Magnetic fluid flow control method and system based on spatial fractional order model

Abstract

The present disclosure provides a magnetic fluid flow control method and system based on a spatial fractional order model, which relates to the field of magnetic fluid mechanics. The method includes constructing a coupling model of velocity, magnetic field and temperature of magnetic fluid flow in a thermonuclear reaction process; considering the velocity and magnetic field in a certain direction, obtaining a two-dimensional dimensionless coupled spatial fractional order equation through variable transformation; using a backward difference method for discretization in the time direction, using a spectral point matching method for discretization in the spatial direction, obtaining a full matrix generated by a spatial discrete fractional order Laplace operator through matrix transfer, solving the full matrix by constructing a Krylov subspace and solving a shifted linear system, and controlling the temperature change in the thermonuclear reaction process according to numerical simulation. The present disclosure effectively improves the acceleration efficiency of complex magnetic fluids with long-range correlation.

Description

Technical Field

[0001] The present disclosure relates to the technical field of magnetofluid mechanics, and in particular to a magnetofluid flow control method and system based on a spatial fractional order model. Background Art

[0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art.

[0003] Magnetohydrodynamics is a discipline that combines the methods of classical fluid mechanics and electrodynamics to study the laws of motion of conductive fluids (plasma, liquid metal or electrolyte, etc.) in electromagnetic fields and their interactions. The most widely studied is the interaction between plasma and electromagnetic fields, which is closely related to aviation applications. As a continuous medium and electromagnetic medium, magnetic fluid has many important properties that ordinary fluids do not have. It presents more special magnetic, optical and electrical phenomena than ordinary fluids, and has better ductility and fluidity than ordinary solid magnetic materials. At present, with the progress of artificial ionization technology and the research of superconducting materials, various new plasma generation methods are being developed. The lightweight carbon nanotube superconducting materials developed have shown great application potential in aviation engineering, making it possible to use the magnetohydrodynamic effect to control the external and internal flow of aircraft into engineering applications.

[0004] Energy issues have always been a hot topic of concern in today's society. Since a large amount of nuclear energy can be released during thermonuclear reactions, which is the main energy source of the sun, stars and hydrogen bombs, thermonuclear reactions have received widespread attention. Controlled thermonuclear reactions are carried out under controllable conditions. The reaction process is not as violent as a hydrogen bomb, and the released energy can be converted into electrical energy, effectively alleviating the energy shortage problem faced today and providing a large amount of energy for production and life. However, temperature changes in this process will have a certain impact and even produce adverse consequences. Since magnetic fluids have the magnetism of magnets, the electromagnetic induction phenomenon and magnetic confinement characteristics they possess can be used to effectively control temperature changes during thermonuclear reactions. Since magnetic fluids have both magnetic properties and fluidity, in the above process, the magnetic fluids themselves will also be accompanied by temperature changes, which will also have an impact on the flow of magnetic fluids.

[0005] According to the characteristics of magnetic fluid flow, people use the magnetic field to preserve the magnetic confinement of plasma to constrain the speed and temperature during the flow process, thus realizing the application of magnetic fluid acceleration technology. At present, magnetic fluid acceleration wind tunnels have been used in aerospace hypersonic aircraft and their power plants and other scientific and technological fields, bringing new concepts and innovations to aerospace aircraft or propulsion system test technology, and greatly promoting the progress and development of magnetic fluid in the application of aerospace technology.

[0006] With the development of experimental technology, people have discovered a large number of systems that exhibit anomalous transport behaviors. Their physical manifestation is that the transport process no longer obeys various standard "gradient" laws, and their theoretical essence lies in the fact that the central limit theorem is not followed. Whether from the perspective of basic theoretical research or engineering application research, how to accurately characterize this physical process is a challenge. Since the end of the 20th century, due to the relevant research on anomalous diffusion, porous media mechanics, non-Newtonian fluids, viscoelastic mechanics, and turbulence, the research and application of fractional operator theory has received widespread attention. The engineering and mechanical modeling of fractional operators is essentially different from the integer derivative modeling. The integer spatial derivative describes the local properties of a physical quantity at a certain position, while the spatial fractional operator describes the entire space involved in the physical quantity. In general, fractional derivative modeling can provide a more profound and comprehensive explanation of the "abnormal" properties such as memory and heredity, non-locality, self-similarity, and path dependence involved in complex environments.

[0007] The spatial fractional-order model of magnetic fluid has practical significance and broad application prospects in magnetohydrodynamics. However, for this type of model, the exact solution is generally difficult to obtain through analytical methods, and there is no mature numerical calculation software at present; the coefficient matrix of the linear equations obtained by the numerical method is often a full matrix, which brings great difficulties and challenges to both calculation and storage, making the flow control efficiency of magnetic fluid low. Summary of the invention

[0008] In order to solve the above problems, the present invention proposes a magnetic fluid flow control method and system based on a spatial fractional order model, solves the model based on a matrix function-vector product method, effectively improves the acceleration efficiency of complex magnetic fluids with long-range correlations, derives a coupling model of the velocity, magnetic field and temperature of the magnetic fluid flow, and effectively controls the temperature changes during thermonuclear reactions.

[0009] According to some embodiments, the present disclosure adopts the following technical solutions:

[0010] The magnetic fluid flow control method based on the spatial fractional order model includes:

[0011] Construct a coupled model of the velocity, magnetic field and temperature of magnetic fluid flow during thermonuclear reactions;

[0012] Considering the velocity and magnetic field in a certain direction, the two-dimensional dimensionless coupled spatial fractional-order equation is obtained by variable transformation;

[0013] The time direction is discretized by the backward difference method, and the space direction is discretized by the spectral collocation method. Through matrix transfer, the full matrix generated by the spatial discrete fractional-order Laplace operator is obtained. The full matrix is ​​solved by constructing a Krylov subspace and solving the shifted linear system. According to numerical simulation, the temperature change in the thermonuclear reaction process is controlled.

[0014] According to some embodiments, the present disclosure adopts the following technical solutions:

[0015] A magnetic fluid flow control system based on a spatial fractional order model, including:

[0016] Model building module, used to build a coupled model of velocity, magnetic field and temperature of magnetic fluid flow during thermonuclear reaction;

[0017] The model solving module is used to consider the velocity and magnetic field in a certain direction and obtain the two-dimensional dimensionless coupled spatial fractional equation through variable transformation;

[0018] The time direction is discretized by the backward difference method, and the space direction is discretized by the spectral collocation method. Through matrix transfer, the full matrix generated by the spatial discrete fractional-order Laplace operator is obtained. The full matrix is ​​solved by constructing a Krylov subspace and solving the shifted linear system. According to numerical simulation, the temperature change in the thermonuclear reaction process is controlled.

[0019] According to some embodiments, the present disclosure adopts the following technical solutions:

[0020] A computer-readable storage medium stores a plurality of instructions, wherein the instructions are suitable for being loaded and executed by a processor of a terminal device for the magnetic fluid flow control method based on a spatial fractional order model.

[0021] According to some embodiments, the present disclosure adopts the following technical solutions:

[0022] A terminal device includes a processor and a computer-readable storage medium, wherein the processor is used to implement various instructions; the computer-readable storage medium is used to store multiple instructions, wherein the instructions are suitable for being loaded by the processor and executing the magnetic fluid flow control method based on the spatial fractional order model.

[0023] Compared with the prior art, the present invention has the following beneficial effects:

[0024] The present invention establishes a fast calculation framework of a full matrix based on a symmetric Lanczos algorithm and a polynomial preprocessing method, and uses a spatial fractional-order operator to numerically calculate a corresponding matrix, which is a full matrix, greatly improving the optimization and calculation efficiency of the magnetic fluid model. Based on the matrix-function-vector product method, a fast calculation method is developed to solve the obtained linear system. First, a Krylov subspace is constructed and the symmetric Lanczos algorithm is used to reduce the solution dimension, and then a polynomial preprocessing method is used to improve the solution speed and reduce the storage amount. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The accompanying drawings constituting a part of the present disclosure are used to provide a further understanding of the present disclosure. The illustrative embodiments of the present disclosure and their descriptions are used to explain the present disclosure and do not constitute an improper limitation on the present disclosure.

[0026] Figure 1 A flowchart of a fast algorithm for a magnetic fluid spatial fractional-order model according to an embodiment of the present disclosure;

[0027] Figure 2 A comparison chart of the calculation time of the fast algorithm and the direct method of the embodiment of the present disclosure. DETAILED DESCRIPTION

[0028] The present disclosure is further described below in conjunction with the accompanying drawings and embodiments.

[0029] It should be noted that the following detailed descriptions are all illustrative and are intended to provide further explanation of the present disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present disclosure belongs.

[0030] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present disclosure. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0031] Example 1

[0032] In one embodiment of the present disclosure, a magnetic fluid flow control method based on a spatial fractional order model is provided, comprising the following steps:

[0033] Step 1: Construct a coupled model of the velocity, magnetic field and temperature of the magnetic fluid flow during the thermonuclear reaction;

[0034] Step 2: Considering the velocity and magnetic field in a certain direction, obtain the two-dimensional dimensionless coupled spatial fractional-order equation through variable transformation;

[0035] Step 3: The time direction is discretized by the backward difference method, and the space direction is discretized by the spectral collocation method. Through matrix transfer, the full matrix generated by the spatial discrete fractional-order Laplace operator is obtained. The full matrix is ​​solved by constructing a Krylov subspace and solving the shifted linear system. According to numerical simulation, the temperature change during the thermonuclear reaction is controlled.

[0036] As an embodiment, the present disclosure establishes a fast calculation framework for full matrices based on the symmetric Lanczos algorithm and the polynomial preprocessing method, and develops a fast calculation method based on the matrix function vector product method to solve the obtained linear system. The specific control method is implemented as follows:

[0037] Since the magnetic fluid involves complex coupling effects of flow field, magnetic field and electric field, in order to study the velocity field of magnetic fluid movement and the changing law of electromagnetic field inside it, based on the continuity equation, momentum equation, energy equation, law of electromagnetic induction, and considering the influence of Hall effect, the temperature equation with fractional heat diffusion term is derived using Boussinesq equation, and the coupling equation of spatial fractional fluid flow and magnetic field change is obtained as follows. Since magnetic fluid has the magnetic properties of magnets, its electromagnetic induction phenomenon and magnetic confinement can be used to effectively control the temperature change during thermonuclear reaction. Since magnetic fluid has both magnetic properties and fluidity, in the above process, the magnetic fluid itself will also be accompanied by temperature changes, which will also affect the flow of magnetic fluid. Based on this, a coupling model of velocity, magnetic field and temperature of magnetic fluid flow is derived.

[0038] Provides fast algorithms for spatial fractional MHD flow and heat transfer coupled models, see Figure 1 The flowchart of the fast algorithm of the magnetic fluid spatial fractional order model is shown in FIG. 1 , and the steps of the method are:

[0039] Step 1: Assume that the direction of the gravitational acceleration vector is the same as the direction of the velocity vector, and the direction of the magnetic field vector is perpendicular to the direction of the velocity vector. Based on the spatial fractional constitutive model without fluid pressure, the generalized Ohm's law, the magnetic equation with spatial fractional magnetic diffusion, and the spatial fractional energy equation with Joule heating effect, the following model is obtained. Formulas (1)-(5) are the coupled models of velocity, magnetic field, and temperature of magnetic fluid flow.

[0040] The momentum equation for unsteady MHD free convection can be given as:

[0041]

[0042] Where u is the velocity vector, b is the magnetic field vector, S is the Cauchy stress tensor, T is the temperature, ρ is the fluid density, and βT is the thermal expansion coefficient, g is the gravitational acceleration vector, J is the current density vector, is the gradient operator. Assume that the direction of the gravitational acceleration vector is the same as the direction of the velocity vector, and the direction of the magnetic field vector is perpendicular to the direction of the velocity vector. The spatial fractional constitutive model without fluid pressure is:

[0043]

[0044] Among them, v α is the fractional dynamic viscosity, α is the fractional order parameter, ▽ α-1 is the fractional gradient operator. Ignoring the influence of the electric field, the generalized Ohm's law with the Hall effect can be written as:

[0045] J+ξ h (J×b)=σ h (u×b), (3)

[0046] Among them, ξ h is the parameter of the Hall effect, σ h is the electrical conductivity of the fluid.

[0047] The magnetic equation with spatial fractional magnetic diffusion is:

[0048]

[0049] Among them, β is the fractional order parameter, μ β is the magnetic field viscosity coefficient.

[0050] The spatial fractional-order energy equation with Joule heating effect is:

[0051]

[0052] Among them, γ is the fractional order parameter, C p is the heat capacity, v γ is the thermal conductivity. R j is the Joule heating effect, expressed as

[0053] The process of step 2 to obtain the two-dimensional dimensionless coupled spatial fractional-order equation is as follows: introduce dimensionless quantities, consider the velocity and magnetic field in a certain direction, and obtain the two-dimensional dimensionless coupled spatial fractional-order equation with homogeneous boundary conditions and initial conditions through variable transformation.

[0054] Specifically, the following dimensionless quantities are introduced:

[0055]

[0056] Where h is the characteristic length, U0 is the characteristic velocity, B0 is the characteristic magnetic field, and T0 is the characteristic temperature. v and μ are the viscosity parameters of velocity and magnetic field, respectively. K γ is a parameter that represents the relationship between energy and momentum transfer, G r is the Grahof number, M is the Hartmann number, m is the Hall parameter, H γ is the Joule heating parameter.

[0057] Considering the velocity and magnetic field in a certain direction, through variable transformation, in order to study the general case, the following two-dimensional dimensionless coupled spatial fractional equation with homogeneous boundary conditions and initial conditions (remove the asterisk) is obtained:

[0058]

[0059]

[0060]

[0061]

[0062]

[0063] here is a first-order differential operator in the direction d = {x, y, z}, u, b are the velocity and magnetic field in a specific direction, θ is the temperature of the fluid, and u0, b0, θ0 are the initial condition functions of velocity, magnetic field and temperature. (-Δ) α / 2 , (-Δ) β / 2 and (-Δ) γ / 2 represents the two-dimensional fractional Laplace operator of order 1<α,β,γ≤2.

[0064] For any f(x,y) and 1<σ≤2, (-Δ) σ / 2 f(x,y) is defined as:

[0065]

[0066] in (λ ij ,φ ij ), i, j = 1, 2, ... are the eigenvalues ​​and orthogonal eigenfunctions of the standard Laplace operator (-Δ) under the corresponding homogeneous boundary conditions on Ω, that is, (-Δ)φ ij =λ ij φ ij .

[0067] Step 3: Establish a numerical method to solve the two-dimensional dimensionless coupled spatial fractional-order equations, including: discretizing the time direction using the backward difference method, discretizing the spatial direction using the spectral collocation method, defining an approximate space to represent the approximate matrix of the first-order differential operator and the standard Laplace operator, and constructing an approximate matrix of the fractional-order Laplace operator through matrix transfer.

[0068] Specifically, a numerical method is established to solve equations (6)-(10). The time direction is discretized using the backward difference method, and the space direction is discretized using the spectral point method. The following symbols are introduced

[0069] Let t∈(0,T), t n =nτ,n=0,1,…,n T , where τ = T / n T is the time step, n T is a positive integer. Let N be a positive integer, the approximate space can be defined as

[0070]

[0071] in Then we get the fully discrete solution: find So that for 1≤n≤n T and 2≤i,j≤N-1,

[0072]

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] Let U n , B n , Θ n Respectively represent u N (x,y,t n ), b N (x,y,t n ) and θ N (x,y,t n ) expansion coefficient vector. The approximate matrix representation of the first-order differential operator and the standard Laplace operator can be expressed as M P,d and M L . And through the matrix transfer technique, the fractional Laplace operator (-Δ)σ / 2 The approximate matrix is Therefore, the matrix representation of equations (11)-(16) is:

[0079]

[0080]

[0081]

[0082] Among them, M B is the basic function matrix, i=1,2,3 depends on The vector of k,l=1,2,…,N.

[0083] Step 4: Obtain a full matrix generated by a spatial discrete fractional-order Laplace operator according to the approximate matrix, and solve the full matrix generated by the spatial discrete fractional-order Laplace operator using a fast algorithm.

[0084] First, construct a Krylov subspace to reduce the solution dimension. Let A be an approximate matrix, r be a vector, Λ and Q represent the eigenvalue diagonal matrix and orthogonal eigenvector matrix of matrix A respectively. From the Cauchy integral formula, we know that for any analytical function f, f(A)r can be written as

[0085]

[0086] Where C is a known closed contour and i is a complex unit. It can be seen that the above formula can be expressed as:

[0087]

[0088] in

[0089]

[0090] λ1,λ N denote the minimum and maximum eigenvalues ​​of A, respectively. sn(ζ), cn(ζ) and dn(ζ) are Jacobi elliptic functions, K and K′ are the The full elliptic integral of . Using the midpoint approximation rule, we can know that f(A)r can be approximately expressed as:

[0091]

[0092] in

[0093]

[0094] Here P is the number of orthogonal points, ζ j is the summing point. Using the symmetric Lanczos algorithm, we can see that as well as Linear equation (z j The solution of IA)x=r is:

[0095] x m =‖r‖2V m (z j IT m ) -1 e1,

[0096] Where V m and T m It is given by the symmetric Lancaos algorithm. m is the dimension of the corresponding Krylov subspace K(A,r), which can be obtained from the error and tolerance e of the Lanczos algorithm. tol Calculated.

[0097] Next, based on the polynomial preprocessing method, a set of orthogonal eigenvectors are recalculated according to the minimum l eigenvalue of A, so that f(A)r can be approximated as

[0098]

[0099] in ω j are orthogonal weights. j For the equation The solution. To reduce the matrix, we map the smallest l-th eigenvalue of A to a given value λ * As established above, it is defined as Error and tolerance using Lanczos algorithm tol The correction value m can be recalculated, and m and l are when κ=λ N / λ l+1 When , the value that minimizes l+2m. Suppose there are two q-order polynomials and p(x), satisfying p(x) is the Jacobi weight The least squares polynomial of zj (x) is the value of z j Suppose there exists a polynomial about z j Parameters Make Using the above formula we can get and Next, construct the modified Lanczos decomposition:

[0100]

[0101] Then the approximate solution can be expressed as

[0102]

[0103] Thus, the final solution expression can be obtained.

[0104] Here, the general fast calculation algorithm is as follows:

[0105] Fast Algorithm for Solving f(A)r

[0106] Input: f(x),A,r,p(x),l,ω j ,z j ,P.

[0107] Output: f(A)r.

[0108] Step 1: Deflation preprocessing

[0109]

[0110] Step 2: Polynomial preprocessing

[0111]

[0112] in is the solution of the shift system Constructing the preprocessed Lanczos decomposition

[0113]

[0114] therefore in It can be calculated by the following equation

[0115]

[0116] Step 3: Let f(x) = 1 / x. Apply the above process and substitute the result into the numerical process to obtain the final result.

[0117] Step 5: Based on the fast calculation in step 4, calculate the numerical format in step 3.

[0118] Based on the magnetic induction phenomenon and magnetic confinement, the model and the proposed numerical algorithm simultaneously obtain the changes in speed, magnetic field and temperature. The purpose is to obtain the changes in speed and temperature, and further realize the magnetic fluid acceleration technology.

[0119] In the experimental verification of the present disclosure, Figure 2, the calculation time of the fast method and the direct method are plotted. It can be clearly seen that the calculation time of the fast method is less than that of the direct method. Therefore, it can be shown that the fast method is effective in saving calculation time.

[0120] Example 2

[0121] In one embodiment of the present disclosure, a magnetic fluid flow control system based on a spatial fractional order model is provided, comprising:

[0122] Model building module, used to build a coupled model of velocity, magnetic field and temperature of magnetic fluid flow during thermonuclear reaction;

[0123] The model solving module is used to consider the velocity and magnetic field in a certain direction and obtain the two-dimensional dimensionless coupled spatial fractional equation through variable transformation;

[0124] The time direction is discretized by the backward difference method, and the space direction is discretized by the spectral collocation method. Through matrix transfer, the full matrix generated by the spatial discrete fractional-order Laplace operator is obtained. The full matrix is ​​solved by constructing a Krylov subspace and solving the shifted linear system. According to numerical simulation, the temperature change in the thermonuclear reaction process is controlled.

[0125] Example 3

[0126] In one embodiment of the present disclosure, a computer-readable storage medium is provided, in which a plurality of instructions are stored, and the instructions are suitable for being loaded and executed by a processor of a terminal device to control the magnetic fluid flow based on a spatial fractional order model.

[0127] Example 4

[0128] In one embodiment of the present disclosure, a terminal device is provided, including a processor and a computer-readable storage medium, the processor is used to implement various instructions; the computer-readable storage medium is used to store multiple instructions, and the instructions are suitable for being loaded by the processor and executing the magnetic fluid flow control method based on the spatial fractional order model.

[0129] The present disclosure is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present disclosure. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1A device that provides the functions specified in a block or multiple blocks.

[0130] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0131] Although the above describes the specific implementation methods of the present disclosure in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present disclosure. Technical personnel in the relevant field should understand that on the basis of the technical solution of the present disclosure, various modifications or variations that can be made by those skilled in the art without creative work are still within the scope of protection of the present disclosure.

Claims

1. A magnetic fluid flow control method based on a spatial fractional order model, characterized in that: include: Construct a coupled model of the velocity, magnetic field and temperature of magnetic fluid flow during thermonuclear reactions; Considering the velocity and magnetic field in a certain direction, the two-dimensional dimensionless coupled spatial fractional-order equation is obtained by variable transformation; The time direction is discretized by the backward difference method, and the space direction is discretized by the spectral collocation method. Through matrix transfer, the full matrix generated by the spatial discrete fractional-order Laplace operator is obtained. The full matrix is ​​solved by constructing the Krylov subspace and solving the shifted linear system. According to the numerical simulation, the temperature change in the thermonuclear reaction process is controlled. Establish a numerical method to solve the two-dimensional dimensionless coupled spatial fractional-order equations, including: using the backward difference method to discretize the time direction, using the spectral collocation method to discretize the spatial direction, defining the approximate matrix of the first-order differential operator and the standard Laplace operator in the approximate space, and constructing the approximate matrix of the fractional-order Laplace operator through matrix transfer; The approximate matrix obtains a full matrix generated by a spatial discrete fractional-order Laplace operator, and solves the full matrix generated by the spatial discrete fractional-order Laplace operator using a fast algorithm; First, construct a Krylov subspace to reduce the dimension of the solution. is an approximate matrix, is a vector, and Respectively represent matrices The eigenvalue diagonal matrix and orthogonal eigenvector matrix of , from the Cauchy integral formula, we know that for any analytic function , It can be written as in is a known closed contour, is a complex unit, and is mapped by conformal mapping It can be seen that the above formula can be expressed as: in Respectively The minimum and maximum eigenvalues ​​of and is the Jacobi elliptic function, and For about and The full elliptic integral of , using the midpoint approximation rule, is: It can be approximately expressed as: in is the number of orthogonal points, To find the summing point, the symmetric Lanczos algorithm is used, since as well as , the linear equation The solution is: in and Given by the symmetric Lancaos algorithm, is the corresponding Krylov subspace The dimension of , given by the error and tolerance of the Lanczos algorithm Calculated; Based on the polynomial preprocessing method, The minimum The eigenvalues ​​recompute a set of orthogonal eigenvectors, so that Can be approximated as in , are orthogonal weights, For the equation The solution; To reduce the matrix, Minimum The eigenvalue is mapped to a given value As established above, it is defined as , using the error and tolerance of the Lanczos algorithm Correction values ​​can be recalculated , and For When The smallest value; suppose there are two Polynomial and ,satisfy ; For Jacobi weight The least squares polynomial of , About A modified polynomial of Parameters , so that , using the above formula we get and Expression for ; construct the modified Lanczos decomposition: Then the approximate solution is expressed as Get the final solution expression; The general fast calculation algorithm is as follows: Solution Fast algorithm enter: ; Output: ; Step 1: Deflation preprocessing Step 2: Polynomial preprocessing in is the solution of the shift system , construct the preprocessed Lanczos decomposition therefore ,in It can be calculated by the following equation ； Step 3: Order , using the above process, the obtained results are brought into the numerical process to obtain the final result.

2. The magnetic fluid flow control method based on the spatial fractional order model according to claim 1, characterized in that: The process of constructing the coupled model of velocity, magnetic field and temperature of magnetic fluid flow during thermonuclear reaction is as follows: assuming that the direction of the gravitational acceleration vector is the same as the direction of the velocity vector, and the direction of the magnetic field vector is perpendicular to the direction of the velocity vector, the coupled model of velocity, magnetic field and temperature of magnetic fluid flow during thermonuclear reaction is obtained based on the spatial fractional constitutive model without fluid pressure, the generalized Ohm's law, the magnetic equation with spatial fractional magnetic diffusion and the spatial fractional energy equation with Joule heating effect.

3. The magnetic fluid flow control method based on the spatial fractional order model according to claim 1 is characterized in that: The process of obtaining the two-dimensional dimensionless coupled spatial fractional equation is as follows: introducing dimensionless quantities, considering the velocity and magnetic field in a certain direction, and obtaining the two-dimensional dimensionless coupled spatial fractional equation with homogeneous boundary conditions and initial conditions through variable transformation.

4. The magnetic fluid flow control method based on the spatial fractional order model according to claim 1, characterized in that: The process of solving the problem by using a fast algorithm includes: first constructing a Krylov subspace to reduce the dimension of the solution, constructing a fast algorithm by solving a shifted linear system, and performing numerical simulation to obtain a numerical value based on the fast calculation algorithm.

5. The magnetic fluid flow control method based on the spatial fractional order model according to claim 2, wherein the spatial fractional order constitutive model without fluid pressure is: in, is the fractional dynamic viscosity, is the fractional order parameter, is the fractional gradient operator, is the velocity vector.

6. A magnetic fluid flow control system based on a spatial fractional order model, characterized in that: include: Model building module, used to build a coupled model of velocity, magnetic field and temperature of magnetic fluid flow during thermonuclear reaction; The model solving module is used to consider the velocity and magnetic field in a certain direction and obtain the two-dimensional dimensionless coupled spatial fractional equation through variable transformation; The time direction is discretized by the backward difference method, and the space direction is discretized by the spectral collocation method. Through matrix transfer, the full matrix generated by the spatial discrete fractional-order Laplace operator is obtained. The full matrix is ​​solved by constructing the Krylov subspace and solving the shifted linear system. According to the numerical simulation, the temperature change in the thermonuclear reaction process is controlled. Establish a numerical method to solve the two-dimensional dimensionless coupled spatial fractional-order equations, including: using the backward difference method to discretize the time direction, using the spectral collocation method to discretize the spatial direction, defining the approximate matrix of the first-order differential operator and the standard Laplace operator in the approximate space, and constructing the approximate matrix of the fractional-order Laplace operator through matrix transfer; The approximate matrix obtains a full matrix generated by a spatial discrete fractional-order Laplace operator, and solves the full matrix generated by the spatial discrete fractional-order Laplace operator using a fast algorithm; First, construct a Krylov subspace to reduce the dimension of the solution. is an approximate matrix, is a vector, and Respectively represent matrices The eigenvalue diagonal matrix and orthogonal eigenvector matrix of , from the Cauchy integral formula, we know that for any analytic function , It can be written as in is a known closed contour, is a complex unit, and is mapped by conformal mapping It can be seen that the above formula can be expressed as: in Respectively The minimum and maximum eigenvalues ​​of and is the Jacobi elliptic function, and For about and The full elliptic integral of , using the midpoint approximation rule, is: It can be approximately expressed as: in is the number of orthogonal points, To find the summing point, the symmetric Lanczos algorithm is used, since as well as , the linear equation The solution is: in and Given by the symmetric Lancaos algorithm, is the corresponding Krylov subspace The dimension of , given by the error and tolerance of the Lanczos algorithm Calculated; Based on the polynomial preprocessing method, The minimum The eigenvalues ​​recompute a set of orthogonal eigenvectors, so that Can be approximated as in , are orthogonal weights, For the equation The solution; To reduce the matrix, The minimum The eigenvalue is mapped to a given value As established above, it is defined as , using the error and tolerance of the Lanczos algorithm Correction values ​​can be recalculated , and For When The smallest value; suppose there are two Polynomial and ,satisfy ; For Jacobi weight The least squares polynomial of , For about A modified polynomial of Parameters , so that , using the above formula we get and Expression for ; construct the modified Lanczos decomposition: Then the approximate solution is expressed as Get the final solution expression; The general fast calculation algorithm is as follows: Solution Fast algorithm enter: ; Output: ; Step 1: Deflation preprocessing Step 2: Polynomial preprocessing in is the solution of the shift system , construct the preprocessed Lanczos decomposition therefore ,in It can be calculated by the following equation ； Step 3: Order , using the above process, the obtained results are brought into the numerical process to obtain the final result.

7. A computer-readable storage medium, characterized in that: A plurality of instructions are stored therein, and the instructions are suitable for being loaded by a processor of a terminal device and executing the magnetic fluid flow control method based on a spatial fractional order model as described in any one of claims 1-5.

8. A terminal device, characterized in that: It includes a processor and a computer-readable storage medium, the processor is used to implement various instructions; the computer-readable storage medium is used to store multiple instructions, and the instructions are suitable for being loaded by the processor and executing the magnetic fluid flow control method based on the spatial fractional order model as described in any one of claims 1-5.

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