A method, apparatus, device, and medium for simulating collisionless plasma flow

Abstract

The application discloses a kind of simulation methods, devices, equipment and media of non-collision plasma flow, it is related to plasma physics technical field, including: using non-steady time splitting method Vlasov equation is split into position space convection equation and velocity space convection equation;Using Fourier spectrum method to solve electric field Poisson equation, obtain electric field intensity value;Electric field intensity is determined as the input parameter of velocity space convection equation, and velocity space convection equation is solved using Fourier spectrum method;Using finite volume method to solve position space convection equation, obtain the particle distribution function of next time;On the velocity space, the moment of particle distribution function is integrated to obtain flow field macro parameter, whether to reach flow field convergence condition is judged, otherwise jump to electric field Poisson equation solving step and iteratively cycle.This method can improve the solving speed for non-collision plasma flow problem.

Description

Technical Field

[0001] This invention relates to the field of plasma physics, and in particular to a method, apparatus, device, and medium for simulating collision-free plasma flow. Background Technology

[0002] The plasma plume generated by Hall thrusters can cause thrust vector shifts, spacecraft contamination, and communication interference. To assess the impact of the plume on spacecraft components, plasma flow simulation is essential. Magnetohydrodynamics (MHD) systems primarily consider plasmas in multi-particle systems composed of various freely moving charged particles. In the fluid description of this system, each charged particle system has its own unique set of flow parameters, such as density and temperature. Due to the non-uniform spatial distribution of charge among the charged particles, a self-generated electric field is generated. Simultaneously, the flow of charged fluid elements generates self-generated currents and magnetic fields at spatial points. These electric and magnetic fields, in turn, influence the motion of the charged fluid elements through Coulomb and Lorentz forces. Ultimately, the state of the charged fluid and the distribution of its self-generated electric and magnetic fields can be self-consistently solved by simultaneously solving the fluid dynamics equations (NS equations) and Maxwell's electromagnetic equations.

[0003] However, magnetohydrodynamics treats plasma as a continuous conductive fluid, making it unable to handle collision-free plasma flow. The BGK-Maxwell equations can describe both equilibrium and non-equilibrium plasma flow; in the absence of collisions, the BGK-Maxwell equations become the Vlasov-Maxwell equations. The Unified Gas Kinetic Scheme (UGKS) uses the finite volume method to solve the Vlasov-Maxwell equations, which can handle collision-free plasma flow, but the Maxwell equations describing the electromagnetic field are complex, leading to slow computation and low efficiency.

[0004] As can be seen from the above, improving the solution speed for collisionless plasma flow problems is an urgent problem to be solved. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a method, apparatus, device, and medium for simulating collisionless plasma flow, which can improve the solution speed for collisionless plasma flow problems. The specific solution is as follows: In a first aspect, this application provides a method for simulating collision-free plasma flow, comprising: The Vlasov-Poisson equations are determined to describe the particle motion of the target collisionless plasma. Based on the Vlasov equations in the Vlasov-Poisson equations, the current time step is split using the time splitting method to obtain the position space convection motion equations and the velocity space convection motion equations. The target collisionless plasma is plasma generated by the Hall electric propulsion engine in the spacecraft. The initial particle distribution function of the plasma initial state is determined, and the Poisson equation in the Vlasov-Poisson equation system is solved using the Fourier spectral method to obtain the electric field intensity. The electric field strength and the initial particle distribution function are input into the velocity space convection equation and solved using the Fourier spectrum method to obtain the particle distribution function. Based on the particle distribution function, the spatial convection motion equations are solved using the finite volume method to obtain the target particle distribution function at the next moment. The target particle distribution function is integrated and moments are calculated in velocity space to obtain macroscopic flow field parameters. Based on the macroscopic flow field parameters, it is determined whether the convergence condition of the target flow field is met. If the target flow field convergence condition is met, the flow process of the target collisionless plasma generated by the Hall electric propulsion engine is simulated based on the macroscopic parameters of the flow field.

[0006] Optionally, the step of splitting the current time step based on the Vlasov equations in the Vlasov-Poisson equations system and using the time splitting method to obtain the position space convection equations and velocity space convection equations includes: The Vlasov equations in the Vlasov-Poisson equation system are split into the current time step particle motion using the non-constant time splitting method to obtain the position space convection motion equation corresponding to the particle position movement and the velocity space convection motion equation corresponding to the particle velocity change.

[0007] Optionally, determining the initial particle distribution function of the plasma initial state and solving the Poisson equation in the Vlasov-Poisson equations using the Fourier spectral method to obtain the electric field intensity includes: The initial particle distribution function of the plasma initial state is determined, and the initial particle distribution function is integrated in the discrete velocity domain to obtain the particle number density; The particle number density is subjected to a Fourier transform to obtain the first Fourier coefficient. The first Fourier coefficient is then substituted into the Poisson equation in the Vlasov-Poisson equation set to obtain the second Fourier coefficient corresponding to the electric field strength. The electric field strength is obtained by performing an inverse Fourier transform on the second Fourier coefficient.

[0008] Optionally, the step of inputting the electric field intensity and the initial particle distribution function into the velocity space convection equation and solving it using the Fourier spectrum method to obtain the particle distribution function includes: The initial particle distribution function is subjected to a Fourier transform to obtain the third Fourier coefficients; The third Fourier coefficient is substituted into the velocity space convection equation to obtain the corresponding target equation. The target Fourier coefficient at the next moment is determined based on the analytical solution corresponding to the target equation, and the inverse Fourier transform is performed on the target Fourier coefficient to obtain the particle distribution function.

[0009] Optionally, the step of solving the spatial convection motion equations based on the particle distribution function and using the finite volume method to obtain the target particle distribution function at the next moment includes: Based on the particle distribution function, the position space convection motion equations are solved using the second-order MUSCL, Minmod limiter, and finite volume method to obtain the target particle distribution function at the next moment.

[0010] Optionally, the step of solving the position space convection motion equations based on the particle distribution function and using the second-order MUSCL, Minmod limiter, and finite volume method to obtain the target particle distribution function at the next moment includes: The position space corresponding to the position space convection motion equation is discretized using the finite volume method to obtain each grid, and the discrete equation corresponding to the position space convection motion equation is determined. Based on the particle distribution function and using a second-order MUSCL and Minmod limiter, the flux of particles in the plasma through each grid is determined, and the flux is used to determine the right-hand side of the discrete equation. Based on the distribution information corresponding to the right-hand term and the grid, and using the second-order Runge-Kutta method for time-progression solution, the target particle distribution function at the next time step is obtained.

[0011] Optionally, after determining whether the target flow field convergence condition is met based on the macroscopic parameters of the flow field, the method further includes: If the target flow field convergence condition is not met, then proceed to the step of splitting the current time step based on the Vlasov equation in the Vlasov-Poisson equation set and using the time splitting method, until the target flow field convergence condition is met.

[0012] Secondly, this application provides a device for simulating collision-free plasma flow, comprising: The equation splitting module is used to determine the Vlasov-Poisson equations describing the particle motion of the target collisionless plasma. Based on the Vlasov equations in the Vlasov-Poisson equations, the current time step is split using the time splitting method to obtain the position space convection motion equations and velocity space convection motion equations; wherein, the target collisionless plasma is plasma generated by the Hall electric propulsion engine in the spacecraft. The initial function determination module is used to determine the initial particle distribution function of the plasma initial state and to solve the Poisson equation in the Vlasov-Poisson equation system using the Fourier spectral method to obtain the electric field intensity. The equation solving module is used to input the electric field intensity and the initial particle distribution function into the velocity space convection motion equation, and solve it using the Fourier spectrum method to obtain the particle distribution function; The objective function determination module is used to solve the position space convection motion equation based on the particle distribution function and using the finite volume method to obtain the target particle distribution function at the next moment. The parameter judgment module is used to integrate and calculate the moment of the target particle distribution function in the velocity space to obtain the macroscopic parameters of the flow field, and to determine whether the convergence condition of the target flow field is met based on the macroscopic parameters of the flow field. The flow process simulation module is used to simulate the flow process of the target collisionless plasma generated by the Hall electric propulsion engine based on the macroscopic parameters of the flow field if the target flow field convergence condition is met.

[0013] Thirdly, this application provides an electronic device, comprising: Memory, used to store computer programs; A processor is used to execute the computer program to implement the aforementioned method for simulating collision-free plasma flow.

[0014] Fourthly, this application provides a computer-readable storage medium for storing a computer program, wherein the computer program, when executed by a processor, implements the aforementioned method for simulating collision-free plasma flow.

[0015] This application identifies the Vlasov-Poisson equations for describing the particle motion of a target collisionless plasma. Based on the Vlasov equations in the Vlasov-Poisson equations, the current time step is split using the time splitting method to obtain the position space convection equations and velocity space convection equations. The target collisionless plasma is plasma generated by a Hall electric propulsion engine in a spacecraft. The initial particle distribution function of the plasma's initial state is determined, and the Poisson equations in the Vlasov-Poisson equations are solved using the Fourier spectral method to obtain the electric field intensity. The electric field strength and the initial particle distribution function are input into the velocity space convection equations and solved using the Fourier spectrum method to obtain the particle distribution function. Based on the particle distribution function, the position space convection equations are solved using the finite volume method to obtain the target particle distribution function at the next moment. The target particle distribution function is integrated and moments are obtained in velocity space to obtain macroscopic flow field parameters. Based on the macroscopic flow field parameters, it is determined whether the target flow field convergence condition is met. If the target flow field convergence condition is met, the flow process of the target collisionless plasma generated by the Hall electric propulsion engine is simulated based on the macroscopic flow field parameters.

[0016] As can be seen from the above, this application selects the Vlasov-Poisson equations as the core model to describe the coupling relationship between the target collisionless plasma particle motion and the self-generated electric field generated by the Hall electric propulsion engine in the spacecraft. The Vlasov equations are split into position space convection and velocity space convection equations using the time splitting method, which greatly reduces the difficulty of solving the problem. An initial particle distribution function is determined to complete the state initialization of the Hall electric propulsion plasma simulation. The electric field intensity can be quickly obtained by solving the Poisson equation using the Fourier spectral method. The electric field intensity and the initial particle distribution function are input into the velocity space convection motion equation to realize the real-time coupling iteration of particle motion and electric field. The Fourier spectral method is used to solve the equation to obtain the particle distribution with high accuracy at the current time step. Based on the particle distribution function, the position space convection motion equation is solved using the finite volume method to obtain the target particle distribution function at the next time step. The velocity space integral of the target particle distribution function is performed to obtain the distance, transforming the microscopic particle distribution into macroscopic flow field parameters such as density, temperature, flow velocity, and current density. Convergence judgment is performed based on the macroscopic parameters to achieve adaptive stopping iteration. In this way, the complete flow process of collisionless plasma in a Hall electric propulsion engine can be reproduced based on convergent macroscopic parameters, which not only solves the simulation problem of collisionless plasma, but also achieves high-speed computational results. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0018] Figure 1 This is a flowchart of a method for simulating collision-free plasma flow disclosed in this application; Figure 2 This is a comparative schematic diagram of an electric field attenuation curve disclosed in this application; Figure 3 This is a schematic diagram of a conservation quantity curve disclosed in this application; Figure 4 This is a schematic diagram of the structure of a collision-free plasma flow simulation device disclosed in this application; Figure 5 This is a structural diagram of an electronic device disclosed in this application. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Currently, the unified gas kinetic scheme uses the finite volume method to solve the Vlasov-Maxwell equations, which can handle collisionless plasma flow. However, the Maxwell equations describing the electromagnetic field are complex, leading to slow computation speed and low efficiency. Therefore, this application provides a method for simulating collisionless plasma flow. Based on convergent macroscopic parameters, it can reproduce the complete flow process of collisionless plasma in a Hall electric propulsion engine, solving the simulation challenges of collisionless plasma while achieving high-speed computation.

[0021] See Figure 1 As shown, this embodiment of the invention discloses a method for simulating collisionless plasma flow, comprising: Step S11: Determine the Vlasov-Poisson equations for describing the particle motion of the target collisionless plasma. Based on the Vlasov equations in the Vlasov-Poisson equations, split the current time step using the time splitting method to obtain the position space convection motion equation and the velocity space convection motion equation; wherein, the target collisionless plasma is plasma generated by the Hall electric propulsion engine in the spacecraft.

[0022] In this embodiment, the Vlasov-Poisson equations for describing the particle motion of a collisionless plasma are first determined. The Vlasov-Poisson equations include the Vlasov equations for describing particle motion and the Poisson equations for describing the relationship between the electric field and particle density. The formulas corresponding to the Vlasov equations are as follows: ; in, is the particle distribution function of the plasma; For time; The velocity of the plasma is a vector, having both magnitude and direction. Spatial location; This represents the electric field intensity vector, i.e., the electric force generated by the plasma itself. The corresponding formula for the Poisson equation is as follows: ; in, The electric field intensity vector; Spatial location; It is the electric potential; This represents the particle number density.

[0023] Understandably, taking a one-dimensional flow problem as an example, since computers can only process discrete data, space, velocity, and time are divided into grids. The physical space... Speed ​​space The subscripts are j and k, and the corresponding grid points are as follows: ; ; ; in, For discrete grid points in physical space; The simulated spatial range, such as the length L of the engine passage; The physical space grid step size; The number of grid cells in the physical space; For discrete grid points in velocity space; The simulated speed range; The number of grids in the velocity space; The velocity space grid step size; For discrete time steps, i.e., the time of the nth time step; This represents the total number of time steps. This is the time step size, i.e., the interval between adjacent time steps; This represents the time range for the simulation.

[0024] Furthermore, the Vlasov equations are split using an unsteady time-split method to obtain two independent equations concerning positional movement and velocity variation: the positional convection equation and the velocity convection equation. The positional convection equation is shown below: ; in, is the particle distribution function of the plasma; For time; This is a one-dimensional velocity, a scalar quantity with no direction. The location space is one-dimensional. The equations of convection motion in the velocity space are as follows: ; in, is the particle distribution function of the plasma; For time; One-dimensional velocity; The electric field strength is one-dimensional.

[0025] Specifically, the step of splitting the Vlasov equations in the Vlasov-Poisson equation set into the current time step using the time splitting method to obtain the position space convection motion equations and velocity space convection motion equations includes: using the undetermined time splitting method to split the Vlasov equations in the Vlasov-Poisson equation set into the particle motion of the current time step to obtain the position space convection motion equations corresponding to particle position movement and the velocity space convection motion equations corresponding to particle velocity change.

[0026] Step S12: Determine the initial particle distribution function of the plasma initial state, and use the Fourier spectral method to solve the Poisson equation in the Vlasov-Poisson equation set to obtain the electric field intensity.

[0027] In this embodiment, Fourier series expansions are performed on the electric field strength and the particle number density, respectively. The expansion corresponding to the electric field strength is as follows: ; in, Let x be the electric field strength to be solved, which varies with position x and time t. This represents the total number of Fourier modes in the spatial direction. The Fourier coefficients of the electric field strength are called the electric field coefficients. Number the Fourier modes in the spatial direction; This represents the total length of the space. The unit is the imaginary number. The expansion of the particle number density is as follows: ; in, The particle number density varies with position x and time t; This represents the total number of Fourier modes in the spatial direction. The Fourier coefficients of the particle number density; Number the Fourier modes in the spatial direction; This represents the total length of the space. It is the imaginary unit.

[0028] It is understandable that substituting the two expansions above into the Poisson equation yields the following formula: ; in, This represents the total number of Fourier modes in the spatial direction. Number the Fourier modes in the spatial direction; This represents the total length of the space. The imaginary unit; The Fourier coefficients of the electric field strength are called the electric field coefficients. Here are the Fourier coefficients for the particle number density. Solving the above formula yields the Fourier coefficients corresponding to the electric field strength. Performing an inverse Fourier transform on these coefficients yields the electric field strength of the plasma at the current time step.

[0029] Specifically, determining the initial particle distribution function of the plasma initial state and solving the Poisson equation in the Vlasov-Poisson equation system using the Fourier spectrum method to obtain the electric field intensity includes: determining the initial particle distribution function of the plasma initial state and integrating the initial particle distribution function in the discrete velocity domain to obtain the particle number density; performing a Fourier transform on the particle number density to obtain the first Fourier coefficient; substituting the first Fourier coefficient into the Poisson equation in the Vlasov-Poisson equation system to obtain the second Fourier coefficient corresponding to the electric field intensity; and performing an inverse Fourier transform on the second Fourier coefficient to obtain the electric field intensity.

[0030] Step S13: Input the electric field strength and the initial particle distribution function into the velocity space convection equation and solve it using the Fourier spectrum method to obtain the particle distribution function.

[0031] In this embodiment, after determining the initial particle distribution function, a Fourier series expansion is performed on the initial particle distribution function to obtain the third Fourier coefficient, and the corresponding formula is as follows: ; in, Let the initial particle distribution function be... Let J be the coordinates of the center position of the j-th spatial grid. For speed, For time; For the first Fourier coefficients of each mode; The imaginary unit; This represents the total length of the speed range; This represents the velocity offset relative to the starting point. Let be the total number of Fourier modes in the velocity direction. Substituting the above expansion into the velocity-space convection equation, we obtain the following equation: ; in, Let J be the coordinates of the center position of the j-th spatial grid. For speed, For time; This represents the total number of Fourier modes in the velocity direction. The imaginary unit; Number the Fourier modes in the velocity direction; This refers to the time corresponding to the nth time step; For the first Fourier coefficients of each mode; This represents the total length of the speed range; This represents the velocity offset relative to the starting point.

[0032] In this embodiment, since the equation is linear, the coefficients are equal, and the above equation can be simplified to: ; in, For the first Fourier coefficients of each mode; The coordinates of the center position of the j-th spatial grid; For time; The imaginary unit; Number the Fourier modes in the velocity direction; This represents the total length of the speed range; Let be the one-dimensional electric field strength. The simplified equation above has an analytical solution, and the corresponding formula is as follows: ; in, For the first Fourier coefficients of each mode; The coordinates of the center position of the j-th spatial grid; This refers to the time corresponding to the nth time step; This is the time corresponding to the (n+1)th time step; The imaginary unit; Number the Fourier modes in the velocity direction; This represents the total length of the speed range; The electric field strength is one-dimensional.

[0033] Specifically, the step of inputting the electric field strength and the initial particle distribution function into the velocity space convection equation and solving it using the Fourier spectrum method to obtain the particle distribution function includes: performing a Fourier transform on the initial particle distribution function to obtain a third Fourier coefficient; substituting the third Fourier coefficient into the velocity space convection equation to obtain a corresponding target equation; determining the target Fourier coefficient at the next moment based on the analytical solution corresponding to the target equation; and performing an inverse Fourier transform on the target Fourier coefficient to obtain the particle distribution function.

[0034] Step S14: Based on the particle distribution function, solve the spatial convection motion equation using the finite volume method to obtain the target particle distribution function at the next moment.

[0035] In this embodiment, after obtaining the particle distribution function, the spatial convection motion equations are solved based on the particle distribution function using the finite volume method. Specifically, the spatial location is divided into a uniform grid, and the spatial convection motion equations are discretized to obtain discrete equations. The formulas corresponding to the discrete equations are as follows: ; in, Let be the particle distribution function for the j-th spatial grid and the k-th velocity grid; For time; Let be the right-hand side term of the discrete equation; wherein the formula corresponding to the right-hand side term is as follows: ; ; in, For the right-hand side of the discrete equation; This represents the spatial grid step size; Let f be the particle flux corresponding to the k-th velocity grid on the grid boundary line between position grid j and grid + 1; The velocity value of the k-th velocity grid; This indicates that the particle is moving to the right, and the particle distribution on the left side of the mesh interface is taken. For flux; conversely, This indicates that the particle is moving to the left, and the particle distribution on the right side of the mesh interface is taken. For flux.

[0036] Understandably, the particle distribution at the mesh interface can be reconstructed using a second-order MUSCL and a Minmod limiter, with the following formula: ; ; in, The particle distribution on the left side of the mesh interface; The particle distribution on the right side of the mesh interface; Let be the particle distribution function for the j-th spatial grid and the k-th velocity grid; The coordinates of the center position of the j-th spatial grid; This is the function corresponding to the Minmod limiter. To ensure time accuracy, a second-order Runge-Kutta method is used to advance the time step to obtain the particle distribution function of the plasma, and the corresponding formula is as follows: ; ; in, It is an intermediate transitional distribution; Let n be the current time, the nth Location grid, first Particle distribution in the velocity grid; For the spatial and velocity grid numbers; The target side term of the discrete equation; This is the target particle distribution function for the next time step.

[0037] Specifically, the step of solving the position space convection motion equation based on the particle distribution function and using the finite volume method to obtain the target particle distribution function at the next moment includes: solving the position space convection motion equation based on the particle distribution function and using a second-order MUSCL, a Minmod limiter, and the finite volume method to obtain the target particle distribution function at the next moment.

[0038] Specifically, the step of solving the position space convection motion equations based on the particle distribution function using a second-order MUSCL, Minmod limiter, and finite volume method to obtain the target particle distribution function at the next time step includes: discretizing the position space corresponding to the position space convection motion equations using the finite volume method to obtain each grid and determining the discrete equations corresponding to the position space convection motion equations; determining the flux of particles in the plasma flowing through each grid based on the particle distribution function using a second-order MUSCL and Minmod limiter, and using the flux to determine the right-hand side terms of the discrete equations; and performing time-progression solving based on the right-hand side terms and the distribution information corresponding to the grids using a second-order Runge-Kutta method to obtain the target particle distribution function at the next time step.

[0039] Step S15: Integrate the target particle distribution function in velocity space to obtain the macroscopic parameters of the flow field, and determine whether the convergence condition of the target flow field is met based on the macroscopic parameters of the flow field.

[0040] In this embodiment, after obtaining the target particle distribution function, the target particle distribution function is integrated and moments are calculated in velocity space to compress the velocity dimension, transforming the microscopic particle statistical information into macroscopic flow information, thereby obtaining macroscopic flow field parameters. These macroscopic flow field parameters may include particle number density, macroscopic flow velocity, plasma temperature, flow pressure, and current density. The macroscopic flow field parameters at the current time step are compared with those at the previous time step. If the difference between the two parameters is less than a preset threshold, it indicates that the flow field is no longer changing, and the convergence condition of the target flow field is met. The preset threshold can be set according to actual conditions.

[0041] Understandably, if the target flow field convergence condition is not met, the target particle distribution function will be used as the initial particle distribution function for the next iteration. Then, the process jumps to the step of splitting the current time step based on the Vlasov equations in the Vlasov-Poisson equations system using the time splitting method, achieving a complete time step iteration until the target flow field convergence condition is met. Specifically, after determining whether the target flow field convergence condition is met based on the macroscopic flow field parameters, the process further includes: if the target flow field convergence condition is not met, jumping to the step of splitting the current time step based on the Vlasov equations in the Vlasov-Poisson equations system using the time splitting method, until the target flow field convergence condition is met.

[0042] Step S16: If the target flow field convergence condition is met, then simulate the flow process of the target collisionless plasma generated by the Hall electric propulsion engine based on the macroscopic parameters of the flow field.

[0043] In this embodiment, if the target flow field convergence condition is met, the flow process of the target collisionless plasma generated by the Hall electric propulsion engine is simulated using the converged and stable macroscopic parameters of the flow field.

[0044] Understandably, linear Landau decay is a classic verification problem in collisionless plasma physics. Theoretical values ​​exist for this problem and can be used to verify the correctness and accuracy of this scheme. The standard initial condition for the linear Landau decay problem, i.e., the initial state of the electron distribution function, is: ; in, Let be the initial distribution function of electrons; For the electron's one-dimensional velocity variable; For the one-dimensional position variable of the electron; Wave number; Let be the amplitude of the disturbance. Define the electric field strength at... The norm value in space is: ; in, For function exist Norms in space; The order of the norm is used. In this test case, the actual order used is 2, i.e., the L2 norm. The electric field strength is the function being measured.

[0045] Furthermore, Figure 2This is a schematic diagram comparing electric field decay curves. The x-axis represents time t, i.e., a normalized time scale without physical units, and the y-axis represents the L2 norm of the electric field intensity. , where is a dimensionless quantity. The black dashed line represents the analytical solution determined by Landau's linear theory, i.e., the theoretical decay curve; the red solid line represents the numerical simulation results of this method. The periodic peaks on the red curve are the eigenoscillations of the Langmuir wave, superimposed on the exponential decay. It can be seen that the electric field decay rate obtained from the numerical simulation of this method is consistent with the theoretical value, indicating that this method accurately captures the exponential decay rate of the electric field. Figure 3 This is a schematic diagram of a conserved quantity curve. The x-axis represents time t, which is a normalized time scale and has no physical unit. The y-axis represents the value of the conserved quantity, which is a dimensionless quantity. The gray line represents the total number of electrons, i.e., the number of particles. The blue line represents the total energy, including electron kinetic energy and electric potential energy. The red line represents the energy norm of the distribution function. The green line represents the total impulse, i.e., the total momentum. All curves are horizontal straight lines, indicating that the energy dissipation of this method is extremely low and the calculation results are reliable.

[0046] As can be seen from the above, this application selects the Vlasov-Poisson equations as the core model to describe the coupling relationship between the target collisionless plasma particle motion and the self-generated electric field generated by the Hall electric propulsion engine in the spacecraft. The Vlasov equations are split into position space convection and velocity space convection equations using the time splitting method, which greatly reduces the difficulty of solving the problem. An initial particle distribution function is determined to complete the state initialization of the Hall electric propulsion plasma simulation. The electric field intensity can be quickly obtained by solving the Poisson equation using the Fourier spectral method. The electric field intensity and the initial particle distribution function are input into the velocity space convection motion equation to realize the real-time coupling iteration of particle motion and electric field. The Fourier spectral method is used to solve the equation to obtain the particle distribution with high accuracy at the current time step. Based on the particle distribution function, the position space convection motion equation is solved using the finite volume method to obtain the target particle distribution function at the next time step. The velocity space integral of the target particle distribution function is performed to obtain the distance, transforming the microscopic particle distribution into macroscopic flow field parameters such as density, temperature, flow velocity, and current density. Convergence judgment is performed based on the macroscopic parameters to achieve adaptive stopping iteration. In this way, the complete flow process of collisionless plasma in a Hall electric propulsion engine can be reproduced based on convergent macroscopic parameters, which not only solves the simulation problem of collisionless plasma, but also achieves high-speed computational results.

[0047] Accordingly, see Figure 4 As shown, this application also provides a device for simulating collision-free plasma flow, comprising: Equation splitting module 11 is used to determine the Vlasov-Poisson equations for describing the particle motion of the target collisionless plasma. Based on the Vlasov equations in the Vlasov-Poisson equations, the current time step is split using the time splitting method to obtain the position space convection motion equation and the velocity space convection motion equation; wherein, the target collisionless plasma is plasma generated by the Hall electric propulsion engine in the spacecraft. The initial function determination module 12 is used to determine the initial particle distribution function of the plasma initial state and to solve the Poisson equation in the Vlasov-Poisson equation system using the Fourier spectral method to obtain the electric field intensity. The equation solving module 13 is used to input the electric field intensity and the initial particle distribution function into the velocity space convection motion equation and solve it using the Fourier spectrum method to obtain the particle distribution function; The objective function determination module 14 is used to solve the position space convection motion equation based on the particle distribution function and using the finite volume method to obtain the target particle distribution function at the next moment. The parameter judgment module 15 is used to integrate and calculate the moment of the target particle distribution function in the velocity space to obtain the macroscopic parameters of the flow field, and to judge whether the convergence condition of the target flow field is met based on the macroscopic parameters of the flow field. The flow process simulation module 16 is used to simulate the flow process of the target collisionless plasma generated by the Hall electric propulsion engine based on the macroscopic parameters of the flow field if the target flow field convergence condition is met.

[0048] In some specific embodiments, the equation splitting module 11 may specifically include: The equation splitting unit is used to split the Vlasov equations in the Vlasov-Poisson equation system into the current time step particle motion using the non-constant time splitting method, so as to obtain the position space convection motion equation corresponding to the particle position movement and the velocity space convection motion equation corresponding to the particle velocity change.

[0049] In some specific embodiments, the initial function determination module 12 may specifically include: The function integration unit is used to determine the initial particle distribution function of the plasma initial state and integrate the initial particle distribution function in the discrete velocity domain to obtain the particle number density. The density transformation unit is used to perform a Fourier transformation on the particle number density to obtain a first Fourier coefficient, and substitute the first Fourier coefficient into the Poisson equation in the Vlasov-Poisson equation set to obtain a second Fourier coefficient corresponding to the electric field strength. The second coefficient transformation unit is used to perform an inverse Fourier transformation on the second Fourier coefficient to obtain the electric field strength.

[0050] In some specific embodiments, the equation solving module 13 may specifically include: The function transformation unit is used to perform a Fourier transformation on the initial particle distribution function to obtain the third Fourier coefficient; The target coefficient transformation unit is used to substitute the third Fourier coefficient into the velocity space convection motion equation to obtain the corresponding target equation, determine the target Fourier coefficient at the next moment based on the analytical solution corresponding to the target equation, and perform inverse Fourier transformation on the target Fourier coefficient to obtain the particle distribution function.

[0051] In some specific embodiments, the objective function determination module 14 may specifically include: The position equation solving submodule is used to solve the position space convection motion equation based on the particle distribution function and using the second-order MUSCL, Minmod limiter and finite volume method to obtain the target particle distribution function at the next moment.

[0052] In some specific embodiments, the position equation solving submodule may specifically include: The location space discretization element is used to discretize the location space corresponding to the location space convection motion equation using the finite volume method to obtain each grid and determine the discrete equation corresponding to the location space convection motion equation. The right-hand side term determination unit is used to determine the flux of particles in the plasma through each grid based on the particle distribution function and using a second-order MUSCL and a Minmod limiter, and to determine the right-hand side term of the discrete equation using the flux. The time-advancing solution unit is used to perform time-advancing solution based on the distribution information corresponding to the right-hand term and the grid, and using the second-order Runge-Kutta method, so as to obtain the target particle distribution function at the next moment.

[0053] In some specific embodiments, the simulated collision-free plasma flow device may further include: The convergence condition judgment unit is used to jump to the step of splitting the current time step based on the Vlasov equation in the Vlasov-Poisson equation set and using the time splitting method if the target flow field convergence condition is not met, until the target flow field convergence condition is met.

[0054] Furthermore, embodiments of this application also disclose an electronic device, Figure 5 This is a structural diagram of an electronic device 20 according to an exemplary embodiment. The content of the diagram should not be construed as limiting the scope of this application. Specifically, the electronic device 20 may include: at least one processor 21, at least one memory 22, a power supply 23, a communication interface 24, an input / output interface 25, and a communication bus 26. The memory 22 stores a computer program, which is loaded and executed by the processor 21 to implement the relevant steps in the simulated collisionless plasma flow method disclosed in any of the foregoing embodiments. Furthermore, the electronic device 20 in this embodiment may specifically be an electronic computer.

[0055] In this embodiment, the power supply 23 is used to provide operating voltage for each hardware device on the electronic device 20; the communication interface 24 can create a data transmission channel between the electronic device 20 and external devices, and the communication protocol it follows can be any communication protocol applicable to the technical solution of this application, and is not specifically limited here; the input / output interface 25 is used to acquire external input data or output data to the outside world, and its specific interface type can be selected according to specific application needs, and is not specifically limited here.

[0056] In addition, the memory 22, as a carrier for resource storage, can be a read-only memory, random access memory, disk or optical disk, etc. The resources stored thereon can include operating system 221, computer program 222, etc., and the storage method can be temporary storage or permanent storage.

[0057] The operating system 221 is used to manage and control the various hardware devices on the electronic device 20 and the computer program 222, which may be Windows Server, Netware, Unix, Linux, etc. In addition to including a computer program capable of performing the simulated collisionless plasma flow method executed by the electronic device 20 as disclosed in any of the foregoing embodiments, the computer program 222 may further include a computer program capable of performing other specific tasks.

[0058] Furthermore, this application also discloses a computer-readable storage medium for storing a computer program; wherein, when the computer program is executed by a processor, it implements the aforementioned method for simulating collisionless plasma flow. Specific steps of this method can be found in the corresponding content disclosed in the foregoing embodiments, and will not be repeated here.

[0059] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0060] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0061] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0062] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0063] The technical solutions provided in this application have been described in detail above. Specific examples have been used 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. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for simulating collision-free plasma flow, characterized in that, include: The Vlasov-Poisson equations are determined to describe the particle motion of the target collisionless plasma. Based on the Vlasov equations in the Vlasov-Poisson equations, the current time step is split using the time splitting method to obtain the position space convection motion equations and the velocity space convection motion equations. The target collisionless plasma is plasma generated by the Hall electric propulsion engine in the spacecraft. The initial particle distribution function of the plasma initial state is determined, and the Poisson equation in the Vlasov-Poisson equation system is solved using the Fourier spectral method to obtain the electric field intensity. The electric field strength and the initial particle distribution function are input into the velocity space convection equation and solved using the Fourier spectrum method to obtain the particle distribution function. Based on the particle distribution function, the spatial convection motion equations are solved using the finite volume method to obtain the target particle distribution function at the next moment. The target particle distribution function is integrated and moments are calculated in velocity space to obtain macroscopic parameters of the flow field. Based on the macroscopic parameters of the flow field, it is determined whether the convergence condition of the target flow field is met. If the target flow field convergence condition is met, the flow process of the target collisionless plasma generated by the Hall electric propulsion engine is simulated based on the macroscopic parameters of the flow field.

2. The method for simulating collision-free plasma flow according to claim 1, characterized in that, The process of splitting the current time step based on the Vlasov equations in the Vlasov-Poisson equations system and using the time splitting method to obtain the position space convection equations and velocity space convection equations includes: The Vlasov equations in the Vlasov-Poisson equation system are split into the current time step particle motion using the non-constant time splitting method to obtain the position space convection motion equation corresponding to the particle position movement and the velocity space convection motion equation corresponding to the particle velocity change.

3. The method for simulating collision-free plasma flow according to claim 1, characterized in that, The determination of the initial particle distribution function of the plasma initial state, and the solution of the Poisson equation in the Vlasov-Poisson equation system using the Fourier spectral method to obtain the electric field intensity, includes: The initial particle distribution function of the plasma initial state is determined, and the initial particle distribution function is integrated in the discrete velocity domain to obtain the particle number density; The particle number density is subjected to a Fourier transform to obtain the first Fourier coefficient. The first Fourier coefficient is then substituted into the Poisson equation in the Vlasov-Poisson equation set to obtain the second Fourier coefficient corresponding to the electric field strength. The electric field strength is obtained by performing an inverse Fourier transform on the second Fourier coefficient.

4. The method for simulating collision-free plasma flow according to claim 1, characterized in that, The process of inputting the electric field intensity and the initial particle distribution function into the velocity space convection equations and solving them using the Fourier spectrum method to obtain the particle distribution function includes: The initial particle distribution function is subjected to a Fourier transform to obtain the third Fourier coefficients; The third Fourier coefficient is substituted into the velocity space convection equation to obtain the corresponding target equation. The target Fourier coefficient at the next moment is determined based on the analytical solution corresponding to the target equation, and the inverse Fourier transform is performed on the target Fourier coefficient to obtain the particle distribution function.

5. The method for simulating collision-free plasma flow according to claim 1, characterized in that, The step of solving the spatial convection motion equations based on the particle distribution function and using the finite volume method to obtain the target particle distribution function at the next moment includes: Based on the particle distribution function, the position space convection motion equations are solved using the second-order MUSCL, Minmod limiter, and finite volume method to obtain the target particle distribution function at the next moment.

6. The method for simulating collision-free plasma flow according to claim 5, characterized in that, The process of solving the position space convection motion equations based on the particle distribution function and using second-order MUSCL, Minmod limiter, and finite volume method to obtain the target particle distribution function at the next moment includes: The position space corresponding to the position space convection motion equation is discretized using the finite volume method to obtain each grid, and the discrete equation corresponding to the position space convection motion equation is determined. Based on the particle distribution function and using a second-order MUSCL and Minmod limiter, the flux of particles in the plasma through each grid is determined, and the flux is used to determine the right-hand side of the discrete equation. Based on the distribution information corresponding to the right-hand term and the grid, and using the second-order Runge-Kutta method for time-progression solution, the target particle distribution function at the next time step is obtained.

7. The method for simulating collision-free plasma flow according to any one of claims 1 to 6, characterized in that, After determining whether the target flow field convergence condition is met based on the macroscopic parameters of the flow field, the method further includes: If the target flow field convergence condition is not met, then proceed to the step of splitting the current time step based on the Vlasov equation in the Vlasov-Poisson equation set and using the time splitting method, until the target flow field convergence condition is met.

8. A device for simulating collision-free plasma flow, characterized in that, include: The equation splitting module is used to determine the Vlasov-Poisson equations describing the particle motion of the target collisionless plasma. Based on the Vlasov equations in the Vlasov-Poisson equations, the current time step is split using the time splitting method to obtain the position space convection motion equations and velocity space convection motion equations; wherein, the target collisionless plasma is plasma generated by the Hall electric propulsion engine in the spacecraft. The initial function determination module is used to determine the initial particle distribution function of the plasma initial state and to solve the Poisson equation in the Vlasov-Poisson equation system using the Fourier spectral method to obtain the electric field intensity. The equation solving module is used to input the electric field intensity and the initial particle distribution function into the velocity space convection motion equation, and solve it using the Fourier spectrum method to obtain the particle distribution function; The objective function determination module is used to solve the position space convection motion equation based on the particle distribution function and using the finite volume method to obtain the target particle distribution function at the next moment. The parameter judgment module is used to integrate and calculate the moment of the target particle distribution function in the velocity space to obtain the macroscopic parameters of the flow field, and to determine whether the convergence condition of the target flow field is met based on the macroscopic parameters of the flow field. The flow process simulation module is used to simulate the flow process of the target collisionless plasma generated by the Hall electric propulsion engine based on the macroscopic parameters of the flow field if the target flow field convergence condition is met.

9. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the method for simulating collision-free plasma flow as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, Used to store a computer program, wherein the computer program, when executed by a processor, implements the method for simulating collisionless plasma flow as described in any one of claims 1 to 7.

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