Method for realizing fluid stealth effect by regulating permeability in porous medium through conformal auxiliary tracking method

Abstract

The invention discloses a method for realizing a fluid stealth effect by regulating and controlling permeability in a porous medium through a conformal auxiliary tracking method. The method comprises the following steps of: solving a Darcy flow field control equation in a porous medium to generate an orthogonal conformal grid formed by streamlines and isobaric lines; in combination with the Darcy law, scalar distribution of isotropic permeability is designed along a flow line and an isobaric line, then pressure boundary conditions and speed boundary conditions are accurately matched, the influence of geometric distortion on a flow field is compensated, extension invariance of a conformal grid is maintained, uniform streaming of fluid in a target area is completed, and the stealth function of the Darcy flow field is achieved. According to the method, the porous medium metamaterial model with the permeability capable of being precisely regulated and controlled is given, a fluid regulation and control mechanism based on geometry-physical cooperation is constructed through conformal scalar design of isotropic permeability, and the method is suitable for functional areas in any shape and has important application value in micro-fluidic stealth, underground water pollution isolation and thermal management optimization.

Description

Technical Field

[0001] This invention relates to the field of porous media flow control and metamaterial design technology, specifically, to a method for controlling the permeability of porous media to achieve fluid stealth effect using a conformal assisted tracking method. Background Technology

[0002] In fields such as oil extraction, groundwater pollution control, and microfluidic chip design, precise control of the Darcy flow field within porous media is crucial. "Flow field stealth" technology aims to make a specific target area "invisible" to the background flow field, thereby optimizing flow efficiency, protecting critical components, or preventing harmful diffusion. Current technologies primarily rely on two strategies: structural design and material composites. Structural design guides streamlines by constructing complex physical flow-guiding structures, but its drawbacks include: poor flexibility, difficulty adapting to irregular targets or dynamic flow fields; complex manufacturing, especially costly and impractical in microscale or underground environments. Material composites involve arranging materials with different permeabilities around the target, but its limitations include: insufficient control precision, reliance on pre-set discrete material combinations, difficulty in achieving spatially continuous permeability gradients; and susceptibility to flow field distortion and additional pressure drop at interfaces. Therefore, there is an urgent need to develop a method that is flexible, efficient, and applicable to various irregular shapes.

[0003] In summary, existing methods are limited by fixed geometric configurations or material properties, making it difficult to flexibly adapt to complex target shapes and background flow fields. Furthermore, the control process is often invasive and destructive. The Conformal Assisted Tracking (CAT) method utilizes the conformal properties of conformal meshes to match the flow field stealth requirements and combines the relationship between permeability and porosity to achieve dynamic parameter adjustment. It can be introduced into porous media to achieve flow field stealth control. Summary of the Invention

[0004] To address the shortcomings and deficiencies of the existing technologies, this invention provides a method for controlling permeability in porous media to achieve fluid stealth. This method leverages the advantages of conformal-assisted tracking—no analytical functions required, adaptability to arbitrary shapes, and reliance on isotropic media—by presenting a porous media metamaterial model with precisely controllable permeability. Through conformal scalar design of isotropic permeability, a fluid control mechanism based on geometric-physical coordination is constructed, applicable to functional regions of arbitrary shapes. This has significant application value in microfluidic stealth, groundwater pollution isolation, and thermal management optimization.

[0005] The technical details of this invention are described below.

[0006] A method for controlling permeability in porous media to achieve fluid stealth effect using conformal assisted tracking includes the following steps:

[0007] (1) By solving the Darcy flow field control equation in porous media, an orthogonal conformal grid composed of streamlines and isobars is generated, realizing the conformal mapping from the original porous medium region to the regular region;

[0008] (2) Combining Darcy's law, design a scalar distribution of isotropic permeability along streamlines and isobars;

[0009] (3) By accurately matching the pressure boundary conditions and velocity boundary conditions, the influence of geometric distortion on the flow field is compensated, the elongation invariance of the conformal grid is maintained, the uniform flow of fluid around the target area is completed, and finally the stealth function of the Darcy flow field is realized.

[0010] In this invention, the original porous medium region refers to the overall porous medium space containing the target stealth region, which is a naturally existing complex porous space; the regular region is an artificially simplified ideal porous space; the background region and functional region of the stealth device are structural subdivisions of the original region; the background region provides stable flow field boundary conditions to drive fluid flow; the functional region generates a conformal grid composed of streamlines and isobars by precisely controlling the permeability, guiding the flow field around the central region (i.e., the target stealth region), ensuring that the flow field in the background region remains continuous and uniform after passing through the functional region, and ultimately achieving the stealth effect of the Darcy flow field in the entire original porous medium region.

[0011] In this invention, the fluids applicable to the flow field include Newtonian fluids (such as water, polyethylene glycol aqueous solution, etc.) and non-Newtonian fluids (such as starch solution, paint, etc.).

[0012] In this invention, the background area of ​​the stealth functional device is rhomboid, with two concentric circles set in the middle of the area. The annular area enclosed by the concentric circles is the functional area, and the entire device is laid with a porous medium.

[0013] In this invention, in step (1), by solving the Darcy flow field control equation in the porous medium, an orthogonal conformal grid composed of streamlines and isobars is generated to conformally map the original porous medium region containing the target stealth region to a regular region. Then, an isotropic scalar distribution of permeability is designed along the streamlines and isobars. At the same time, the final permeability is designed by matching pressure boundary conditions and velocity boundary conditions to achieve the stealth function of the target region; specifically as follows:

[0014] Solve the Darcy flow field governing equations in porous media, i.e., the Laplace equations:

[0015]

[0016] Where: p represents pressure.

[0017] Numerical solutions to the Laplace equation yield the spatial distribution of pressure p in the original region, allowing us to understand the flow field characteristics under complex geometries and laying the foundation for subsequent mesh generation and parameter design. Streamlines (fluid trajectories, with tangents aligned with velocity) and isobars (pressure contour lines, with normals aligned with pressure gradients) are mathematically orthogonal because they satisfy the Cauchy-Riemann equations. This ensures that conformal meshes composed of streamlines and isobars can replace analytical functions in traditional conformal mappings.

[0018] In this invention, step (2) incorporates Darcy's law:

[0019]

[0020] Where: p represents pressure, μ is viscosity coefficient, κ is permeability, and v is fluid velocity.

[0021] In this invention, in step (3), the pressure boundary condition requires matching the boundary normal velocity V. n The permeability along the streamline is:

[0022]

[0023] Where: κ0 is the matrix permeability, η is the initial permeability coefficient, and v n and v' n The boundary normal velocity before and after design.

[0024] Velocity boundary conditions: The tangential pressure gradient must be matched to the boundary conditions; the permeability along the isobars is:

[0025]

[0026] Where: κ0 is the matrix permeability, η is the initial permeability coefficient, and G p and G' p This represents the boundary tangential pressure gradient before and after the design.

[0027] Since streamlines and isobars are orthogonal, the product of their permeabilities is the final scalar permeability. Therefore, the final permeability is:

[0028]

[0029] This formula compensates for the influence of geometric distortion on the flow field by using the ratio of normal velocity to tangential pressure gradient, maintains the "stretch invariance" of the conformal grid, and makes the flow field in complex regions equivalent to the ideal flow field in regular regions, thus achieving simplified control by "scalar parameters replacing tensor parameters".

[0030] In a specific embodiment of this invention, the pressure boundary condition for the stealth functional device is set to P = -x, where x is a physical quantity describing the coordinates; the velocity boundary condition is set to N = -1 × 10⁻¹⁰. 6 *nx, where nx is the normal vector;

[0031] In this invention, pressure boundary conditions and velocity boundary conditions can be reset for different fluid densities and viscosities, matrix permeability of different porous media distributions, and different stealth device structures.

[0032] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0033] This invention presents a porous medium metamaterial model with precisely controllable permeability distribution. The invention is verified using finite element method (FEM) software. The structural geometry is set with a rhomboid background material region, concentric circles in the center of the region, the smaller circle representing the central region, and the annular region outside the smaller circle representing the functional region. The stealth functional material device structure of this invention is laid out as a fluid material structure. The pressure boundary condition is set as P = -x, where x is a physical quantity describing the coordinates; the velocity boundary condition is set as N = -1 × 10⁻¹⁰. 6 *nx, where nx is the normal direction. This invention, under composite boundary conditions, verifies the effect of modulating the spatial distribution of isotropic permeability of porous media on the stealth effect of Darcy flow; the results show that:

[0034] (1) This invention achieves the effect of precise control of permeability and stealth of Darcy flow field.

[0035] (2) This invention breaks through the limitation of anisotropic permeability tensor and is applicable to porous media of any shape, such as regular shapes (circles, etc.) and irregular shapes (arbitrary polygons, etc.).

[0036] (3) This invention can achieve the effect of matching the pressure boundary condition P = -x and the velocity boundary condition N = -1 × 10 6 *nx generates a conformal mesh applicable to any shape, significantly improving accuracy and efficiency. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the permeability distribution in a porous medium.

[0038] Figure 2 This is a diagram showing the streamline distribution of the Darcy flow field.

[0039] Figure 3 This is a diagram showing the isobaric distribution of the Darcy flow field.

[0040] Figure 4 A custom expression diagram for pressure boundary conditions.

[0041] Figure 5 A graph of custom expressions for velocity boundary conditions.

[0042] Figure 6 This is a spatial distribution diagram of the permeability of porous media under pressure boundary conditions.

[0043] Figure 7 This is a spatial distribution diagram of the permeability of porous media under velocity boundary conditions.

[0044] Figure 8 This is a pressure distribution diagram after permeability regulation under pressure boundary conditions.

[0045] Figure 9 This is a pressure distribution diagram after permeability regulation under velocity boundary conditions.

[0046] Figure 10 This is a comparison diagram of the pressure magnitude at different locations under pressure boundary conditions between theoretical and simulated conditions.

[0047] Figure 11 This is a comparison diagram of the pressure magnitude at different locations under velocity boundary conditions between theoretical and simulated conditions. Detailed Implementation

[0048] The present invention will now be described clearly and completely with reference to the accompanying drawings and embodiments.

[0049] This invention generates an orthogonal conformal grid composed of streamlines and isobars by solving the Darcy flow field governing equations in porous media. Combining Darcy's law, a scalar distribution of isotropic permeability is designed, and then the final permeability is synergistically controlled by matching pressure and velocity boundary conditions, achieving precise control of permeability and thus achieving a stealth effect. The main scientific principles of this method will be detailed below:

[0050] 1. Generate conformal mesh

[0051] Solve the Darcy flow field governing equations in porous media, i.e., the Laplace equations:

[0052]

[0053] Where: p represents pressure.

[0054] Numerical solutions to the Laplace equation yield the spatial distribution of pressure p in the original region, allowing us to understand the flow field characteristics under complex geometries and laying the foundation for subsequent mesh generation and parameter design. Streamlines (fluid trajectories, with tangents aligned with velocity) and isobars (pressure contour lines, with normals aligned with pressure gradients) are mathematically orthogonal because they satisfy the Cauchy-Riemann equations. This ensures that conformal meshes composed of streamlines and isobars can replace analytical functions in traditional conformal mappings.

[0055] 2. Design a scalar of isotropic permeability based on Darcy's law.

[0056] Darcy's Law:

[0057]

[0058] Where: p represents pressure, μ is viscosity coefficient, κ is permeability, and v is fluid velocity.

[0059] The pressure boundary condition matches the normal velocity along the boundary, and the permeability along the streamline is:

[0060]

[0061] The velocity boundary condition matches the boundary tangential pressure gradient, and the permeability along the isobars is:

[0062]

[0063] Where: κ0 is the matrix permeability, η(x0,y0) is the initial permeability coefficient, and Vn(y(x0,y0)) and V' are... n (y(x0,y0)) represents the boundary normal velocity before and after the design; G p (x(x0,y0) and G' p (x(x0,y0) represents the boundary tangential pressure gradient before and after the design.)

[0064] Since streamlines and isobars are orthogonal, the product of their permeabilities is the final scalar permeability. Therefore, the final permeability is:

[0065]

[0066] This formula compensates for the influence of geometric distortion on the flow field by using the ratio of normal velocity to tangential pressure gradient, maintains the "stretch invariance" of the conformal grid, and makes the flow field in complex regions equivalent to the ideal flow field in regular regions, thus achieving simplified control by "scalar parameters replacing tensor parameters".

[0067] 3. Boundary conditions

[0068] Boundary conditions are key inputs for constraining flow field characteristics and defining the "stealth target" of the flow field. This invention sets pressure boundary conditions and velocity boundary conditions respectively, and through the synergistic constraint of the two boundary conditions, it ensures that the flow field is undisturbed outside the target region.

[0069] Pressure boundary conditions specify the pressure values ​​at the inlet and outlet of a porous medium flow field, which are used to drive fluid flow and constrain the flow field distribution.

[0070] Pressure and velocity boundary conditions are set for different fluid densities and viscosities, matrix permeability of different porous media distributions, and stealth device structures.

[0071] In a specific implementation of this invention, pressure boundary conditions are set:

[0072] P = -x

[0073] Velocity boundary conditions define the fluid velocity at the boundary of a porous medium flow field, constraining the direction and rate of fluid motion. In this invention, the following relationship is considered between velocity and inward mass flux of the fluid:

[0074] N = ρ·v

[0075] Where: N is the inward mass flux, ρ is the fluid density, and v is the fluid velocity.

[0076] Based on Darcy's law, the viscosity coefficient μ is set to 0.001 Pa·s, and the permeability κ is set to 1 m. 2 Therefore, k / μ = 1000, and since The gradient operator is directional; for a pure background, the direction is x; the fluid is chosen to be water with a density ρ = 1000 kg / m³. 3 Therefore, this invention sets velocity boundary conditions:

[0077] N = -1 × 10 6 *nx

[0078] By using a coordinated control mechanism of pressure boundary conditions and velocity boundary conditions, the conformal mesh can be made to strictly satisfy elongation invariance at the boundary. Combined with 1 and 2, the conformal mesh has angularity, elongation invariance, and parameter continuity. Therefore, the conformal mesh can be applied to complex geometries (i.e., stealth functional devices of various shapes). On this conformal mesh, we can precisely control the isotropic permeability to achieve uniform flow around the target area. Even if the fluid neither enters the stealth area nor generates detectable flow field disturbances on the periphery, the stealth effect can be achieved.

[0079] In summary, the above theoretical methods are scientifically feasible. We further extend them to finite element simulation to verify their feasibility through numerical simulation. We apply them to the Darcy flow field in porous media, analyzing streamline and isobar distribution maps. Using these maps, we plot custom expressions under pressure and velocity boundary conditions. We then derive the coordinates of isobar nodes and corresponding pressure values ​​under pressure boundary conditions, and the coordinates of streamline nodes and inward mass flux under velocity boundary conditions. Using these discrete permeability data as input, we construct a continuous permeability distribution using interpolation functions. Through simulation, we analyze the spatial distribution of permeability, the pressure distribution after permeability adjustment, and the comparison of pressure magnitudes at different locations between the theoretical and simulated methods. This verifies whether the permeability distribution achieves a stealth effect in the Darcy flow field within the porous media, thus validating the feasibility of this invention.

[0080] This invention uses COMSOL Multiphysics finite element simulation to design a model of thermal superstructure materials. For example... Figure 1 As shown, for simple fluid mass transfer, the Darcy's law module under porous media is used for design: the structure is designed with inner and outer circles, and the annular region is the functional area. Water is used as the fluid, and each region is set with isotropic permeability. The background plate size is 6×6m. 2 The central circle has a radius of 0.8m, and the outer circle has a radius of 1m. The background region (Zone I) and the central region (Zone III) are set with the same isotropic permeability, i.e., K. Ⅲ and K Ⅰ All are 1m 2 The isotropic permeability K of functional zone (zone II) Ⅱ Set to 1×10 -5 m 2 The distribution of this permeability is a preliminary distribution obtained based on conformal mapping theory, the determinant of the Jacobian matrix, and Darcy's law.

[0081] Subsequently, this invention generates conformal meshes adapted to complex geometries by matching boundary conditions. For example... Figure 2 The figure shows the streamline distribution of the Darcy flow field under pressure boundary conditions, which can be obtained by setting the pressure boundary condition P = -x at the material boundary. The figure presents the streamline trajectories of the flow field, with the horizontal and vertical axes ranging from -4 to 4 m. The streamlines exhibit a smooth flow around the target area, uniformly bypassing it in the central region without significant convergence or divergence, verifying the guiding effect of the conformal grid on the fluid flow direction. Streamline density reflects the velocity distribution—sparser streamlines in the edge region indicate higher velocity; denser streamlines near the central target area indicate slower velocity. Figure 3 The diagram shows the isobaric distribution of the Darcy flow field under velocity boundary conditions. This is achieved by setting the velocity boundary condition N = -1 × 10⁻¹⁰ at the material boundary.6 *nx is obtained. Isobars are regularly parallel and evenly spaced within the range of -4 to 4 m, without local distortion. The pressure gradient in the edge region is stable, while the isobars around the central target area transition smoothly without abrupt pressure changes. The conformal mesh obtained by matching pressure and velocity boundary conditions consists of streamlines and isobars. Combined with previous theories, this conformal mesh possesses conformal geometry, invariant scaling factor, and parameter continuity, allowing for precise control of isotropic permeability.

[0082] Next, we use custom expressions to convert mathematical formulas into calculable physical quantities. For example... Figure 4 The diagram shows a custom expression under pressure boundary conditions. The horizontal axis (x-axis) represents the y-direction of the spatial coordinate system, corresponding to the direction perpendicular to the two-dimensional flow field. The vertical axis (y-axis) represents the custom expression: 1e 3 *nx / (nx·dl.u+ny·dl.v). Where nx and ny are the x and y components of the normal unit vector of the boundary, and dl.u and dl.v are the x and y components of the total Darcy velocity field. This custom expression refers to the expression for the streamline permeability: Where (x0, y0) are the coordinates of any point. As the x-value changes from -4 to 4, the permeability ratio exhibits a wave-like trend. This is due to the change in the boundary normal velocity ratio V'n / Vn, reflecting the compensating effect of streamline permeability on geometric distortion. The streamline permeability curve shows a peak near x = ±2, gradually decreasing towards both sides, indicating that a higher permeability is needed in the central region to guide the fluid flow around it. Figure 2 The streamlines are distributed uniformly. For example... Figure 5 The diagram shows a custom expression under velocity boundary conditions. The horizontal axis (x-axis) represents the x-direction of the spatial coordinate system, corresponding to the horizontal direction of the two-dimensional flow field. The vertical axis (y-axis) represents the custom expression: -(dtang(p2,x)*tx+dtang(p2,y)*ty) / tx. Here, p2 is the pressure in the Darcy field, and tx and ty are the x and y components of the tangential unit vector of the boundary. This custom expression refers to the expression for permeability along isobars. Where (x0, y0) are the coordinates of any point. As the value of x changes from -4 to 4, the permeability ratio exhibits a wave-like changing trend. This is due to the change in the tangential pressure gradient ratio Gt' / Gt, reflecting the compensating effect of permeability along the isobaric direction on geometric distortion. The isobaric permeability curve shows a peak near x = ±2, gradually decreasing towards both sides, indicating that a higher permeability is required in the central region to guide fluid flow around the curve. Figure 3 The isobars are distributed in a consistent manner.

[0083] Next, the coordinates of isobaric nodes and corresponding pressure values ​​under pressure boundary conditions and the coordinates of streamline nodes and inward mass flux under velocity boundary conditions are exported respectively. These discrete permeability data are used as inputs, and a continuous permeability distribution is constructed using an interpolation function.

[0084] After constructing a continuous permeability distribution using an interpolation function, such as Figure 6-11 To verify whether this permeability distribution enables the Darcy flow field in porous media to achieve a stealth effect, we analyzed and plotted the spatial distribution of permeability in porous media under different boundary conditions, the pressure distribution after permeability regulation under different boundary conditions, and the comparison of theoretical and simulated pressure at different locations under different boundary conditions. These findings verified the feasibility and scalability of the invention from different perspectives.

[0085] Figure 6 This is a spatial distribution map of the permeability of a porous medium under pressure boundary conditions. The permeability is represented by a color gradient. Due to the isotropic nature of permeability, the X component equals the Y component, which equals the Z component. The map shows that the central region is darker, representing higher permeability. Based on the color legend, the permeability is approximately 1.2 × 10⁻⁶. -12 m 2 It gradually becomes lighter towards the edges, with the permeability decreasing to approximately 0.2 × 10⁻⁶. -12 m 2 .

[0086] Figure 7 This is a spatial distribution map of the permeability of porous media under velocity boundary conditions. The central region is darker in color, and based on the color legend, the permeability is approximately 1.8 × 10⁻⁶. -12 m 2 The edge penetration rate is approximately 0.4 × 10⁻⁶. -12 m 2 The gradient change is steeper. According to Figure 6 and Figure 7 It can be seen that the larger geometric distortion in the central region requires a higher permeability to compensate for it, thereby guiding the fluid to flow around it uniformly, while the smooth transition of the color gradient indicates the continuous spatial regulation of permeability.

[0087] Figure 8 This is a pressure distribution diagram after permeability regulation under pressure boundary conditions. The isobars are smooth curves in the range of -5 to 5 m. The isobars in the central target area show no obvious distortion and are consistent with the pressure gradient in the edge region.

[0088] Figure 9 This is a pressure distribution diagram after permeability regulation under velocity boundary conditions. The shape of the isobars and... Figure 8 The overall pattern remains consistent, but the pressure gradient varies slightly, reflecting the impact of adjusting the velocity boundary conditions on the pressure field. According to... Figure 8 and Figure 9 It can be seen that after permeability control, the pressure field still satisfies the linear distribution of Darcy's law, and there is no pressure abrupt change due to the presence of the target area. The regular distribution of isobars further verifies that the conformal assisted tracking method achieves pressure field homogenization through permeability control, ensuring that the flow field forms a stable flow state around the target area, thus achieving a stealth effect.

[0089] Figure 10 This is a comparison graph showing the pressure magnitude at different locations under pressure boundary conditions, based on theoretical and simulated values. In polar coordinates, the solid lines represent the theoretical pressure values ​​at different locations along the four sides of the rhombus, while the dashed lines represent the simulated pressure values ​​at different locations along the four sides of the rhombus. The comparison reveals that the theoretical curves and simulated data almost perfectly overlap.

[0090] Figure 11 This is a comparison graph showing the pressure magnitude at different locations under velocity boundary conditions between theoretical and simulated values. In polar coordinates, the solid lines represent the theoretical pressure values ​​at different locations along the four sides of the rhombus, while the dashed lines represent the simulated pressure values ​​at the same locations. The comparison reveals that the theoretical curves and simulated data completely overlap. Based on... Figure 10 and Figure 11 The curve shows no fluctuations, verifying the uniformity of the flow field across the entire angular range using the conformal-assisted tracking method. Regardless of geometric rotation, the pressure distribution around the target area remains symmetrical, indicating that this method has a universal stealth effect on porous media with arbitrary polygons, breaking through the limitations of traditional methods on regular geometry.

[0091] This invention proposes a conformal-assisted tracking method to control permeability in porous media to achieve fluid stealth, enabling precise control of permeability in the Darcy flow field within porous media. By solving the Darcy flow field control equations in the porous media, an orthogonal conformal mesh composed of streamlines and isobars is generated. Combining Darcy's law, an isotropic scalar distribution of permeability is designed along the streamlines and isobars. Permeability is then synergistically controlled by matching pressure and velocity boundary conditions. Simultaneously, a custom expression is used to transform the mathematical formula into calculable physical quantities, and data on isobar node coordinates and corresponding pressure values ​​under pressure boundary conditions, and streamline node coordinates and inward mass flux under velocity boundary conditions, are derived. These discrete permeability data are used as input, and an interpolation function is used to construct a continuous permeability distribution. This permeability distribution promotes uniform flow around the target region, ultimately achieving a stealth effect. Finally, finite element simulation is used to verify the feasibility of the design method. This invention overcomes the limitations of traditional anisotropic permeability tensors, is applicable to porous media of arbitrary shapes, and possesses high computational efficiency and control accuracy.

Claims

1. A method for controlling permeability in porous media to achieve fluid stealth effect using a conformal assisted tracking method, characterized in that, Includes the following steps: (1) By solving the Darcy flow field control equation in porous media, an orthogonal conformal grid composed of streamlines and isobars is generated, realizing the conformal mapping from the original porous media region to the regular region; (2) Combining Darcy's law, design a scalar distribution of isotropic permeability along streamlines and isobars; (3) By accurately matching the pressure boundary conditions and velocity boundary conditions, the influence of geometric distortion on the flow field is compensated, the elongation invariance of the conformal grid is maintained, the uniform flow of fluid around the target area is completed, and finally the stealth function of the Darcy flow field is realized.

2. The method according to claim 1, characterized in that, The fluids in the applicable flow field can be Newtonian or non-Newtonian fluids; Newtonian fluids include water or aqueous solutions of polyethylene glycol, and non-Newtonian fluids include starch solutions or paint.

3. The method according to claim 1, characterized in that, The background area of ​​the stealth device is rhomboid, with two concentric circles in the middle. The annular area enclosed by the concentric circles is the functional area, and the entire device is covered with a porous medium.

4. The method according to claim 3, characterized in that, In step (1), based on solving the Darcy flow field control equation in the porous medium, the original porous medium region containing the target stealth zone is conformally mapped to the regular region; specifically as follows: The Darcy flow field governing equation in porous media, also known as the Laplace equation: Where: p represents pressure; By numerically solving the Laplace equation, the spatial distribution of pressure p in the original region is obtained, thereby revealing the flow field characteristics under complex geometry, laying the foundation for subsequent mesh generation and parameter design. Since streamlines and isobars satisfy the Cauchy-Riemann equation, they are mathematically orthogonal, which ensures that the conformal mesh composed of streamlines and isobars can replace the analytical functions in the traditional conformal mapping.

5. The method according to claim 3, characterized in that, In step (3), the pressure boundary condition matches the boundary normal velocity, and the permeability along the streamline is: The velocity boundary condition matches the boundary tangential pressure gradient, and the permeability along the isobar is: Where: κ0 is the matrix permeability, η(x0,y0) is the initial permeability coefficient, and Vn(y(x0,y0)) and V' are... n (y(x0,y0)) represents the boundary normal velocity before and after the design; G p (x(x0,y0) and G' p (x(x0,y0) represents the boundary tangential pressure gradient before and after the design.) Since streamlines and isobars are orthogonal, the product of their permeabilities is the final scalar permeability. Therefore, the final permeability is: This formula compensates for the influence of geometric distortion on the flow field by using the ratio of normal velocity to tangential pressure gradient, maintains the "stretch invariance" of the conformal grid, and makes the flow field in complex regions equivalent to the ideal flow field in regular regions, thus achieving simplified control by "scalar parameters replacing tensor parameters".

6. The method according to claim 3, characterized in that, The pressure boundary condition for the stealth device is set to P = -x, where x is a physical quantity describing the coordinates; the velocity boundary condition is set to N = -1 × 10⁻¹⁰. 6 *nx, where nx is the normal vector.

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