Improved sp method, device and storage medium applied to numerical simulation of compressible gas-particle two-phase flow

Abstract

This invention proposes an improved SPH method for numerical simulation of compressible gas-particle two-phase flow. This method addresses the decrease in computational accuracy caused by the disordered motion distribution of particles under the influence of vortex structures in the flow field and particle pulsations based on particle kinetics. It introduces the Navier-Stokes equations in a completely smooth length SPH discrete form and a kernel function gradient correction technique. Furthermore, to account for the influence of compressibility on the momentum coupling between the gas and particle phases, a modified Huilin-Gidaspow drag model for dense particle flows is constructed. Finally, the effectiveness of this method for compressible gas-particle two-phase flow is verified by solving a classic JPL nozzle flow field numerical simulation problem.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation technology for gas-particle two-phase flow, specifically to an improved SPH method, equipment, and storage medium for numerical simulation of compressible gas-particle two-phase flow. Background Technology

[0002] The gas flow in the internal flow field of a solid rocket motor (SRM) is essentially a dense particle-gas two-phase flow containing large-scale particles. The flow field structure is complex and transonic flow exists. Therefore, for numerical simulation of the gas flow process in the internal flow field, high-resolution algorithms are needed to better describe its nonlinear evolution process. At the same time, for the dense particle transport process in the internal flow field, it has the flow characteristics of a continuous medium on a macroscopic level, but it is still a discrete particle on a microscopic level. The solution method should ideally cover both of these characteristics.

[0003] For the particle transport process in SRM, the existing technology proposes to use the Smoothed Particle Hydrodynamics (SPH) method for solving the problem. However, due to the influence of the vortex structure of the flow field and the particle pulsation based on particle kinetics, the particle motion distribution in SPH is relatively disordered, which reduces the calculation accuracy of the traditional SPH approximation. In addition, since the flow field inside SRM is a high-speed gas-particle two-phase flow, the influence of compressibility effect on the coupling between gas and particles must also be considered. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention proposes an improved SPH method, equipment, and storage medium for numerical simulation of compressible gas-particle two-phase flow.

[0005] The technical solution of this invention is as follows:

[0006] An improved SPH method for numerical simulation of compressible gas-particle two-phase flow includes the following steps:

[0007] Step 1: Perform numerical simulations of the gas phase flow field and particle phase flow field of the compressible gas-particle two-phase flow field inside the solid rocket motor. For the particle phase flow field, the smoothed particle hydrodynamics method is used to construct SPH particles and initialize the SPH particles.

[0008] Step 2: Calculate the time step and perform neighbor particle search and kernel function calculation. During kernel function calculation, a kernel function gradient correction method is used to correct the kernel function. The SPH particle source term is substituted into the NS equation using the fully variable length SPH discrete form, and the equation is solved based on the corrected kernel function to update the density, velocity, and temperature of the SPH particles. The SPH particle source term includes drag force, heat conduction, and volume fraction. The drag force is calculated using the SPH particle drag force model, and the heat conduction and volume fraction are obtained from numerical simulation of the gas phase flow field.

[0009] Step 3: Determine if the simulation time exceeds the set time. If yes, the method ends; otherwise, return to Step 2 and perform the next time step calculation.

[0010] Furthermore, the Navier-Stokes equations in the discrete form of the fully variable length SPH are obtained through the following process:

[0011] Suppose SPH particles Surrounded by a smooth length The radius is the range of particles Given a support region containing particles of a certain mass, the equation for the variable smooth length is:

[0012]

[0013] in Let be the spatial dimension. For particles The density; the variable smooth length equation is processed using a symmetric kernel approximation, and the processed variable smooth length equation is introduced into the Springel fully conserved SPH discrete form of the NS equation, resulting in the fully variable smooth length SPH discrete form of the NS equation:

[0014] { d ρ i dt = ∑ j = 1 N m j [( v i − v j ) ⋅∇ i W ij + 1 2 ( dh i dt + dh j dt ) ∂ W ij ∂ h ] dv i dt = ∑ j = 1 N m j ( f j p j ρ j 2 + f i p i ρ i 2 ) ∇ i W ij de i dt = p i ρ i 2 ∑ j = 1 N m j [( v i − v j ) ⋅∇ i W ij + 1 2 ( dh i dt + dh j dt ) ∂ W ij ∂ h ]

[0015] in for Within the particle support domain Particle number, for Particle mass, , for Particles and The speed of the particles, for Particle pairs The kernel function of particle interaction. For kernel function about The gradient of the particle, for Particle smooth length, , for Particles and Correction coefficients for particles, , for Particles and The pressure of the particles, , for Particles and Particle density, for The energy of a particle.

[0016] Furthermore, Particles and The formula for calculating the correction coefficient of a particle is:

[0017] ;

[0018] .

[0019] Furthermore, in step 2, according to the formula

[0020]

[0021] Perform kernel function gradient correction, where the subscript express Particle, subscript express Within the particle support domain particle, for Particle pairs The kernel function of particle interaction. For kernel function about The gradient of the particle, for The field function of the particle, For the set invertible matrix, For the corrected kernel function about The gradient of a particle.

[0022] Furthermore, in step 2, the invertible matrix for:

[0023]

[0024] in yes Particle volume, , , , express The coordinates of the particle express The coordinates of the particle.

[0025] Furthermore, in step 2, the SPH particle drag model is a modified Gidaspow drag model that considers compressibility effects:

[0026]

[0027]

[0028] in This is the drag force of the gas phase relative to the particle phase. For gas phase velocity, For particle phase velocity, This is the drag coefficient. It is a relaxation factor;

[0029]

[0030]

[0031] in , These represent the volume fractions of the particulate phase and the gas phase, respectively. This refers to the gas phase shear viscosity. The particle diameter is For gas phase density, This is the drag coefficient acting on a single particle.

[0032] The present invention also proposes a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps described above.

[0033] The present invention also proposes a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps described above.

[0034] Beneficial effects

[0035] This invention proposes an improved SPH method for numerical simulation of compressible gas-particle two-phase flow. Addressing the issue of decreased computational accuracy caused by the disordered particle motion distribution under the influence of vortex structures in the flow field and particle pulsation based on particle kinetics, this invention introduces the Navier-Stokes equations in a fully variable-length SPH discrete form and a kernel function gradient correction technique. Furthermore, to account for the influence of compressibility on the momentum coupling between the gas and particle phases, a modified Huilin-Gidaspow drag model for dense particle flow is constructed. Finally, the effectiveness of this method for compressible gas-particle two-phase flow is verified by solving a classic JPL nozzle flow field numerical simulation problem.

[0036] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0037] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0038] Figure 1 Schematic diagram of the virtual particle method;

[0039] Figure 2 JPL nozzle calculation model; (a) JPL nozzle 1 / 4 cross-sectional dimensions, (b) JPL nozzle 1 / 4 mesh model;

[0040] Figure 3 : JPL nozzle pressure and Mach number calculation results cloud map; (a) JPL nozzle pressure cloud map, (b) JPL nozzle Mach number cloud map;

[0041] Figure 4 Comparison of experimental measurement data and calculation results of JPL nozzle; (a) Comparison of pressure between nozzle axis and wall surface, (a) Comparison of Mach number between nozzle axis and wall surface;

[0042] Figure 5 Two-phase flow particle distribution;

[0043] Figure 6 Comparison of numerical simulation results of two-phase flow in JPL nozzle; (a) Particle velocity vector diagram, (b) DPM calculation results.

[0044] Figure 7 Comparison of temperature and Mach number for single-phase and two-phase flows; (a) gas phase temperature distributed along the axis, (b) gas phase Mach number distributed along the axis. Detailed Implementation

[0045] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0046] The improved SPH method proposed in this invention for numerical simulation of compressible gas-particle two-phase flow includes the following steps:

[0047] Step 1: Perform numerical simulation of the gas phase and particle phase of the compressible gas-particle two-phase flow in the internal flow field of the solid rocket motor. For the particle phase, the smoothed particle hydrodynamics method is used to construct SPH particles and initialize the SPH particles.

[0048] Step 2: Calculate the time step and perform neighbor particle search and kernel function calculation. During kernel function calculation, a kernel function gradient correction method is used to correct the kernel function. The SPH particle source term is substituted into the NS equation using the fully variable length SPH discrete form, and the equation is solved based on the corrected kernel function to update the density, velocity, and temperature of the SPH particles. The SPH particle source term includes drag force, heat conduction, and volume fraction. The drag force is calculated using the SPH particle drag force model, and the heat conduction and volume fraction are obtained from numerical simulation of the gas phase flow field.

[0049] Step 3: Determine if the simulation time exceeds the set time. If yes, the method ends; otherwise, return to Step 2 and perform the next time step calculation.

[0050] The key technologies in the above steps are described in detail below:

[0051] 1. Control equations for particle transport

[0052] By adding the energy equation and the source term for the gas-particle two-phase transfer to the mass, momentum, and pulsating energy conservation equations based on particle kinetics, the discrete phase control equations are obtained as follows:

[0053] (1)

[0054] (2)

[0055] ∂ ∂ t ( α p ρ p h p ) +∇⋅ ( α p ρ p h p v p ) =−∇⋅ α p q p + T gp + τ p ∇⋅ v p + α p [ ∂ ∂ t p p + v p ∇ p p ] (3)

[0056] 3 2 [ ∂ ∂ t ( ρ p α p θ p ) +∇⋅ ( ρ p α p v p θ p )] = ( − p p I + τ p ): ∇ v p +∇⋅ ( k p ∇ θ p ) − N c θ p + ϕ gp (4)

[0057] In the above system of equations, For discrete phase volume fraction, and For discrete phase density and velocity, For the gas phase pressure gradient, For discrete phase pressure gradient, These are discrete phase enthalpy values. For discrete phase thermal conductivity, , For discrete phase pressure; The simulated temperature of the particles is used to characterize the velocity fluctuations of the particles; Unit tensor; This is the double dot product operator; The energy dissipation coefficient, The energy dissipation coefficient caused by inelastic particle collisions; For the interparticle interaction forces, this study primarily considers drag force; other unsteady forces such as virtual mass force, buoyancy, Basset force, rotational lift, and shear lift are ignored. It can be represented as , This is the drag coefficient; Energy loss due to air particle friction. .

[0058] For particle adhesion stress, according to the formula

[0059] (5)

[0060] The calculation yields the following result: For discrete phase shear viscosity, The viscosity is for discrete phases.

[0061] 2. Construct the Navier-Stokes equations in the discrete form of the fully variable smooth length SPH.

[0062] In the SPH particle approximation, the smoothing length of the kernel function directly affects the size of the particle support domain and the calculation of the kernel function value; therefore, the smoothing length... The value of is very important. Here, the fully variable smooth length SPH method is used to improve the accuracy of the SPH nucleus approximation.

[0063] Ideally, the SPH method should maintain a constant number of neighboring particles for each SPH particle during computation, ensuring consistent kernel approximation accuracy across the entire computational domain. Therefore, the SPH particle... Surrounded by a smooth length The radius is the range of particles Given a supporting region containing particles of a certain mass, the equation for the variable smooth length can be obtained as follows:

[0064] (6)

[0065] in Let be the spatial dimension. For particles The density. Based on equation (6), the variable smooth length equation is processed using the symmetric kernel approximation form. The processed variable smooth length equation is then introduced into the Springel fully conserved SPH discrete form of the NS equation, resulting in the fully variable smooth length SPH discrete form of the NS equation:

[0066] { d ρ i dt = ∑ j = 1 N m j [( v i − v j ) ⋅∇ i W ij + 1 2 ( dh i dt + dh j dt ) ∂ W ij ∂ h ] dv i dt = ∑ j = 1 N m j ( f j p j ρ j 2 + f i p i ρ i 2 ) ∇ i W ij de i dt = p i ρ i 2 ∑ j = 1 N m j [( v i − v j ) ⋅∇ i W ij + 1 2 ( dh i dt + dh j dt ) ∂ W ij ∂ h ] (7)

[0067] in for Within the particle support domain Particle number, for Particle mass, , for Particles and The speed of the particles, for Particle pairs The kernel function of particle interaction. For kernel function about The gradient of the particle, for Particle smooth length, , for Particles and Correction coefficients for particles, , for Particles and The pressure of the particles, , for Particles and Particle density, for The energy of a particle.

[0068] In the formula Particles and The formula for calculating the correction coefficient of a particle is:

[0069] (8)

[0070] (9)

[0071] It can be seen from equations (6) and (7) above that and Implicitly related, therefore, when performing numerical calculations on equation (7), the solution is first iteratively obtained. and (Initial settings) Then, calculate equations (8) and (9) in the same way, and then solve for the solution. Finally, due to Given that it can be explicitly calculated .

[0072] 3. Kernel function gradient correction method

[0073] Due to the influence of particle pulsation and air-particle interaction, the SPH particle distribution is relatively disordered, which reduces the accuracy of the SPH approximation. Therefore, this invention employs a kernel function gradient correction method to improve the accuracy of kernel function gradient calculation. The field function is then set at a point... Taylor expansion yields:

[0074] (10)

[0075] From formula (10), the derivative of the field function can be approximately expressed as:

[0076] (11)

[0077] Therefore,

[0078] (12)

[0079] Using the SPH particle approximation, the above equation can be written as:

[0080] (13)

[0081] It is the particle volume. From the above equation, we know that when...

[0082] (14)

[0083] When true, equation (13) has second-order accuracy; therefore, it is required that...

[0084] ∑ j ( x j − x i ) ∇ i W ij V j = [ 1 , 0 , 0 ] T ∑ j ( y j − y i ) ∇ i W ij V j = [ 0 , 1 , 0 ] T ∑ j ( z j − z i ) ∇ i W ij V j = [ 0 , 0 , 1 ] T (15)

[0085] Set an invertible matrix for

[0086] (16)

[0087] in , , , express The coordinates of the particle express The particle's coordinates. This is determined by applying the initial kernel function and its gradient to a locally invertible matrix. Multiplying them together yields the second-order precision corrected kernel function gradient.

[0088] (17)

[0089] 4. Modified Gidaspow drag model considering compressibility effect

[0090] In the gas-particle two-phase flow problem involving dense particles, the Gidaspow drag model is currently widely used for momentum source term exchange between gas and particles. Its main idea is to employ a method suitable for dilute phase flow, i.e., when the particle volume fraction is small. For dense phase flow, i.e., when the particle volume fraction is large, the equation is adopted. The equation is provided. However, the calculation of the single-particle drag coefficient in the model does not consider the compressibility effect when the particle interacts with the high-speed fluid. Therefore, this invention adopts a single-particle drag force model that considers the compressibility effect to modify the Gidaspow model, constructing a modified Gidaspow drag force model that considers the compressibility effect. The calculation method is shown below.

[0091] Drag coefficient based on Gidaspow model The expression is:

[0092] (18)

[0093] in , These represent the volume fractions of the particulate phase and the gas phase, respectively. This refers to the gas phase shear viscosity. The particle diameter is For gas phase density, Let be the drag coefficient acting on a single particle. Based on a modification of the E. Loth calculation model, it can be expressed as:

[0094] C D = { 24 α g Re p [ 1 + 0 . 15 ( α g Re p ) 0 . 687 ] H M + 0 . 42 C M 1 + 42500 G M ( α g Re p ) 1 . 16 Re p > 45 C D , K n , R e + M p 4 C D , f m , R e 1 + M p 4 Re p ≤ 45 (19)

[0095] The relative Reynolds number is defined as:

[0096] (20)

[0097] To account for the compressibility effect in the drag ratio,

[0098] C M = { 5 3 + 2 3 tanh 3 ln( M p + 0 . 1 )] M p ≤ 1 . 45 2 . 044 + 0 . 2 exp{ − 1 . 8 [ln( M p / 1 . 5 )] 2 } M p > 1 . 45 (twenty one)

[0099] The relative Mach number of the particles.

[0100] (twenty two)

[0101] In equation (19), , For empirical functions,

[0102] G M = { 1 − 1 . 525 M p 4 M p ≤ 0 . 89 0 . 0002 + 0 . 0008 tanh 12 . 77 ( M p − 2 . 02 )] M p > 0 . 89 (twenty three)

[0103] (twenty four)

[0104] In equation (19) For Knudsen number-based Corrected drag coefficient:

[0105] C D , K n , R e = 24 α g Re p [ 1 + 0 . 15 ( α g Re p ) 0 . 687 ] f Kn (25)

[0106] Knudsen correction factor:

[0107] f Kn = 1 1 + Kn p [ 2 . 514 + 0 . 8 exp( − 0 . 55 / Kn p )] (26)

[0108] For Knudsen number

[0109] (27)

[0110] To account for the corrected drag coefficient in the free molecule limit:

[0111] (28)

[0112] To account for the drag coefficient of inviscid free molecules

[0113] (29)

[0114] The free molecular drag coefficient at equilibrium particle temperature is defined as

[0115] (30)

[0116] The molecular rate ratio is:

[0117] (31)

[0118] Equation (18) is a piecewise function with discontinuities, while the traction coefficient... Is it following Since it changes continuously, a relaxation factor needs to be introduced for the drag coefficient. The piecewise function representation is smoothed, and the relaxation factor is applied. It can be represented as:

[0119] φ gp = arctan 150 × 1 . 75 ( 0 . 2 − α p )] π + 0 . 5 (32)

[0120] Therefore, the drag coefficient Ultimately, it can be expressed as:

[0121] (33)

[0122] 5. Boundary condition settings

[0123] The approximation of physical quantities at the SPH particle is a weighted average of the information of all particles within its kernel function support domain. When an SPH particle is near the boundary of the computational domain, its kernel function support domain may extend beyond the boundary. Microscopically, there are no particles outside the boundary, and the SPH particle is only affected by particles within the boundary. This unilateral effect can lead to significant deviations in the calculation results. Macroscopically, in the integral expression of the spatial derivative of the SPH field function, the area integral term is not zero because the kernel function is truncated by the boundary, which will cause calculation errors. Therefore, appropriate boundary conditions need to be applied to correct this effect. This invention employs the virtual particle method, which involves extending and arranging a considerable number of virtual particles outside the boundary and setting appropriate constraints to allow them to participate in the calculation of particles within the computational domain.

[0124] The equation for the interaction between the particle and the boundary is:

[0125] (34)

[0126] ( d v i dt ) b = { [ − m b ( p i + p b ρ i ρ b ) n b ⋅∇ i W ib ] n b , if ( p i + p b ) > 0 0 ， else (35)

[0127] , They are boundary virtual particles For particles The density and velocity increments resulting from the action; virtual particles The unit normal vector, The interaction between SPH particles and virtual particles is as follows: Figure 1 As shown.

[0128] virtual particles For particles The generated pressure acts on Place Expanding, we get:

[0129] (36)

[0130] virtual particles The unit tangential vector. Particle For virtual particles The normal and tangential pressure gradients generated by the action are:

[0131] (37)

[0132] (38)

[0133] Substituting equations (37) and (38) into equation (36), we get:

[0134] (39)

[0135] Based on CSPM interpolation, virtual particles The pressure is:

[0136] (40)

[0137] Based on the above, the method proposed in this invention will be verified by numerical simulation of the flow field in a JPL nozzle:

[0138] 1. Calculation Model

[0139] In 1969, the Jet Propulsion Laboratory (JPL) in the United States conducted relatively accurate measurements of the gas-phase flow field of relevant nozzles, obtaining detailed data. The numerical simulation of the gas-phase flow field in the JPL nozzle has become a classic example in the numerical simulation of flow fields within the SRM (Single-Phase Flow Mechanism). This paper presents numerical simulations of single-phase and two-phase flows in the JPL nozzle to verify the accuracy of the proposed algorithm in the numerical simulation of flow fields within the SRM.

[0140] Here, a quarter of the JPL nozzle flow field is selected for modeling and calculation. Its cross-sectional dimensions and mesh model are as follows: Figure 2 As shown, the number of grids is 38148.

[0141] According to the literature, the initial parameters of the flow field are set as shown in Table 1:

[0142] Table 1 Initial Parameter Settings for Flow Field

[0143]

[0144] The boundary conditions are set as follows: the left inlet is the injection boundary for SPH particles and gas, the right side is the outlet, the upper surface is set as a solid wall boundary condition for particles, a no-slip boundary condition for gas phase, a rigid constraint boundary condition for particle phase, and a symmetric boundary condition for lower surface.

[0145] 2. Results Analysis

[0146] a) Single-phase flow

[0147] The nozzle pressure and Mach number cloud diagram calculated in this paper is shown below. Figure 3 As shown in the figure. The calculation results in this paper are compared with the experimental data, for example... Figure 4 As shown, by Figure 4 It can be seen that the results calculated by the method in this paper match the experimental data well.

[0148] b) Two-phase flow

[0149] The particle distribution in the nozzle flow field is as follows: Figure 5 As shown, a particle-free region appears in the nozzle expansion section. This is compared with literature using the particle trajectory model (DPM). Figure 6 b) The results showed a good match.

[0150] Figure 6 The distribution curves of gas phase temperature and Mach number along the axis are plotted on... Figure 7 In the process, the addition of particles in the flow field brings about a velocity lag effect, and the resistance between the gas and the particles generates heat, making the gas temperature higher in the two-phase flow. Due to the velocity loss, the gas Mach number in the pure gas phase flow field is greater than the gas Mach number in the two-phase flow field at the same location.

[0151] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. An improved SPH method for numerical simulation of compressible gas-particle two-phase flow, characterized in that: Includes the following steps: Step 1: Perform numerical simulations of the gas phase flow field and particle phase flow field of the compressible gas-particle two-phase flow field inside the solid rocket motor. For the particle phase flow field, the smoothed particle hydrodynamics method is used to construct SPH particles and initialize the SPH particles. Step 2: Calculate the time step and perform neighbor particle search and kernel function calculation. During kernel function calculation, a kernel function gradient correction method is used to correct the kernel function. The SPH particle source term is substituted into the NS equation using the fully variable length SPH discrete form, and the equation is solved based on the corrected kernel function to update the density, velocity, and temperature of the SPH particles. The SPH particle source term includes drag force, heat conduction, and volume fraction. The drag force is calculated using the SPH particle drag force model, and the heat conduction and volume fraction are obtained from numerical simulation of the gas phase flow field. Step 3: Determine if the simulation time exceeds the set time. If yes, the method ends; otherwise, return to Step 2 and perform the next time step calculation.

2. The improved SPH method for numerical simulation of compressible gas-particle two-phase flow as described in claim 1, characterized in that: The Navier-Stokes equations in the discrete form of the fully variable smooth length SPH are obtained through the following process: Suppose SPH particles Surrounded by a smooth length The radius is the range of particles Given a support region containing particles of a certain mass, the equation for the variable smooth length is: in Let be the spatial dimension. For particles The density; the variable smooth length equation is processed using a symmetric kernel approximation, and the processed variable smooth length equation is introduced into the Springel fully conserved SPH discrete form of the NS equation, resulting in the fully variable smooth length SPH discrete form of the NS equation: in for Within the particle support domain Particle number, for Particle mass, , for Particles and The speed of the particles, for Particle pairs The kernel function of particle interaction, For kernel function about The gradient of the particle, for Particle smooth length, , for Particles and Correction coefficients for particles, , for Particles and The pressure of the particles, , for Particles and Particle density, for The energy of a particle.

3. The improved SPH method for numerical simulation of compressible gas-particle two-phase flow as described in claim 2, characterized in that: Particles and The formula for calculating the correction coefficient of a particle is: ； 。 4. The improved SPH method for numerical simulation of compressible gas-particle two-phase flow as described in claim 2, characterized in that: In step 2, according to the formula Perform kernel function gradient correction, where the subscript express Particle, subscript express Within the particle support domain particle, for Particle pairs The kernel function of particle interaction, For kernel function about The gradient of the particle, for The field function of the particle, For the set invertible matrix, For the corrected kernel function about The gradient of a particle.

5. The improved SPH method for numerical simulation of compressible gas-particle two-phase flow as described in claim 4, characterized in that: In step 2, the invertible matrix for: in yes Particle volume, , , , express The coordinates of the particle express The coordinates of the particle.

6. The improved SPH method for numerical simulation of compressible gas-particle two-phase flow as described in claim 1, characterized in that: In step 2, the SPH particle drag model is a modified Gidaspow drag model that considers compressibility effects: in This is the drag force of the gas phase relative to the particle phase. For gas phase velocity, For particle phase velocity, This is the drag coefficient. It is a relaxation factor; in , These represent the volume fractions of the particulate phase and the gas phase, respectively. This refers to the gas phase shear viscosity. The particle diameter is For gas phase density, This is the drag coefficient acting on a single particle.

7. A computer device, characterized in that: It includes a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the steps of the method according to any one of claims 1 to 6.

8. A computer-readable storage medium, characterized in that: The device contains a computer program that, when executed by a processor, causes the processor to perform the steps of the method according to any one of claims 1 to 6.

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