comprehensive data support for subsequent unit-by-unit statistical analysis, group-by-group target distribution construction, and group-by-group multimodal energy exchange. Second, by updating the free transport position based on particle velocity and original position, the system can numerically simulate the collision-free spatial motion of particles, providing accurate spatial attribution for macroscopic quantity statistics within the computational unit. Third, by simultaneously statistically analyzing the macroscopic quantities of components and the mixture within each unit, the system can simultaneously acquire data on the overall state of the mixed gas and the independent states of each component, taking into account both the flow characteristics of the mixed system and individual components. Furthermore, by using the macroscopic quantities of the mixture to solve for the mixture relaxation time, and simultaneously combining the macroscopic quantities of the components to construct the target distribution function group-by-group, different components can match their own specific equilibrium distribution based on a unified mixing relaxation scale, achieving coupled solution of multi-component gases. By employing the Crank-Nicolson scheme to discretize the multi-component BGK equations over time and update particle velocities, second-order accurate time-discrete solutions for particle collision processes can be achieved, adapting to multi-scale flow simulations. By sequentially performing translational-rotational energy exchange and full-modal energy exchange, and treating the internal energy evolution of translational, rotational, and vibrational modes in a layered manner, the non-equilibrium energy change process of multi-component gases in multiple modes can be fully characterized. This achieves a unified description of multi-component and multi-energy modes in complex flows, improving the accuracy of numerical simulations under complex flow conditions. By sequentially applying momentum and energy conservation corrections to the particle velocities after collisions, macroscopic quantity drift caused by random particle updates is corrected, ensuring the physical conservation of momentum and energy throughout the simulation process, further enhancing the accuracy of numerical simulations. Furthermore, by iteratively substituting the corrected particle velocities into the free transport step, iterative calculations can be continuously performed to complete long-scale flow evolution iterations in the computational domain, outputting complete simulation results of the global flow evolution across the computational domain. Attached Figure Description

[0017] It can achieve a unified description of multi-component and multi-energy modes in complex flows, improving the accuracy of numerical simulations under complex flow conditions. 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.

[0018] Figure 1 An application environment diagram for a multi-component gas asymptotically maintained random particle BGK solution method provided in an embodiment of this application; Figure 2 A flowchart illustrating a method for solving the BGK problem for a multi-component gas with asymptotically maintained random particles, provided in an embodiment of this application; Figure 3 This is a schematic diagram of the BGK solution principle for asymptotically maintained random particles in a multi-component gas according to an embodiment of this application. Figure 4 A schematic diagram of the geometric structure of a 70° blunt cone model provided in an embodiment of this application; Figure 5 A comparative cloud map of translational temperature in the flow field of the method of this application and the DSMC method provided for an embodiment of this application; Figure 6 A comparison cloud map of rotational temperature in the flow field of the method of this application and the DSMC method provided in an embodiment of this application; Figure 7 A comparison cloud map of vibration temperature in the flow field of the method of this application and the DSMC method provided in an embodiment of this application; Figure 8 A schematic diagram showing the temperature comparison curves of each mode in front of the stagnation point on the axis of symmetry of the method and the DSMC method provided in an embodiment of this application; Figure 9 A schematic diagram comparing the heat flux density and pressure distribution on the blunt cone surface of the method and the DSMC method provided in an embodiment of this application; Figure 10 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0019] 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 skilled in the art without creative effort are within the scope of protection of this application.

[0020] The purpose of this application is to provide a method and related apparatus for solving multi-component gas asymptotically maintained random particle BGK, which is applicable to numerical calculation scenarios of hypersonic multi-scale flow, rarefied multi-component mixed gas, and strongly thermal non-equilibrium gas dynamics. It can achieve a unified description of multi-component and multi-energy modes in complex flow, improve the accuracy of numerical simulation under complex flow conditions, and solve the problem that the existing CN-SPBGK method is only applicable to monatomic gases and cannot accurately handle multi-component coupling and multi-modal energy exchange.

[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] The multi-component gas asymptotically maintained random particle BGK solution method provided in this application embodiment can be applied to, for example... Figure 1 In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be set up independently, integrated into server 104, or placed in the cloud or on another server. Terminal 102 can send initialization particle data to server 104. After receiving the initialization particle data, server 104 updates the position information of each particle at different time steps during free transport based on the velocity information and position information, obtaining updated position information. Based on the updated position information, component information, and energy information, it statistically analyzes the macroscopic quantities of all particles in each computational unit within the computational domain, including the macroscopic quantities of the components and the macroscopic quantities of the mixture. Based on the macroscopic quantities of the mixture, it calculates the mixture relaxation time and, combined with the macroscopic quantities of the components, constructs a corresponding target distribution function for each component particle. Based on the mixture relaxation time and the target distribution function, it applies the multi-component BGK equation. The Crank-Nicolson scheme is used for time discretization and particle velocity updates to obtain the particle velocities after collision. Based on the energy information and the macroscopic components, translational-rotational energy exchange and full-modal energy exchange are performed on each particle sequentially to obtain new translational energy, rotational energy, and vibrational energy. Based on the new translational, rotational, and vibrational energy, momentum conservation correction and energy conservation correction are performed on the particle velocities after collision for all particles sequentially to obtain the corrected velocities of each particle. The corrected velocities of each particle are used as the velocity information, and the steps of updating the position information during the free transport of particles to momentum conservation correction and energy conservation correction are repeated until the full-time flow simulation in the computational domain is completed. The server 104 can feed back the final solution simulation results to the terminal 102. In addition, in some embodiments, the multi-component gas asymptotically maintained random particle BGK solution method can also be implemented by the server 104 or the terminal 102 separately. For example, the terminal 102 can directly perform multi-component gas asymptotically maintained random particle BGK solution processing on the initialized particle data, or the server 104 can obtain the initialized particle data from the data storage system and perform multi-component gas asymptotically maintained random particle BGK solution processing on the initialized particle data.

[0023] The terminal 102 can be, but is not limited to, various desktop computers, laptops, smartphones, tablets, and IoT devices. The server 104 can be implemented using a standalone server or a server cluster consisting of multiple servers, or it can be a cloud server.

[0024] In one exemplary embodiment, such as Figure 2 As shown, a method for solving the BGK problem using asymptotically maintained random particles in a multi-component gas is provided. This method is executed by a computer device, specifically a terminal or server, or both. In this embodiment, the method is applied to... Figure 1 Taking server 104 as an example, the following steps are included: S1: Construct a multi-component gas random particle system based on the computational domain, and obtain the initial particle data of the multi-component gas random particle system. The initial particle data includes: component information, position information, velocity information, and energy information of each particle. The energy information includes: translational energy, rotational energy, and vibrational energy.

[0025] S2: Based on the velocity information and the position information, update the position information of each particle at different time steps during free transport to obtain the updated position information.

[0026] S3: Based on the updated position information, the component information, and the energy information, respectively calculate the macroscopic quantities of the components and the macroscopic quantities of the mixture of all particles in each computing unit in the computing domain.

[0027] S4: Calculate the relaxation time of the mixture based on the macroscopic quantities of the mixture, and construct the corresponding target distribution function for each component particle by combining the macroscopic quantities of the components.

[0028] S5: Based on the relaxation time of the mixture and the target distribution function, the multi-component BGK equation is discretized in time using the Crank-Nicolson scheme and the particle velocity is updated to obtain the particle velocity after the collision.

[0029] S6: Based on the energy information and the macroscopic quantities of the components, perform translational-rotational energy exchange and full-modal energy exchange on each particle in sequence to obtain new translational energy, rotational energy and vibrational energy.

[0030] S7: Based on the new translational energy, rotational energy and vibrational energy, the velocity of each particle after the collision is corrected for momentum conservation and energy conservation in sequence to obtain the corrected velocity of each particle.

[0031] S8: Use the corrected velocity of each particle as the velocity information, and repeat the process from step S2 to step S7 until the full-time flow simulation of the computational domain is completed.

[0032] Implementing steps S1 to S8 above enables unified and efficient simulation of multi-component mixed gases and multiple internal energy modes, taking into account both the asymptotic maintenance characteristics of near-continuous flow and the physical prediction accuracy of strong non-equilibrium flow, thereby improving the accuracy of numerical simulation under complex flow conditions.

[0033] As an optional implementation, step S4 specifically includes the following steps: S41: Based on the macroscopic quantities of the mixture, the transport parameters of the mixture are calculated; the transport parameters of the mixture include: the viscosity of the mixture, the thermal conductivity of the mixture, and the specific heat at constant pressure of the mixture.

[0034] S42: Calculate the Prandtl number of the mixture based on the transport parameters of the mixture.

[0035] S43: Calculate the relaxation time of the mixture based on the Prandtl number of the mixture.

[0036] S44: Based on the macroscopic quantities of the mixture and the macroscopic quantities of the components, construct the corresponding target distribution function for the particles of each component.

[0037] As an optional implementation, the target distribution function is a Maxwell distribution function, an ellipsoidal BGK (ES-BGK) distribution function, or a Shakhov-type BGK (S-BGK) distribution function.

[0038] As an optional implementation, step S5 specifically includes the following steps: S51: Based on the relaxation time of the mixture and the target distribution function, construct the multi-component BGK equation.

[0039] S52: The multi-component BGK equation is discretized in time using the Crank-Nicolson scheme to obtain the Crank-Nicolson time discretization result.

[0040] S53: Based on the Crank-Nicolson time discretization results, update the particle velocity according to the relationship between the time step and twice the mixture relaxation time to obtain the particle velocity after the collision.

[0041] S54: Based on the Crank-Nicolson time discretization results, the particle velocity is updated according to the relationship between the time step and twice the mixture relaxation time, and the particle velocity after the collision is obtained, specifically including the following two cases: (1) When the time step value is less than or equal to twice the mixture relaxation time value, the particle velocity is updated according to the Crank-Nicolson time discretization result to obtain the particle velocity after the collision.

[0042] (2) When the time step value is greater than twice the mixture relaxation time value, the particle velocity is sampled from the macroscopic non-equilibrium correction distribution and used as the particle velocity after the collision.

[0043] As an optional implementation, the macroscopic nonequilibrium correction distribution is preferably the Grad-13 distribution.

[0044] As an optional implementation, in step S7, the momentum conservation correction is to apply a uniform offset to the velocities of all particles; the energy conservation correction is to perform a uniform scaling process on the velocities of all particles.

[0045] In an exemplary embodiment, to illustrate the technical solutions provided in the embodiments of this application in detail, the following are provided: Figure 3 The BGK solution method for asymptotically maintained random particles in multi-component gases, as shown, has the following core steps in its implementation: Step 1: Construct and initialize a multi-component gas random particle system.

[0046] In this embodiment, a multi-component gas random particle system is established within the computational domain, and the composition, position, velocity, and energy information of each particle are recorded. The multi-component gas random particle system initializes the particle information according to the initial and boundary conditions required for computation. The energy information includes translational energy, rotational energy, and vibrational energy.

[0047] In this embodiment, the constructed multi-component gas random particle system is arranged within a preset computational domain. The system contains simulated particles corresponding to various gas components. Each particle fully stores independent component information (i.e., component information), spatial coordinates (i.e., position information), microscopic instantaneous velocity (i.e., velocity information), and three types of modal energy data (i.e., translational energy, rotational energy, and vibrational energy). This multi-component gas random particle system serves as the carrier for numerical simulation. It can perform free transport movement following the time step, and the computational unit statistically obtains the macroscopic quantities of the components and the mixture. This provides fundamental particle data support for solving the mixture relaxation time, constructing the target distribution function of each component, Crank-Nicolson discrete solution of the BGK equation, hierarchical modal energy exchange, and momentum and energy conservation correction throughout the entire process. Through iterative evolution, it fully reproduces the dynamic evolution process of multi-component gas non-equilibrium flow.

[0048] In this embodiment, before the simulation begins, global initial conditions are set. Within the computational domain, a multi-component initial particle field carrying components, positions, microscopic velocities, and translational, rotational, and vibrational multi-modal energy is generated according to the given incoming flow properties, component proportions, number density, temperature, and flow velocity, thus completing the flow field initialization. During the calculation, corresponding boundary conditions are applied to each boundary of the computational domain. Fixed-state incoming flow particles are continuously injected into the far-field inlet. The blunt cone solid wall uses a molecular diffuse reflection model to realize the exchange of particle momentum and energy. Particles that have passed through the boundary are directly removed from the outflow outlet. The symmetry axis adopts the mirror reflection rule. The initial conditions provide complete initial particle data for iterative calculation. Various boundary conditions constrain the particle increase, decrease, reflection, and exchange behavior, accurately reproducing the real flow environment outside the blunt cone and ensuring the stable evolution of the flow field during iteration.

[0049] Step 2: Free transport of particles.

[0050] In this embodiment, within each time step, the particle positions of each component particle are updated by free transport based on the current velocity. At the initial calculation time, a multi-component gas random particle system is first generated within the computational domain according to given initial and boundary conditions. For each particle, its component, position, velocity, and internal energy information should be recorded. Subsequently, at each time step... Within, a free transport process is performed on all particles, that is, based on the particle's current velocity. Update its spatial location It can be expressed as the following formula: (1).

[0051] in, The current particle position. The particle's current velocity. This represents the position of the updated particle.

[0052] Step 3: Calculate the macroscopic quantities of the multi-component mixture.

[0053] In this embodiment, within each computing unit, macroscopic quantities of the components and the mixture are calculated based on the velocities of each component particle. The macroscopic quantities of the components include component mass, component rotational temperature, and component vibrational temperature; the macroscopic quantities of the mixture include mixture pressure and mixture translational temperature. The statistical analysis of these macroscopic quantities can employ random interpolation or linear interpolation methods.

[0054] Step 4: Calculate the transport parameters and relaxation time of the mixture.

[0055] In this embodiment, the transport parameters of the mixture are calculated based on the macroscopic quantities of the mixture. These transport parameters should include at least the mixture viscosity, the mixture thermal conductivity, and the mixture specific heat at isobaric pressure. The relaxation time of the mixture is determined based on the mixture viscosity, the mixture pressure, and the Prandtl number. The Prandtl number is calculated from the mixture viscosity, the mixture thermal conductivity, and the mixture specific heat at isobaric pressure.

[0056] When performing macroscopic quantity statistics on each component particle within each computational unit, if it is necessary to construct an ES-BGK model as... The target distribution and Grad-13 distribution at time are used as If the macroscopic nonequilibrium correction distribution at that time is considered, then at least the translational temperature of the mixture should be statistically analyzed. ,pressure Unscented stress tensor Heat flux and component mass Rotation temperature With vibration temperature Furthermore, the transport parameters of the mixture calculated from these macroscopic quantities include the viscosity of the mixture. thermal conductivity Compared with specific heat at constant pressure The Prandtl number of the mixture can be calculated using these transport parameters. With the relaxation time of the mixture The calculation formula is: (2).

[0057] Thus, for the simulation of particle collision processes in the Crank-Nicolson time-discrete scheme, when The particle velocity is updated according to the Crank-Nicolson time discretization result, when Particle velocity sampling is performed from the Grad-13 distribution.

[0058] Step 5: Construct the multi-component objective distribution function.

[0059] In this embodiment, for each component, a target distribution function is constructed based on the macroscopic quantity of the mixture. The target distribution function can be a Maxwell distribution function, an ellipsoidal BGK distribution function, or a Shakhov-type BGK distribution function.

[0060] Step 6: Crank-Nicolson time discretization and particle collision.

[0061] In this embodiment, the multi-component BGK equation is discretized in time using the Crank-Nicolson scheme. The multi-component BGK equation is defined as follows: (3).

[0062] in, Components The original distribution function, Components The target distribution function, Indicates time, The particle's current velocity. The relaxation time of the mixture. For the partial derivative sign, This is the spatial gradient operator.

[0063] In this embodiment, Crank-Nicolson is a second-order precision, implicit time discretization scheme used for numerically solving the time term of partial differential equations. Crank-Nicolson time discretization introduces an auxiliary distribution function. and Implementation. The auxiliary distribution function. and Defined as follows: (4).

[0064] in, The first auxiliary distribution function is based on the implicit auxiliary quantity in the first half step, derived from the original distribution. It is obtained by back-stepping half-step relaxation towards the equilibrium state and used for implicit term discretization in the Crank-Nicolson scheme; The second auxiliary distribution function is based on the implicit auxiliary quantity in the second half step, derived from the original distribution. The half-step relaxation advance towards the equilibrium state yields the component s-particle distribution function, which characterizes the Crank-Nicolson scheme discrete update and is used to update the particle velocity, outputting the particle velocity after the collision. For time step.

[0065] In this embodiment, the Crank-Nicolson time discretization result is expressed as follows: (5).

[0066] when At that time, the particle velocity is updated according to the Crank-Nicolson time discretization result; when At that time, the particle velocity was sampled separately from the Grad-13 distribution.

[0067] Step 7: Multimodal energy exchange.

[0068] In this embodiment, for each component, translational-rotational energy exchange and full-modal energy exchange are performed sequentially on the energy of the translational, rotational, and vibrational modes to obtain new translational, rotational, and vibrational energies. The translational-rotational energy exchange involves relaxing the current rotational energy to the target rotational energy using rotational relaxation time, and updating the translational energy according to energy conservation. The full-modal energy exchange involves relaxing the current vibrational energy to the target vibrational energy using vibrational relaxation time, and updating the translational and rotational energies proportionally according to energy conservation. The rotational and vibrational relaxation times are calculated using the component rotational collision number and component vibrational collision number from the molecular model parameters, respectively. The target rotational energy is calculated from the current translational energy and the current rotational energy, and the target vibrational energy is calculated from the current translational energy, the current rotational energy, and the current vibrational energy.

[0069] In this embodiment, when performing modal energy exchange on each component particle, for each component, energy exchange between translation and rotation is first performed. This is based on the currently recorded translational energy of the particle. With rotational energy Determine the target translational-rotational temperature It can be expressed as the following formula: (6).

[0070] in, , The target translational-rotational temperatures are respectively Translational and rotational energy.

[0071] Subsequently, the rotational energy relaxes towards the target state according to the component rotational relaxation time, as expressed by the following equation: (7).

[0072] in, To adjust the relaxation time, The updated rotational energy is then used, and the translational energy is adjusted accordingly based on energy conservation. Further, full-modal energy exchange is performed, and the target full-modal equilibrium temperature is defined. It can be expressed as the following formula: (8).

[0073] in, , , These represent the target full-modal equilibrium temperatures. Translational energy, rotational energy, and vibrational energy. This represents the vibrational energy recorded by the current particle.

[0074] The vibrational energy relaxes towards the target state according to the component vibration relaxation time, as expressed by the following formula: (9).

[0075] in, Let be the vibration relaxation time. This is the updated vibrational energy. While the vibrational energy relaxes towards the target state according to the component vibrational relaxation times, the translational and rotational kinetic energies are adjusted accordingly based on the law of conservation of energy.

[0076] Step 8: Momentum conservation correction and energy conservation correction.

[0077] In this embodiment, the velocities of all particles are sequentially corrected for momentum and energy to obtain the corrected velocities of each particle. The momentum correction is a primary correction of the particle velocity, adjusting the particle velocity to make the current macroscopic average velocity consistent with that before the collision. The energy correction is a secondary correction of the particle velocity, uniformly scaling the particle velocity based on the translational energy before and after the collision to make the total energy consistent with that before the collision.

[0078] At the end of each time step, conservation corrections are sequentially performed on the multi-component gas random particle system. First, momentum conservation corrections are performed by applying a uniform offset to the velocities of all particles, ensuring that the updated macroscopic average velocity is consistent with that before the collision, as expressed in the following equation: (10).

[0079] in, This is the particle velocity after momentum conservation correction. This represents the particle velocity before the momentum conservation correction. The macroscopic average velocity before the particle collision. This is the macroscopic average velocity before the momentum conservation correction.

[0080] Then, an energy conservation correction is performed. By uniformly scaling the velocities of all particles, the sum of translational energy and internal energy satisfies energy conservation, expressed as follows: (11).

[0081] in, This is the particle velocity after energy conservation correction. This is the macroscopic average velocity after momentum conservation correction. This is the current translational temperature after correction for momentum conservation. This is the translational temperature before the momentum conservation correction.

[0082] Through the above steps, the particle completes the entire process of this time step. In the next time step, it returns to step 2 and starts a new cycle, re-executing the steps from free transport to momentum and energy conservation correction, until the full-time flow simulation in the computational domain is completed.

[0083] In this embodiment of the application, the basic structural parameters of the 70° blunt cone are as follows: Figure 4 As shown, the outer diameter of the blunt cone is 50.00 mm. The incoming flow is assumed to be a N2-O2-NO mixture, with N2, O2, and NO components in proportions of 50%, 25%, and 25%, respectively. The temperature is 13.3 K, the velocity is 1502 m / s (Mach number Ma=20), and the flow is perpendicular to the windward side. The number density of the mixture is... .

[0084] Figure 5 Comparison of translational temperature contour maps in the flow field between the method of this application and the DSMC method; Figure 6 Comparison contour plots of rotational temperature in the flow field between the method of this application and the DSMC method; Figure 7 Comparison of vibration temperature in the flow field between the method of this application and the DSMC method; Figure 8 This is a schematic diagram comparing the modal temperatures in front of the stagnation point on the axis of symmetry of the method in this application and the DSMC method. Indicates translational temperature. Indicates rotational temperature. Indicates the vibration temperature; Figure 9 This is a schematic diagram comparing the heat flux density and pressure distribution on the blunt cone surface using the method of this application and the DSMC method. Represents heat flux density, It indicates pressure. (Comprehensive) Figures 5 to 9 It can be seen that there is a significant shock wave structure and strong non-equilibrium characteristics in the flow field, especially in the shock layer and near the stagnation point. The gas is in a multi-modal thermal non-equilibrium state. Without considering the multi-component effects and modal energy exchange processes, it is difficult to accurately describe the momentum and energy coupling relationship between different components, and it is also impossible to correctly predict the evolution characteristics of the temperature of each mode in the shock layer. The embodiments of this application introduce a macroscopic quantity of multi-component mixing and a unified relaxation mechanism, so that the momentum and energy of different component particles can be coupled in a unified mixture state. At the same time, through translational-rotational energy exchange and full-modal energy exchange processes, the energy of each mode can gradually tend to thermal equilibrium. The simulation results are in good agreement with the results of the DSMC method, indicating that the embodiments of this application can effectively characterize the temperature distribution and energy evolution of each mode in non-equilibrium flow.

[0085] This application extends the Crank-Nicolson scheme of random particle BGK from monatomic gases to multi-component gas systems, enabling the handling of mixing and transport processes between different components. A unified multi-component BGK relaxation process is constructed by considering macroscopic quantities of the mixture, transport parameters, and relaxation time, allowing momentum and energy coupling between particles in a unified mixture state. By introducing translational-rotational energy exchange and full-modal energy exchange processes, the non-equilibrium evolution of internal energy modes such as rotation and vibration can be uniformly described. Momentum and energy conservation corrections reduce the impact of random sampling errors on macroscopic conserved quantities, improving the stability and physical consistency of the calculation results.

[0086] 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 10 As 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 initialization particle data. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When executed by the processor, the computer program implements a BGK solution method for asymptotically maintained random particles in a multi-component gas.

[0087] Figure 10 The structures shown are merely block diagrams of some structures related to the present application and do 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 shown in the figures, or combine certain components, or have different component arrangements. In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0088] 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.

[0089] 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.

[0090] 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 related data must comply with relevant regulations and be authorized by the owner of the corresponding device.

[0091] Those skilled in the art will understand that all or part of the processes in 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. When executed, the computer program can include the processes of the embodiments described above. 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).

[0092] 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, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0093] 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.

[0094] 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 method for solving the BGK problem of asymptotically maintained random particles in a multi-component gas, characterized in that, include: S1: Construct a multi-component gas random particle system based on the computational domain, and obtain the initial particle data of the multi-component gas random particle system; The initial particle data includes: component information, position information, velocity information and energy information of each particle, and the energy information includes: translational energy, rotational energy and vibrational energy; S2: Based on the velocity information and the position information, update the position information of each particle at different time steps during free transport to obtain the updated position information; S3: Based on the updated position information, the component information, and the energy information, respectively calculate the macroscopic quantities of the components and the macroscopic quantities of the mixture of all particles in each computing unit in the computing domain; S4: Calculate the relaxation time of the mixture based on the macroscopic quantities of the mixture, and construct the corresponding target distribution function for each component particle by combining the macroscopic quantities of the components; S5: Based on the relaxation time of the mixture and the target distribution function, the multi-component BGK equation is discretized in time using the Crank-Nicolson scheme and the particle velocity is updated to obtain the particle velocity after the collision. S6: Based on the energy information and the macroscopic quantities of the components, perform translational-rotational energy exchange and full-modal energy exchange on each particle in sequence to obtain new translational energy, rotational energy and vibrational energy; S7: Based on the new translational energy, rotational energy and vibrational energy, the velocity of each particle after the collision is corrected for momentum conservation and energy conservation in sequence to obtain the corrected velocity of each particle. S8: Use the corrected velocity of each particle as the velocity information, and repeat the process from step S2 to step S7 until the full-time flow simulation of the computational domain is completed.

2. The method for solving the BGK problem for asymptotically maintained random particles in a multi-component gas according to claim 1, characterized in that, Step S4 specifically includes: Based on the macroscopic quantities of the mixture, the transport parameters of the mixture are calculated; the transport parameters of the mixture include: the viscosity of the mixture, the thermal conductivity of the mixture, and the specific heat at constant pressure of the mixture. The Prandtl number of the mixture is calculated based on the transport parameters of the mixture. The relaxation time of the mixture is calculated based on the Prandtl number of the mixture. Based on the macroscopic quantities of the mixture and the macroscopic quantities of the components, a corresponding target distribution function is constructed for the particles of each component.

3. The method for solving the BGK problem for asymptotically maintained random particles in a multi-component gas according to claim 1 or 2, characterized in that, The target distribution function is a Maxwell distribution function, an ellipsoidal BGK distribution function, or a Shakhov-type BGK distribution function.

4. The method for solving the BGK problem for asymptotically maintained random particles in a multi-component gas according to claim 1, characterized in that, Step S5 specifically includes: Based on the relaxation time of the mixture and the target distribution function, a multi-component BGK equation is constructed; The multi-component BGK equation was discretized in time using the Crank-Nicolson scheme to obtain the Crank-Nicolson time discretization result; Based on the Crank-Nicolson time discretization results, the particle velocity is updated according to the relationship between the time step and twice the mixture relaxation time, and the particle velocity after the collision is obtained.

5. The method for solving the BGK problem for asymptotically maintained random particles in a multi-component gas according to claim 4, characterized in that, The multi-component BGK equation is as follows: ； in, Components The original distribution function, Components The target distribution function, Indicates time, The particle's current velocity. The relaxation time of the mixture. For the partial derivative sign, For spatial gradient operators; Time discretization based on the Crank-Nicolson scheme is achieved by introducing an auxiliary distribution function, the expression of which is: ； in, Let the first auxiliary distribution function be based on the implicit auxiliary quantity in the first half step. The second auxiliary distribution function is based on the implicit auxiliary quantity in the second half step. For time step; The Crank-Nicolson time discretization result is expressed as follows: ； Based on the Crank-Nicolson time discretization results, the particle velocity is updated according to the relationship between the time step and twice the mixture relaxation time, resulting in the post-collision particle velocity, specifically including: when At that time, the particle velocity is updated according to the Crank-Nicolson time discretization result to obtain the particle velocity after the collision; when At that time, the particle velocity is updated by sampling from the macroscopic non-equilibrium correction distribution to obtain the particle velocity after the collision.

6. The method for solving the BGK problem for asymptotically maintained random particles in a multi-component gas according to claim 5, characterized in that, The macroscopic nonequilibrium correction distribution adopts the Grad-13 distribution.

7. The method for solving the BGK problem for asymptotically maintained random particles in a multi-component gas according to claim 1, characterized in that, The momentum conservation correction is applied to the velocities of all particles by a uniform offset, expressed as: ； in, This is the particle velocity after momentum conservation correction. This represents the particle velocity before the momentum conservation correction. The macroscopic average velocity before the particle collision. The macroscopic average velocity before momentum conservation correction; The energy conservation correction is a uniform scaling of the velocities of all particles, expressed as: ； in, This is the particle velocity after energy conservation correction. This is the macroscopic average velocity after momentum conservation correction. This is the current translational temperature after correction for momentum conservation. This is the translational temperature before the momentum conservation correction.

8. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that the processor executes the computer program to implement the BGK solution method for asymptotically maintained random particles in multi-component gases as described in any one of claims 1-7.

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 BGK solution method for asymptotically maintained random particles in multi-component gases as described in any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the BGK solution method for asymptotically maintained random particles in multi-component gases as described in any one of claims 1-7.

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