An efficient numerical method, system, device and medium for simulating the flow of the entire river basin

Abstract

The present invention discloses an efficient numerical method, system, device and medium for simulating the flow in the whole basin, including: obtaining the geometric parameters of the aircraft shape and gas flow information; constructing the physical grid of the aircraft; obtaining the equilibrium distribution function of the velocity grid based on the macroscopic quantities stored in the physical grid; obtaining the adaptive criterion value based on the macroscopic quantities stored in the physical grid and the distribution function of the velocity grid; comparing the adaptive criterion value with the coarsening threshold and refinement threshold of the velocity grid adaptation respectively to determine whether to perform velocity grid adaptation; updating the cell center distribution function in the reconstructed velocity grid again to obtain the updated flow field physical quantities; determining whether the flow field converges; processing the converged flow field to obtain the flow characteristic parameters. The present invention avoids updating the distribution function by interpolation reconstruction when exchanging information between the physical grid and the corresponding velocity grid, improves the calculation efficiency and reduces the calculation amount.

Description

Technical Field

[0001] The present invention belongs to the technical field of fluid mechanics and relates to an efficient numerical method, system, device and medium for simulating the flow in the entire basin. Background Art

[0002] Near-space hypersonic vehicles involve both traditional aviation airspace and near space in terms of flight altitude, with a large altitude span and complex flight conditions. In actual flight, they will face multi-scale cross-basin problems and flow non-equilibrium problems. At the same time, due to the extremely high flight Mach number of near-space hypersonic vehicles (generally above Mach 5), the airflow on the windward side of the vehicle is sharply compressed, while the airflow on the leeward side expands sharply, resulting in a drastic change in gas density at different positions in the entire flow field around the vehicle. The mean free path of gas molecules will differ by several orders of magnitude, thus forming a more complex single-flow-field continuum-rarefied cross-basin problem (multi-scale local rarefied flow problem). In addition, in microelectromechanical systems, there are usually situations where there is both overall macroscopic flow and local microscopic flow. So far, it is very difficult to analyze and predict such complex problems with multiple flow scales existing simultaneously in a single flow field.

[0003] The deterministic unified algorithm is based on the integral solution or numerical solution of the Boltzmann model equation, coupling particle migration and collision. It is a cross-basin and multi-scale method that can simulate the flow problems in the entire basin and the entire speed range. However, compared with traditional macroscopic methods, due to the fact that the unified algorithm describes the flow field information through the distribution function number based on the discrete velocity space, the amount of calculation and storage is extremely large (proportional to the product of the physical grid and the velocity grid). Among them, the distribution function f is a function of the coordinate molecular velocity and time t, used to represent the number density of molecules arriving at the coordinate at time t with velocity . Under the equilibrium state, the distribution function is determined by macroscopic quantities (density ρ, velocity temperature T and gas constant R), and obeys the equilibrium distribution (normal distribution):

[0004]

[0005] Figure 1 Such as Figure 1As shown in the figure, a schematic diagram of the DVS and distribution function of geometric objects in two-dimensional cases; in numerical calculations, the continuous velocity space is discretized into finite points to form a velocity space grid. The more discrete points there are, the denser the grid, the higher the resolution, and the greater the computational and storage requirements. The unified algorithm generally uses a uniformly discretized velocity space to facilitate the use of the composite Newton-Cotes integration method with higher integration accuracy to obtain macroscopic quantities. However, in reality, for hypersonic flows across different flow regimes, the particle velocities are very large, resulting in the need for the velocity grid to cover a sufficiently large area; when the flow is sufficiently rarefied, a large number of particles will gather in a very small area, requiring the velocity grid to have a very high resolution. Since the number of velocity grid points plays a decisive role in the computational cost of the method, it is necessary to use a sufficiently small but representative number of velocity points to accurately capture the flow characteristics. If the uniformly discretized velocity space is continued to be used, the computational and storage requirements will be unacceptable.

[0006] Grid adaptation refers to dynamically adjusting the resolution of the grid according to the flow field information. The velocity adaptation technology is generally divided into two types: "steady-state" and "unsteady-state"; "steady-state" means that the velocity grid is obtained by performing adaptation on the predicted flow field, and then the flow field evolution is carried out using this velocity grid until the flow field converges (the velocity grid remains unchanged); "unsteady-state" means that the velocity grid is refined and coarsened to different degrees according to different time and space positions (the velocity grid is variable). Compared with the global velocity grid, that is, the velocity grids corresponding to all physical grids are exactly the same, one of the difficulties of the local velocity grid, that is, the velocity grids corresponding to physical grids are not exactly the same, is to exchange information between the velocity space grids between two adjacent physical space units. The evolution process requires continuous interpolation and reconstruction of the distribution function, which increases the complexity and computational cost of the method to a certain extent and is not conducive to parallel computing. Summary of the Invention

[0007] The purpose of the present invention is to solve the problems in the prior art that information is exchanged between the velocity grids between two adjacent physical units, the interpolation and reconstruction of the distribution function need to be continuously carried out during the evolution process, which increases the complexity and computational cost of the method and is not conducive to parallel computing, and to provide an efficient numerical method, system, device and medium for simulating the flow of the entire flow regime.

[0008] To achieve the above object, the present invention adopts the following technical solutions:

[0009] An efficient numerical method for simulating the flow of the entire flow regime, including:

[0010] Step 1: Obtain the geometric parameters of the aircraft shape and the gas flow information; based on the obtained geometric parameters of the aircraft shape and the gas flow information, construct the physical grid of the aircraft.

[0011] Step 2: Based on the macroscopic quantities stored in the physical grid, obtain the equilibrium distribution function of the velocity grid;

[0012] Step 3: Based on the macroscopic quantities stored in the physical grid and the distribution function of the velocity grid, obtain several adaptive criterion values that are numerically different; select the adaptive criterion value with the largest numerical value among the several adaptive criterion values, and compare the selected adaptive criterion value with the coarsening threshold and refinement threshold for velocity grid adaptation respectively to determine whether to perform velocity grid adaptation. If so, reconstruct the cell-centered distribution function in the velocity grid; if not, do nothing; where the velocity grid distribution function at the initial moment is equal to the equilibrium distribution function of the velocity grid;

[0013] Step 4: Based on the macroscopic quantities stored in the physical grid, the equilibrium distribution function of the velocity grid, and the distribution function of the velocity grid, update the cell-centered distribution function in the reconstructed velocity grid again to obtain the updated flow field physical quantities;

[0014] Step 5: Based on several updates, determine whether the flow field converges based on the updated flow field physical quantities. If so, execute Step 6; if not, jump to Step 3 and Step 4 until the flow field converges;

[0015] Step 6: Process the converged flow field to obtain the flow characteristic parameters.

[0016] A further improvement of the present invention lies in:

[0017] Based on the macroscopic quantities stored in the physical grid, obtain the equilibrium distribution function of the velocity grid, specifically:

[0018]

[0019] where u, R, T, and U are the discrete velocity, gas constant, temperature, and velocity respectively; the macroscopic quantities include the density, velocity, and temperature of the gas.

[0020] Based on the macroscopic quantities stored in the physical grid and the distribution function of the velocity grid, obtain several adaptive criterion values; specifically:

[0021]

[0022]

[0023] where is the area or volume of the velocity grid cell u k and u k is the k-th velocity grid cell; is the cell-centered distribution function; ρ i 、 ρ iE i They are respectively the density, velocity, kinetic energy, and total energy of the gas in the $i$-th physical grid cell;

[0024] The number of adaptive criterion values is twice the number of physical grid cells; each physical grid cell contains two adaptive criterion values.

[0025] Select the adaptive criterion value with the largest numerical value among several adaptive criterion values, specifically:

[0026]

[0027] Compare the selected adaptive criterion value with the coarsening threshold and refinement threshold for velocity grid adaptation respectively, specifically:

[0028] The adaptive refinement threshold and coarsening threshold are $C1$ and $C2$ respectively. When , the velocity grid cell $u$ k is marked as a cell that needs to be refined. When , the velocity grid cell $u$ k is marked as a cell that needs to be coarsened. When , the velocity grid cell $u$ k does not require adaptation;

[0029] The adaptive refinement threshold and coarsening threshold are both set artificially; among them, adaptive refinement means splitting a velocity grid into several sub-velocity grids; adaptive coarsening means merging several velocity grids into a parent velocity grid.

[0030] Reconstruct the cell-centered distribution function in the velocity grid, specifically:

[0031] When , the velocity grid cell $u$ k is marked as a cell that needs to be refined. The velocity grid cell $u$ k splits into several sub-velocity grid cells, and the cell-centered distribution function of each sub-velocity grid cell is the same as that of the velocity grid cell $u$ k ; each sub-velocity grid cell splits again to obtain second-level sub-velocity grid cells, and the cell-centered distribution function of each sub-velocity grid cell is the same as that of its own second-level sub-velocity grid cell;

[0032] When , the velocity grid cell $u$ k is marked as a cell that needs to be coarsened. Several velocity grid cells $u$ k merge into a parent velocity grid cell; the cell-centered distribution function of the parent velocity grid cell is the average value after adding the cell-centered distribution functions of several velocity grid cells $u$ k .

[0033] Reconstructing the cell-centered distribution function in the velocity grid further includes:

[0034] Performing conservation correction on the cell-centered distribution function obtained by splitting or merging, specifically:

[0035]

[0036] wherein, is the macroscopic quantity at physical unit i, is the cell-centered distribution function after adaptation, and g is the Maxwell equilibrium distribution.

[0037] Judging whether the flow field converges, specifically:

[0038] Taking the velocity residual as the convergence criterion, and the criterion formula is:

[0039]

[0040] where and represent the velocity fields separated by n iterative steps, and ε is the convergence threshold.

[0041] An efficient numerical system for simulating the flow in the entire basin, including:

[0042] A construction module, which is used to obtain the geometric parameters of the aircraft shape and the gas flow information; based on the obtained geometric parameters of the aircraft shape and the gas flow information, construct the physical grid of the aircraft;

[0043] A first acquisition module, which is used to acquire the equilibrium distribution function of the velocity grid based on the macroscopic quantities stored in the physical grid;

[0044] A first judgment module, which is used to obtain several unequal adaptive criterion values based on the macroscopic quantities stored in the physical grid and the distribution function of the velocity grid; select the adaptive criterion value with the largest numerical value among the several adaptive criterion values, and compare the selected adaptive criterion value with the coarsening threshold and the refinement threshold of the velocity grid adaptation respectively to judge whether to perform velocity grid adaptation; wherein, the velocity grid distribution function at the initial moment is equal to the equilibrium distribution function of the velocity grid;

[0045] An update module, which is used to update the cell-centered distribution function in the reconstructed velocity grid again based on the macroscopic quantities stored in the physical grid, the equilibrium distribution function of the velocity grid and the distribution function of the velocity grid, and obtain the updated flow field physical quantities;

[0046] The second judgment module, which judges whether the flow field converges based on the updated physical quantities of the flow field after several updates.

[0047] The second acquisition module, which is used to process the converged flow field to obtain the flow characteristic parameters.

[0048] A terminal device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the above method are implemented.

[0049] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the above method are implemented.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] The present invention reconstructs the cell-centered distribution function in the velocity grid through the macroscopic quantities stored in the physical grid of the aircraft and the distribution function of the velocity grid; and updates the cell-centered distribution function in the reconstructed velocity grid again to judge whether the flow field converges, and finally obtains the flow characteristic parameters of the flow field; the present invention uses a global adaptive velocity grid to reconstruct the cell-centered distribution function; it avoids updating the distribution function by interpolation reconstruction when exchanging information between the physical grid and the corresponding velocity grid, improves the calculation efficiency, and reduces the calculation amount. Description of the Drawings

[0052] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required to be used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention, and therefore should not be regarded as limiting the scope. For those of ordinary skill in the art, other related drawings can be obtained based on these drawings without creative efforts.

[0053] Figure 1 It is a schematic diagram of the discrete velocity space and distribution function of a geometric object in a two-dimensional case; among them, (a) is a diagram of the discrete velocity space of the geometric object; (b) is a schematic diagram of the distribution function of the geometric object in a two-dimensional case;

[0054] Figure 2 It is a schematic diagram of the flow chart of the efficient numerical method for simulating the full-watershed flow of the present invention;

[0055] Figure 3 It is a schematic diagram of the structure of the efficient numerical system for simulating the full-watershed flow of the present invention;

[0056] Figure 4It is a schematic diagram of a quadtree structure and the corresponding velocity grid diagram; among them, (a) is the schematic diagram of the tree structure; (b) is the velocity grid diagram corresponding to the quadtree structure.

[0057] Figure 5 It is the physical space grid of a rarefied hypersonic flat plate; among them, the number of grids is 3869 units.

[0058] Figure 6 It is the adaptive velocity space grid of a rarefied hypersonic flat plate; among them, the number of grids is 748 units.

[0059] Figure 7 It is the pressure and temperature cloud diagram of a rarefied hypersonic flat plate; among them, (a) is the cloud diagram under the density parameter; (b) is the cloud diagram under the equilibrium temperature parameter; (c) is the cloud diagram under the translational temperature parameter; (d) is the cloud diagram under the rotational temperature parameter.

[0060] Figure 8 It is the temperature distribution diagram along the vertical direction at different horizontal positions of a rarefied hypersonic flat plate; among them, (a) is the different temperature distribution diagrams at 5 mm; (b) is the different temperature distribution diagrams at 20 mm. Detailed implementation manners

[0061] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Usually, the components of the embodiments of the present invention described and shown in the accompanying drawings here can be arranged and designed in various different configurations.

[0062] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed present invention, but merely represents the selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0063] It should be noted that: similar reference numerals and letters denote similar items in the following accompanying drawings. Therefore, once an item is defined in one of the accompanying drawings, it does not need to be further defined and explained in the subsequent accompanying drawings.

[0064] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper", "lower", "horizontal", "inner", etc. are used to indicate the orientation or positional relationship, it is based on the orientation or positional relationship shown in the drawings, or the orientation or positional relationship in which the product of the invention is usually placed when in use. This is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as a limitation to the present invention. In addition, terms such as "first", "second", etc. are only used for distinguishing descriptions and cannot be understood as indicating or implying relative importance.

[0065] In addition, if the term "horizontal" appears, it does not mean that the component is required to be absolutely horizontal, but it can be slightly inclined. For example, "horizontal" only means that its direction is more horizontal relative to "vertical", and does not mean that the structure must be completely horizontal, but it can be slightly inclined.

[0066] In the description of the embodiments of the present invention, it should also be noted that unless otherwise clearly specified and limited, if terms such as "set", "installed", "connected", "coupled" are used, they should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0067] The present invention will be further described in detail below with reference to the drawings:

[0068] See Figure 2 , the present invention discloses an efficient numerical method for simulating the flow in the entire basin, including:

[0069] S101: Obtain the geometric parameters of the aircraft shape and gas flow information; based on the obtained geometric parameters of the aircraft shape and gas flow information, construct the physical grid of the aircraft;

[0070] S102: Based on the macroscopic quantities stored in the physical grid, obtain the equilibrium distribution function of the velocity grid; the current time is the n(0) time;

[0071] Based on the macroscopic quantities stored in the physical grid, obtaining the equilibrium distribution function of the velocity grid specifically includes:

[0072]

[0073] where u, R, T, and U are the discrete velocity, gas constant, temperature, and velocity respectively; the macroscopic quantities include the density, velocity, and temperature of the gas.

[0074] Each physical grid stores macroscopic quantities \(W\) (density, velocity, temperature, etc.) and all velocity grid distribution functions \(f(x, u,\) t ) where \(f(x, u,\) t ) represents the mass density of gas molecules located in the physical space \([x - \Delta x, x + \Delta x]\) and the particle velocity space \([u - \Delta u, u + \Delta u]\) at time \(t\).

[0075] Microscopic control equation:

[0076]

[0077] where \(g\) * is the equilibrium distribution function and \(\tau\) is the relaxation time. The macroscopic quantities are obtained by taking moments (integrals) of the distribution function:

[0078] \(W = (\rho, \rho U, \rho E)\) T \(=\int f(x, u, t)\psi(u)du\ (3)\)

[0079] where \(\rho\), \(\rho U\), and \(\rho E\) are density, momentum, and energy respectively, being collision invariants.

[0080] S103: Based on the macroscopic quantities stored in the physical grid and the distribution function of the velocity grid, obtain several unequal adaptive criterion values; select the adaptive criterion value with the largest numerical value among the several adaptive criterion values, compare the selected adaptive criterion value with the coarsening threshold and refinement threshold for velocity grid adaptivity respectively, and determine whether to perform velocity grid adaptivity. If so, reconstruct the cell-centered distribution function in the velocity grid; if not, do nothing;

[0081] Based on the macroscopic quantities stored in the physical grid and the distribution function of the velocity grid, obtain several unequal adaptive criterion values; specifically:

[0082]

[0083]

[0084] where, is the area or volume of the velocity grid cell \(u_k\), and \(u_k\) is the \(k\)-th velocity grid cell; is the cell-centered distribution function; \(\rho\) i , \(\rho\) i \(E\) i are the density, velocity, kinetic energy, and total energy of the gas in the \(i\)-th physical grid cell respectively. The number of adaptive criterion values is the number of physical grid cells multiplied by 2; each physical grid cell contains two adaptive criterion values.

[0085] Select the adaptive criterion value with the largest value among several adaptive criterion values, specifically:

[0086]

[0087] Compare the selected adaptive criterion value with the coarsening threshold and refinement threshold of the velocity grid adaptation respectively, specifically:

[0088] The adaptive refinement threshold and coarsening threshold are C1 and C2 respectively. When the velocity grid cell u k is marked as a cell that needs to be refined. When the velocity grid cell u k is marked as a cell that needs to be coarsened. When the velocity grid cell u k does not need to be adapted;

[0089] Both the adaptive refinement threshold and the coarsening threshold are set manually. Among them, adaptive refinement means that one velocity grid is split into several sub-velocity grids; adaptive coarsening means that several velocity grids are merged into one parent velocity grid.

[0090] Reconstruct the cell-centered distribution function in the velocity grid, specifically:

[0091] When the velocity grid cell u k is marked as a cell that needs to be refined, the velocity grid cell u k is split into several sub-velocity grid cells, and the cell-centered distribution function of each sub-velocity grid cell is the same as that of the velocity grid cell u k ; each sub-velocity grid cell is split again to obtain second-level sub-velocity grid cells, and the cell-centered distribution function of each sub-velocity grid cell is the same as that of its own second-level sub-velocity grid cell;

[0092] When the velocity grid cell u k is marked as a cell that needs to be coarsened, several velocity grid cells u k are merged into one parent velocity grid cell; the cell-centered distribution function of the parent velocity grid cell is the average value after adding the cell-centered distribution functions of several velocity grid cells u k

[0093] Reconstructing the cell-centered distribution function in the velocity grid also includes:

[0094] Perform conservation correction on the cell-centered distribution function obtained by splitting or merging, specifically:

[0095] ​

[0096] Among them, is the macroscopic quantity at the physical grid cell i, is the cell-centered distribution function after adaptation, is the result of integrating to obtain the macroscopic quantity, and g is the Maxwell equilibrium distribution (Equation (1)).

[0097] S104: Based on the macroscopic quantity stored in the physical grid, the equilibrium distribution function of the velocity grid, and the distribution function of the velocity grid, update the cell-centered distribution function in the reconstructed velocity grid again to obtain the updated flow field physical quantity.

[0098] Advance the macroscopic quantity W stored in the physical grid and the distribution function f of the velocity grid from time n to time n + 1, and discretize the microscopic control equation (Equation (2)) in physical and velocity spaces to obtain the discrete Boltzmann-BGK:

[0099]

[0100] where i and k represent the numbers of the physical grid cell (control volume) and the velocity grid cell respectively. Integrate Equation (8) over the physical grid cell and organize it as follows:

[0101]

[0102] where, |V i | represents the volume of the i-th control volume, represents the microscopic flux at the half time:

[0103]

[0104] where, represents the surface of the i-th control volume, dS is the surface element of the control volume, n is the unit outer normal vector of the element, is the distribution function at the half time on the physical unit interface reconstructed by integrating the Boltzmann equation along the characteristic line. It should be noted that in Equation (9), the midpoint formula and the trapezoidal formula are used to numerically integrate the microscopic flux term and the collision term respectively. Taking the moments of Equation (9) in the velocity space, the update equation of the macroscopic quantity can be obtained:

[0105]

[0106] where S represents the source term, and for monatomic gases, the source term is zero. represents the macroscopic flux at the half time:

[0107]

[0108] After obtaining the macroscopic quantities at the (n + 1)-th moment through formula (11), the equilibrium state g in the collision term at the (n + 1)-th moment can be obtained. *,n+1 and the relaxation time t i . Then, the update equation of the distribution function can be obtained:

[0109]

[0110] S105: Based on several updates, determine whether the flow field converges based on the updated flow field physical quantities; if so, execute S106; if not, jump to S103 and S104 until the flow field converges.

[0111] Determining whether the flow field converges specifically includes:

[0112] Taking the velocity residual as the convergence criterion, and the criterion formula is:

[0113]

[0114] where and represent the velocity fields separated by n iterative steps, and ε is the convergence threshold.

[0115] S106: Process the converged flow field to obtain flow characteristic parameters.

[0116] Input the flow field physical quantities into the processing software Tecplot to obtain flow field parameters such as density, velocity, temperature contour maps, etc., and generate pictures or calculate key parameters such as lift and drag.

[0117] See Figure 3 , the present invention discloses an efficient numerical system for simulating the flow in the whole basin, including:

[0118] A construction module, which is used to obtain the aircraft shape geometric parameters and gas flow information; based on the obtained aircraft shape geometric parameters and gas flow information, construct the physical grid of the aircraft.

[0119] A first acquisition module, which is used to obtain the equilibrium state distribution function of the velocity grid based on the macroscopic quantities stored in the physical grid.

[0120] A first judgment module, which is used to obtain several unequal adaptive criterion values based on the macroscopic quantities stored in the physical grid and the distribution function of the velocity grid; select the adaptive criterion value with the largest numerical value among the several adaptive criterion values, and compare the selected adaptive criterion value with the coarsening threshold and refinement threshold of the velocity grid adaptively respectively to determine whether to perform velocity grid adaptation; among them, the velocity grid distribution function at the initial moment is equal to the equilibrium state distribution function of the velocity grid.

[0121] An update module, which updates the cell-centered distribution function in the reconstructed velocity grid again based on the macroscopic quantities stored in the physical grid, the equilibrium distribution function of the velocity grid, and the distribution function of the velocity grid, to obtain the updated flow field physical quantities;

[0122] A second judgment module, which judges whether the flow field converges based on the updated flow field physical quantities after several updates;

[0123] A second acquisition module, which processes the converged flow field to obtain flow characteristic parameters.

[0124] The present invention uses a binary tree or quadtree data structure to store two-dimensional velocity grid information, and an octree data structure to store three-dimensional velocity grid information. For simplicity, the quadtree data structure is used to illustrate the coarsening (merging multiple grids into one grid) and refinement (splitting one grid into multiple grids) processes of velocity grid adaptation.

[0125] The storage of the tree data structure is implemented with a doubly linked list, as Figure 4 (a) shows, the root node is the root node, which can only be split and cannot be merged, and its Level is 0. The root node is split once to obtain four child nodes k1 to k4 at Level 1. Without loss of generality, assume that the child node k4 satisfies the refinement criterion and is split again into four child nodes k41 to k44 at Level 2. At this time, the child node k4 is also the parent node of the child nodes k41 to k44. And so on, the child nodes at Level i that satisfy the refinement criterion can continue to be split to obtain four child nodes at Level i + 1. Generally, a node without child nodes is called a leaf node, such as Figure 4 (a) k1, k2, and k3 are leaf nodes, which are like the leaves at the treetops; four child nodes with the same parent node are called sibling nodes, such as Figure 4 (a) k1 to k4 and k41 to k44. The coarsening process can be regarded as the reverse process of the refinement process. Only when all four sibling nodes are leaf nodes and satisfy the coarsening criterion can they be merged into the parent node. For example, Figure 4 (a) when the child nodes k41 to k44 satisfy the coarsening criterion, they can be merged into their parent node k4. Since the child node k4 is not a leaf node, the child nodes k1 to k4 cannot be merged into their parent node root node. Only when the child nodes k41 to k44 are merged into their parent node k4, and the child nodes k1 to k4 satisfy the coarsening criterion, can they be merged into their parent node root node. And so on, when all four sibling nodes at Level i are leaf nodes and satisfy the coarsening criterion, they can be merged into their parent node at Level i - 1. Figure 4 (b) is Figure 4(a) The velocity grid corresponding to the tree structure, i.e., only the leaf nodes k1, k2, k3, k41, k42, k43, k44 are the units of the velocity grid.

[0126] Perform grid adaptation according to the criteria:

[0127] After storing the tree structure in a doubly linked list, i.e., Figure 4 (a), the coarsening / refinement marking can be performed according to the following density criterion and internal energy criterion, and grid adaptation can be carried out. For the i-th physical grid unit and the k-th velocity grid unit u k , there is:

[0128]

[0129]

[0130] Among them, is the area or volume of the velocity grid unit u k , u k is the k-th velocity grid unit; is the grid-centered distribution function; ρ i , ρ i E i are the density, velocity, kinetic energy, and total energy of the gas in the i-th physical grid unit, respectively.

[0131] Take and the maximum value of as the final judgment criterion for the unit u k :

[0132]

[0133] The adaptive refinement threshold and coarsening threshold are C1 and C2, respectively. When , the velocity grid unit u k is marked as a unit that needs to be refined. When , the velocity grid unit u k is marked as a unit that needs to be coarsened. When , the velocity grid unit u k does not need to perform adaptation. The adaptive refinement threshold and coarsening threshold are both set artificially; among them, adaptive refinement is the splitting of a velocity grid into several sub-velocity grids; adaptive coarsening is the merging of several velocity grids into a parent velocity grid.

[0134] Extract leaf node information to generate a velocity grid and reconstruct the grid-centered distribution function of the physical grid:

[0135] Denote the doubly linked lists before coarsening (before adaptation), after coarsening, and after refinement (after adaptation) as List_old, List_mid, and List_new respectively. Then, the mapping relationships between List_old and List_mid, and between List_mid and List_new can be obtained in sequence, and the mapping relationship between List_old and List_new can also be obtained accordingly. The specific method is as follows:

[0136] If the i-th node in List_mid is obtained by merging 4j nodes in List_old (j represents the number of coarsening times, or the difference in Level values), then the distribution function of the i-th node is equal to the average of the distribution functions of the 4j nodes; if the i-th node in List_new is obtained by splitting the j-th node in List_mid, then the i-th node belongs to the child nodes of the j-th node, and the distribution function of the i-th node is equal to the distribution function of the j-th node; if the i-th node in List_new directly inherits the j-th node in List_old, that is, without coarsening or refinement, the distribution function of the i-th node is equal to the distribution function of the j-th node. Taking Figure 4 (b) as an example, if the velocity grid corresponding to List_old is a grid composed of seven nodes k1, k2, k3, k41, k42, k43, k44, and the velocity grid corresponding to List_mid obtained after one coarsening is a grid composed of four nodes k1, k2, k3, k4, then the distribution functions of nodes k1, k2, k3 in List_mid are equal to the distribution functions of nodes k1, k2, k3 in List_old, and the distribution function of node k4 in List_mid is equal to the average of the distribution functions of the four nodes k41, k42, k43, k44 in List_old; if the velocity grid corresponding to List_old is a grid composed of seven nodes k1, k2, k3, k41, k42, k43, k44, and the velocity grid corresponding to List_mid obtained after two coarsenings is a grid composed of one node root, then the distribution function of the root node in List_mid is equal to the average of the distribution functions of the seven nodes k1, k2, k3, k41, k42, k43, k44 in List_old. If the velocity grid corresponding to List_mid is a grid composed of one node root, then the distribution functions of the nodes split from root in List_new are all equal to the distribution function of root, that is, during the refinement process, Figure 4 the distribution functions of k1, k2, k3, k41, k42, k43, k44 in (b) are all equal to the distribution function of root.

[0137] The distribution function obtained according to the above mapping relationship has errors and needs to be corrected for conservation. Denote the macroscopic quantity at physical unit i as The distribution function obtained after adaptation according to the mapping relationship is denoted as For Taking moments in the velocity space after adaptation gives macroscopic quantities Then the corrected distribution function can be expressed as:

[0138]

[0139] where \(g\) is the Maxwell equilibrium distribution.

[0140] In summary, the technical solution of the velocity grid adaptation technology in S103 is: establish a tree - shaped structure double - linked list, perform grid adaptation according to the criterion, extract leaf node information to generate the velocity grid and reconstruct the physical grid cell - center distribution function.

[0141] The embodiments of the present invention are as follows:

[0142] Step 1: Obtain the geometric parameters of the aircraft shape and gas flow information; based on the obtained geometric parameters of the aircraft shape and gas flow information, construct the physical grid of the aircraft. The physical grid is as Figure 5 shown.

[0143] Step 2: Set the initial flow field, state parameters and boundary conditions according to the flow characteristics. The test conditions are shown in Table 1. The initial flow density, velocity, pressure and equilibrium temperature are all set to the free - stream state. The initial flow field can be directly used to calculate the adaptation criterion. Based on the macroscopic quantities stored in the physical grid, obtain the distribution function of the velocity grid.

[0144] Table 1 Test conditions for a rarefied hypersonic flat plate

[0145] Test group Case1 Working gas Nitrogen Mach number (Ma) 4.89 Knudsen number (Kn) 0.78 Inflow pressure (Pa) 2.12 Inflow temperature (K) 116 Wall temperature (K) 290 Collision model Rykov model Molecular model VHS

[0146] Step 3: Based on the macroscopic quantities stored in the physical grid and the distribution function of the velocity grid, obtain two unequal adaptive criterion values; select the larger value of the two adaptive criteria, and compare the selected adaptive criterion value with the coarsening threshold and refinement threshold of the velocity grid adaptation respectively to determine whether to perform velocity grid adaptation. If so, reconstruct the cell - center distribution function in the velocity grid; if not, do nothing. The adaptively generated velocity grid is as Figure 6 shown.

[0147] Step 4: Based on the macroscopic quantities stored in the physical grid and the distribution function of the velocity grid, update the reconstructed physical cell - center distribution function again to obtain the updated flow field physical quantities.

[0148] Step 5: Based on several updates, determine whether the flow field converges based on the updated flow field physical quantities; if so, execute Step 6; if not, jump to Steps 3 and 4 until the flow field converges;

[0149] Step 6: Process the converged flow field to obtain flow characteristic parameters.

[0150] Figure 7 They are the density, equilibrium temperature, translational temperature, and rotational temperature contour maps of the rarefied hypersonic flat plate, Figure 8 They are the temperature distributions along the vertical direction at different horizontal positions of the rarefied hypersonic flat plate. See Figure 7 and Figure 8 , and the current calculation results are in good agreement with the reference results, verifying the correctness of the method of the present invention.

[0151] For the flow around a thin hypersonic flat plate example, Reference 1 used a Cartesian uniform velocity grid with 4,800 cells, i.e., 80x60, while after using the velocity space adaptive technology in this embodiment, the obtained velocity grid has only 748 cells, which is only 15.6% of the original.

[0152] Reference 1 is Liu S, Yu P, Xu K, et al. Unified gas-kinetic scheme for diatomic molecular simulations in all flow regimes[J]. Journal of Computational Physics, 2014, 259: 96-113.

[0153] The terminal device provided by an embodiment of the present invention. The terminal device of this embodiment includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps in the above-mentioned various method embodiments. Alternatively, when the processor executes the computer program, it implements the functions of each module / unit in the above-mentioned various device embodiments.

[0154] The computer program can be divided into one or more modules / units, and the one or more modules / units are stored in the memory and executed by the processor to complete the present invention.

[0155] The terminal device can be a computing device such as a desktop computer, a notebook, a palm computer, and a cloud server. The terminal device may include, but is not limited to, a processor and a memory.

[0156] The processor may be a Central Processing Unit (CPU), or may also be other general-purpose processors, Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0157] The memory can be used to store the computer program and / or modules. By running or executing the computer program and / or modules stored in the memory, and by invoking the data stored in the memory, the processor realizes various functions of the terminal device.

[0158] If the modules / units integrated in the terminal device are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, to implement all or part of the processes in the above method embodiments of the present invention, it can also be completed by a computer program instructing relevant hardware. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by the processor, the steps of the above various method embodiments can be realized. Among them, the computer program includes computer program code, and the computer program code can be in the form of source code, object code, executable file, or some intermediate form, etc. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disk, computer memory, Read-Only Memory (ROM), Random Access Memory (RAM), electrical carrier signal, telecommunication signal, and software distribution medium, etc. It should be noted that the content included in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, the computer-readable medium does not include electrical carrier signals and telecommunication signals.

[0159] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. An efficient numerical method for simulating the flow of the entire basin, characterized in that, including: Step 1: Obtain the geometric parameters of the aircraft shape and gas flow information; based on the obtained geometric parameters of the aircraft shape and gas flow information, construct the physical grid of the aircraft; Step 2: Based on the macroscopic quantities stored in the physical grid, obtain the equilibrium distribution function of the velocity grid; Specifically: Among them, , , and are the discrete velocity, gas constant, temperature, and velocity respectively; the macroscopic quantities include the density, velocity, and temperature of the gas; Step 3: Based on the macroscopic quantities stored in the physical grid and the distribution function of the velocity grid, obtain several adaptive criterion values with different numerical values; select the adaptive criterion value with the largest numerical value among the several adaptive criterion values, and compare the selected adaptive criterion value with the coarsening threshold and refinement threshold of the velocity grid adaptation respectively to determine whether to perform velocity grid adaptation. If so, reconstruct the cell-centered distribution function in the velocity grid; if not, do nothing; where the velocity grid distribution function at the initial moment is equal to the equilibrium distribution function of the velocity grid; Based on the macroscopic quantities stored in the physical grid and the distribution function of the velocity grid, obtain several adaptive criterion values; Specifically: Among them, is the area or volume of the velocity grid cell , is the th velocity grid cell; is the grid center distribution function; , , , are respectively the density, velocity, kinetic energy, and total energy of the gas in the i-th physical grid cell; Step 4: Based on the macroscopic quantities stored in the physical grid, the equilibrium distribution function of the velocity grid and the distribution function of the velocity grid, update the cell-centered distribution function in the reconstructed velocity grid again to obtain the updated flow field physical quantities; Step 5: Based on several updates, based on the updated flow field physical quantities, determine whether the flow field converges; if so, execute Step 6; if not, jump to Step 3 and Step 4 until the flow field converges; Step 6: Process the converged flow field to obtain the flow characteristic parameters.

2. The efficient numerical method for simulating the flow in the entire river basin according to claim 1, characterized in that The number of adaptive criterion values is the number of physical grid cells multiplied by 2; each physical grid cell contains two adaptive criterion values.

3. The efficient numerical method for simulating the flow in the whole basin according to claim 2, characterized in that The selection of the adaptive criterion value with the largest numerical value among the several adaptive criterion values is specifically: The comparison of the selected adaptive criterion value with the coarsening threshold and refinement threshold of the velocity grid adaptation respectively is specifically: The adaptive refinement threshold and coarsening threshold are respectively and When the velocity grid cell is marked as a cell to be refined. When the velocity grid cell is marked as a cell to be coarsened. When the velocity grid cell does not require adaptation; Both the adaptive refinement threshold and the coarsening threshold are set artificially; where adaptive refinement is that one velocity grid is split into several sub-velocity grids; adaptive coarsening is that several velocity grids are merged into one parent velocity grid.

4. The efficient numerical method for simulating the full-watershed flow according to claim 3, wherein The reconstruction of the cell-centered distribution function in the velocity grid is specifically: When the velocity grid cell is marked as the cell to be refined, the velocity grid cell splits into a number of sub-velocity grid cells, and the grid center distribution function of each sub-velocity grid cell is the same as that of the velocity grid cell ; each sub-velocity grid cell splits again to obtain second-level sub-velocity grid cells, and the grid center distribution function of each sub-velocity grid cell is the same as that of its own second-level sub-velocity grid cell; When the velocity grid cell is marked as a cell to be coarsened, and several velocity grid cells are merged into a parent velocity grid cell; the centroid distribution function of the parent velocity grid cell is the average value after adding the centroid distribution functions of several velocity grid cells .

5. The efficient numerical method for simulating the full-watershed flow according to claim 4, wherein The reconstruction of the cell-centered distribution function in the velocity grid further includes: Perform conservation correction on the cell-centered distribution function obtained by splitting or merging, specifically: wherein, is the macroscopic quantity at physical unit i, is the cell-centered distribution function after adaptation, is the macroscopic quantity obtained by integrating , and g is the Maxwell equilibrium distribution.

6. The efficient numerical method for simulating the full-watershed flow according to claim 5, characterized in that The determination of whether the flow field converges is specifically: Taking the velocity residual as the convergence criterion, and the criterion formula is: wherein and represent the velocity fields between n iterative steps apart, is the convergence threshold.

7. An efficient numerical system for simulating the flow in the entire river basin, based on the efficient numerical method for simulating the flow in the entire river basin according to any one of claims 1 to 6, characterized in that, including: A construction module, which is used to obtain the geometric parameters of the aircraft shape and gas flow information; based on the obtained geometric parameters of the aircraft shape and gas flow information, construct the physical grid of the aircraft; A first acquisition module, which is used to obtain the equilibrium distribution function of the velocity grid based on the macroscopic quantities stored in the physical grid; A first judgment module, which is used to obtain several adaptive criterion values with different numerical values based on the macroscopic quantities stored in the physical grid and the distribution function of the velocity grid; Select the adaptive criterion value with the largest value among several adaptive criterion values, and compare the selected adaptive criterion value with the coarsening threshold and the refinement threshold of the velocity grid adaption respectively to determine whether to perform velocity grid adaption; wherein, the velocity grid distribution function at the initial moment is equal to the equilibrium distribution function of the velocity grid. An update module, which is based on the macroscopic quantities stored in the physical grid, the equilibrium distribution function of the velocity grid, and the distribution function of the velocity grid, and updates the cell-centered distribution function in the reconstructed velocity grid again to obtain the updated flow field physical quantities. A second judgment module, which is based on several updates and judges whether the flow field converges based on the updated flow field physical quantities. A second acquisition module, which is used to process the converged flow field to obtain the flow characteristic parameters.

8. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-6.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the method according to any one of claims 1-6.

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