Multiphysics Coupling Calculation Method for Parachutes Based on Sharp Interface Immersed Boundaries
By combining the sharp interface immersion boundary method with the coupling of CalculiX and the preCICE library, the efficiency and accuracy problems of large deformation and multiphysics coupling during parachute inflation are solved, and a reliable simulation of the parachute inflation process is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
- Filing Date
- 2023-08-09
- Publication Date
- 2026-06-30
Smart Images
Figure CN117131625B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the fields of computational fluid dynamics, computational structural dynamics, and fluid-structure interaction, and specifically relates to a multiphysics coupling calculation method for parachutes based on sharp interface immersion boundaries. Background Technology
[0002] Parachute inflation plays a crucial role in aerospace engineering. Parachute inflation involves complex fluid-structure interaction (FSI) phenomena, and accurately simulating this interaction requires the development of advanced numerical calculation methods.
[0003] Over the past few decades, numerical methods for solving parachute inflation FSI problems have made significant progress. The Arbitrary Lagrangian-Eulerian (ALE) method combines the advantages of Eulerian and Lagrangian methods, allowing the mesh to move and deform with fluid flow while retaining the advantages of the fixed-mesh Eulerian method. Therefore, it is widely used to simulate large deformations of parachute fabrics. The Deformation Space Domain / Stable Spacetime (DSD / SST) method proposed by the T*AFSM research team combines the advantages of the Deformation Space Domain method and the Stable Spacetime method, accurately simulating the dynamic behavior of parachutes during inflation. The Immersed Boundary (IB) method, because it does not require dynamically generating a body-fitted mesh, is suitable for solving problems involving large structural deformations or displacements, and has gradually become a popular method for simulating parachute inflation FSI in recent years. Kim and Peskin used the IB method to study the inflation process of two-dimensional and three-dimensional semi-open parachutes. Xue et al. used the IB method to study the effects of parachute lines, canopy angle of attack, and reentry capsule angle of attack on hemispherical parachute systems. Liu et al. proposed an IB-Lattice Boltzmann (LB) based FSI solver to study the inflation process of different types of parachute systems. Boustani et al. developed a high-fidelity FSI solver based on the IB method and the finite element method to simulate the supersonic parachute inflation process of the ASPIRESR01 flight test.
[0004] The open-source coupling tool preCICE has recently attracted widespread attention for its application in multiphysics coupling. The preCICE library possesses all the necessary functionalities for multiphysics coupling simulations, enabling the rapid development of corresponding multiphysics simulation environments based on existing single-physics black-box solvers. Thanks to these attractive features, the preCICE library has been successfully applied to the simulation of multiphysics coupling processes under various conditions. Summary of the Invention
[0005] Objective: The technical problem this invention aims to solve is to address the shortcomings of existing technologies by providing a multiphysics coupling calculation method for parachutes based on sharp interface immersion boundary. The fluid component is based on the sharp interface immersion boundary method, while the structural component is solved using the open-source finite element code CalculiX. The connection between the fluid and structural solvers is implemented using the open-source multiphysics coupling library preCICE. To overcome the strong added mass effect caused by the lightweight structure of the parachute canopy, an implicit coupling method with internal iteration is adopted within each time step. The method established in this invention can reliably simulate the inflation process of various typical parachutes, possessing certain theoretical research significance and practical application value. This invention specifically includes the following steps:
[0006] Step 1: Establish the governing equations for the fluid;
[0007] Step 2: Establish the governing equations for the structural dynamics of the parachute;
[0008] Step 3: Use the open-source multiphysics coupling library preCICE to connect the IB solver with CalculiX;
[0009] Step 4: Configure the calculation settings for the fluid domain;
[0010] Step 5: Configure the calculation settings for the solid domain;
[0011] Step 6: Conduct a numerical experiment on the typical parachute inflation process.
[0012] Step 1 includes: The governing equations for the fluid are the following three-dimensional unsteady incompressible Navier-Stokes equations:
[0013] (1),
[0014] (2),
[0015] in, , , , These represent the velocity, density, pressure, and kinematic viscosity of the fluid in the i-direction, respectively; i and j take values of 1, 2, and 3, corresponding to the x, y, and z directions, respectively. Cartesian coordinates; ; Cartesian coordinates;
[0016] The governing equations are discretized using the Immersed Boundary (IB) method. The numerical discretization process and the embedding of boundary conditions are independent of each other. The governing equations are discretized for all grid points within the solution domain, while the Navier-Stokes equations are discretized on a fixed Cartesian grid. Flow variables are spatially discretized by storing them in a non-interleaved manner at the cell centers, and time integration uses a fractional-step method: First, the modified momentum equation is solved to obtain intermediate velocities. The convection term uses a second-order Adams-Bashforth scheme, and the diffusion term uses an implicit Crank-Nicholson scheme to eliminate viscous stability constraints. Next, the pressure correction equation is solved using a geometric multigrid method. Once the pressure field is obtained, the final velocity field is updated. For the Immersed Boundary method, a virtual thickness is introduced around the canopy. .
[0017] Step 2 includes: The structural dynamics of the parachute are governed by the Navier equations, which characterize the linear stress-strain relationship.
[0018] (3),
[0019] in, For the density of the structure, For the displacement of the structure, Represents the stress tensor. Represents physical strength, Nabla operator;
[0020] The expression for the stress tensor is:
[0021] (4),
[0022] in, For the Green-Lagrange strain tensor, Lamé's constant, For unit tensors, Indicates trace;
[0023] The finite element method in CalculiX is used to solve equation (3) discretely; the direct integration dynamic analysis method is selected to perform numerical integration of equation (3).
[0024] Step 3 includes:
[0025] Step 3-1, Data mapping between fluid and solid interfaces: For a circular parachute canopy, the data mapping method between the fluid and solid interfaces includes: On the solid side, the canopy surface is discretized using second-order triangular shell elements in CalculiX. The nodes of each element are numbered in a counterclockwise direction as 1, 2, 3, 4, 5, 6. Then, using the nodes, each shell element is further divided into four triangular elements to discretize the canopy surface on the fluid side.
[0026] Step 3-2, Select the coupling method: Use a tight coupling method with under-relaxed iteration, the expression is:
[0027] (5),
[0028] in, This represents the pressure, velocity, or displacement at the fluid-structure interface during the k-th iteration at the n-th time step. These are the predicted values from the structure solver. The number of inner iterations. The under-relaxation factor is dynamically determined using the Aitken acceleration technique. The value;
[0029] Step 3-3, Data transfer method: Throughout the simulation process, the communication between the fluid and solid domains is handled through the preCICE library;
[0030] Steps 3-4 yield the following implicit coupling process between the IB solver based on the preCICE library and CalculiX:
[0031] Step 3-4-1, at each time step The forces in the fluid domain are calculated using the IB solver.
[0032] Step 3-4-2: Map the forces onto the solid surface mesh;
[0033] Step 3-4-3: preCICE transmits the force data to CalculiX;
[0034] Step 3-4-4: CalculiX uses mapped boundary conditions on the solid domain to calculate the displacement of the structure;
[0035] In steps 3-4-5, preCICE transmits the displacement back to the IB solver;
[0036] Steps 3-4-6 are repeated using the Aitken adaptive under-relaxation acceleration technique, from steps 3-4-1 to 3-4-5, until the results between two adjacent sub-iteration steps converge. Then, the IB solver receives the displacement field mapped back from the solid domain and, according to... The fluid-structure interface obtained from the time-step update calculates new forces; when the number of time steps exceeds a threshold... The simulation process ends when the time step (which is related to the size of the time step, and is generally taken as 5000~10000) is reached.
[0037] Step 4 includes: setting the computation domain to... A cuboid, in which The characteristic length of the umbrella canopy is given; the left side of the computational domain is set as a Dirichlet velocity inlet boundary condition, and the incoming flow velocity is... The right side is set as the Neumann velocity exit boundary condition, and the other four sides are set as free slip boundary conditions; Reynolds number Set as air density , The viscosity coefficient of air; a uniform grid is used around the canopy and gradually thins out towards the far field; the uniform grid size near the canopy is... The calculation time is .
[0038] Step 5 includes: setting the thickness of each component of the parachute; each component of the parachute is discretized using the corresponding element type, specifically: the canopy is discretized using shell elements, and the parachute lines and reinforcing strips are discretized using beam elements; CalculiX automatically expands the two-dimensional elements into three dimensions during the calculation process; and specifying material properties for each component of the parachute.
[0039] Two types of displacement boundary conditions are specified for the parachute system: one imposes fixed constraints on the six degrees of freedom at the junction of the parachute lines, and the other imposes binding constraints on the six degrees of freedom at the nodes connecting the canopy, parachute lines, and reinforcing strips.
[0040] Step 6 includes: analyzing the breathing process of different parachutes, vortex shedding near the canopy, canopy displacement, and drag coefficient, where the drag coefficient of the parachute is... Represented as:
[0041] (6),
[0042] in and These represent the drag force experienced by the parachute canopy and the nominal area of the parachute canopy, respectively. Indicates the velocity of the free flow.
[0043] The present invention also provides a storage medium storing a computer program or instructions, which, when the computer program or instructions are run, implement the parachute multiphysics coupling calculation method based on sharp interface immersion boundary.
[0044] The present invention has the following advantages: (1) The fluid solution is based on the sharp submerged boundary method, which does not require dynamic generation of body-fitted mesh. Compared with the traditional body-fitted mesh solution method, it has significant advantages in simulating the large deformation involved in the parachute inflation process; (2) The solid solution is based on the open-source finite element solver CalculiX, which can simulate nonlinear large deformation; (3) The connection between the IB solver and CalculiX is realized through the open-source multiphysics coupling library preCICE, which minimizes the modification of the original IB solver and CalculiX code and provides high flexibility. Attached Figure Description
[0045] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, and the advantages of the present invention in the above and / or other aspects will become clearer.
[0046] Figure 1 This is a schematic diagram illustrating the connection between the IB solver and CalculiX based on the preCICE library.
[0047] Figure 2 This is a schematic diagram of data mapping between fluid-structure interfaces. Figure 3 This is a block diagram of a tightly coupled algorithm based on the preCICE library.
[0048] Figure 4 This is a schematic diagram of the computational grid for the fluid domain.
[0049] Figure 5 This is a schematic diagram of the circular umbrella model and its boundary conditions.
[0050] Figure 6 This is a graph showing the changes in the drag coefficient and the displacement of the center point of the canopy of a square umbrella over time at different moments.
[0051] Figure 7a , Figure 7b , Figure 7c , Figure 7d , Figure 7e , Figure 7f This is a schematic diagram of the typical deformation of the canopy of a square umbrella.
[0052] Figure 8a , Figure 8b , Figure 8c , Figure 8d , Figure 8e , Figure 8f This is a schematic diagram of the velocity field around the canopy of a square umbrella at a typical moment.
[0053] Figure 9 This is a graph showing the changes in the drag coefficient and the displacement of the canopy center point of the cross-shaped umbrella over time at different moments.
[0054] Figure 10a , Figure 10b, Figure 10c , Figure 10d , Figure 10e , Figure 10f This is a schematic diagram of the canopy deformation at a typical moment of a cross-shaped umbrella.
[0055] Figure 11a , Figure 11b , Figure 11c , Figure 11d , Figure 11e , Figure 11f This is a schematic diagram of the velocity field around the canopy at a typical moment in a cross-shaped parachute.
[0056] Figure 12 This is a graph showing the changes in the drag coefficient and the displacement of the center point of the canopy of a circular umbrella over time at different moments.
[0057] Figure 13a , Figure 13b , Figure 13c , Figure 13d , Figure 13e , Figure 13f This is a schematic diagram of the deformation of the canopy of a round umbrella at a typical moment.
[0058] Figure 14a , Figure 14b , Figure 14c , Figure 14d , Figure 14e , Figure 14f This is a schematic diagram of the velocity field around the canopy of a circular umbrella at a typical moment.
[0059] Figure 15 This is a schematic diagram illustrating the identification of grid points near the umbrella canopy film based on the sharp interface IB method. Detailed Implementation
[0060] This invention provides a multiphysics coupling calculation method for parachutes based on sharp interface submerged boundaries. A partitioned fluid-structure interaction (FSI) strategy is employed to establish a FSI method for the parachute inflation process. The fluid component is solved using the sharp interface submerged boundary (IB) method, which can handle arbitrarily complex geometries. The structural component is solved using the open-source finite element code CalculiX, with the parachute canopy and lines discretized using second-order shell elements and beam elements, respectively. The open-source multiphysics coupling library preCICE is used to handle the connection between the IB solver and CalculiX. A tight coupling method is employed to improve the accuracy and stability of the FSI solution. The reliability of the parachute FSI calculation method established in this invention is verified through simulations of several typical parachute inflation processes.
[0061] This invention specifically includes:
[0062] Step 1: The governing equations for the fluid are the three-dimensional unsteady, incompressible Navier-Stokes equations:
[0063] (1),
[0064] (2),
[0065] in, , , , These represent the fluid velocity, density, pressure, and kinematic viscosity, respectively. The governing equations are discretized using the sharp interface IB method. The numerical discretization process and the embedding of boundary conditions are independent. The governing equations are discretized for all grid points within the solution domain, but the discretized form may include some grid points outside the flow field. The Navier-Stokes equations are discretized on a fixed Cartesian grid. Flow variables are spatially discretized in a non-interleaved manner at the cell centers. Time integration uses a fractional-step method: first, the modified momentum equation is solved to obtain the intermediate velocity. The convection term uses a second-order Adams-Bashforth scheme, and the diffusion term uses an implicit Crank-Nicholson scheme to eliminate viscous stability constraints. Next, an efficient geometric multigrid method is used to solve the pressure correction equation. Once the pressure field is obtained, the final velocity field can be updated. For the sharp interface IB method, constructing interpolation or extrapolation templates near the wall requires identifying whether the grid nodes are on the fluid side or the solid side. However, the thickness of the canopy is usually much smaller than its characteristic length, making this identification process difficult. Therefore, this invention introduces a virtual thickness around the canopy. To avoid this problem, such as Figure 15 As shown.
[0066] Step 2: The structural dynamics of the parachute are governed by the Navier equations, which characterize the linear stress-strain relationship:
[0067] (3),
[0068] in, For the density of the structure, For the displacement of the structure, Represents the stress tensor. It represents physical strength.
[0069] The expression for the stress tensor is:
[0070] (4),
[0071] in, For the Green-Lagrange strain tensor, Lamé's constant, It is a unit tensor.
[0072] The structural equations were discretized and solved using the finite element method in CalculiX. The equations of motion were then numerically integrated using the direct integration dynamic analysis method.
[0073] Step 3: Utilize the open-source multiphysics coupling library preCICE to connect the IB solver with CalculiX. This includes data mapping between fluid-structure interfaces, selection of coupling methods, and data transfer methods, such as... Figure 1 As shown.
[0074] For data mapping at the fluid-solid interface, preCICE provides several interpolation-based methods for information exchange between the fluid and solid domains. However, since the parachute canopy can be considered a two-dimensional manifold in three-dimensional space, an accurate and direct data mapping method has been developed. Taking a circular parachute canopy as an example, the data mapping method between the fluid and solid interface is as follows: Figure 2 As shown, firstly, on the solid side, the canopy surface is discretized using second-order triangular shell elements in CalculiX, with the nodes of each element numbered counter-clockwise as (1-2-3-4-5-6). Then, using these nodes, each shell element is further subdivided into four triangular elements (counter-clockwise 1-4-6, 2-5-4, 3-6-5, 4-5-6) to discretize the canopy surface on the fluid side. This accurately maps the solid and fluid meshes at the interface without incorporating any interpolation errors.
[0075] Regarding the selection of the coupling method, since the equivalent mass ratio of the canopy to the surrounding air is much less than 1, resulting in a significant additional mass effect, a tight coupling method with under-relaxed iteration is adopted. This can improve the accuracy and stability of the numerical solution of the fluid solver at each time step, and its expression is as follows:
[0076] (5),
[0077] in, This represents the pressure, velocity, or displacement at the fluid-solid interface. These are the predicted values from the structure solver. The number of inner iterations. This is the under-relaxation factor. To improve the convergence speed of tight coupling, the Aitken acceleration technique is introduced to dynamically determine it. The value of .
[0078] In terms of data transfer methods, the communication between the fluid and solid domains (such as parallel data transmission and synchronization) is efficiently handled by the preCICE library throughout the simulation process.
[0079] In summary, the implicit coupling process between the IB solver based on the preCICE library and CalculiX is as follows: Figure 3 As shown, the specific explanation is as follows: (1) At each time step (1) Calculate the forces in the fluid domain using the IB solver; (2) Map the forces onto the solid surface mesh; (3) preCICE transmits the force data to CalculiX; (4) CalculiX calculates the displacements of the structure using the mapped boundary conditions in the solid domain; (5) preCICE transmits the displacements back to the IB solver. Repeat steps (1)-(5) using the Aitken adaptive under-relaxation acceleration technique until the results between two adjacent sub-iteration steps tend to converge. Then, the IB solver receives the displacement field mapped back from the solid domain and, according to... The fluid-structure interface obtained from the time step update calculates new forces. When the time step count is greater than... When the time is up, the entire simulation process ends.
[0080] Step 4: Calculation settings for the fluid domain. For example... Figure 4 As shown, the computation domain is set to A cuboid, in which The characteristic length of the umbrella canopy is given. The left side of the computational domain is set as a Dirichlet velocity inlet boundary condition, with an incoming flow velocity of... The right side is set as the Neumann velocity exit boundary condition, and the other four sides are set as free-slip boundary conditions. The Reynolds number is set to... air density , Let be the viscosity coefficient of air. A uniform grid is used around the canopy, gradually thinning out towards the far field. The uniform grid size near the canopy is... The calculation time is .
[0081] Step 5: Calculation Setup for the Solid Domain. Each component of the parachute is discretized using appropriate element types: the canopy is discretized using shell elements, and the lines and reinforcing strips are discretized using beam elements. CalculiX automatically expands these two-dimensional elements into three dimensions during the calculation, so the thickness of each component needs to be specified beforehand. Furthermore, material properties such as density and elastic modulus should be specified for each part of the parachute. Two types of displacement boundary conditions are specified for the parachute system: one imposes fixed constraints on the six degrees of freedom at the line junctions, and the other imposes binding constraints on the six degrees of freedom of the nodes connecting the canopy, lines, and reinforcing strips. Figure 5Taking the uninflated circular parachute model shown as an example, the canopy is discretized using second-order shell elements, while the parachute lines and reinforcing strips are discretized using second-order beam elements. Each radial line of the canopy is discretized by a set of evenly spaced control points {M0, M1, M2, M3, M4}, which are considered master nodes. Fixed constraints are applied to the nodes where the parachute lines intersect. The other end of each parachute line is bound to the canopy by applying binding constraints between the master node M0 and the slave node SL0. The reinforcing strips typically coincide with the radial lines of the canopy to maintain the inflated shape. Each reinforcing strip is discretized by a set of control points with the same spacing as the radial lines, i.e., {SR0, SR1, SR2, SR3, SR4}. The reinforcing strips are bound to the canopy by applying binding constraints between node pairs {Mi, SRi} (where i = 0, 1, 2, 3, 4). By specifying the above constraints, the canopy, parachute lines, and reinforcing strips can be assembled into a simple circular parachute system, such as... Figure 5 As shown.
[0082] Step 6: Numerical experiments were conducted on the inflation process of several typical parachutes. The breathing process, vortex shedding near the canopy, canopy displacement, and drag coefficient of different parachutes were analyzed to demonstrate the reliability of the established fluid-structure interaction calculation method. The drag coefficient of the parachute can be expressed as...
[0083] (6),
[0084] in and These represent the drag force experienced by the canopy and the nominal area of the canopy, respectively.
[0085] For square umbrellas, Figure 6 Showing drag coefficient and the displacement of the center point of the parasol Results that change over time Figure 7a , Figure 7b , Figure 7c , Figure 7d , Figure 7e , Figure 7f The umbrella canopy deformation at a typical moment is shown. Figure 8a , Figure 8b , Figure 8c , Figure 8d , Figure 8e , Figure 8f The velocity field around the canopy at a typical moment is shown. The calculated steady-state drag coefficient for the square umbrella is 1.1, which is close to the reference result.
[0086] For the cross umbrella, Figure 9 Showing drag coefficient and the displacement of the center point of the parasol Results that change over time Figure 10a , Figure 10b , Figure 10c , Figure 10d , Figure 10e , Figure 10f The umbrella canopy deformation at a typical moment is shown. Figure 11a , Figure 11b , Figure 11c , Figure 11d , Figure 11e , Figure 11f The velocity field around the canopy at a typical moment is shown. The calculated steady-state drag coefficient of the cross-shaped parachute is 0.7, which is close to the reference result.
[0087] For round umbrellas, Figure 12 Showing drag coefficient and the displacement of the center point of the parasol Results that change over time Figure 13a , Figure 13b , Figure 13c , Figure 13d , Figure 13e , Figure 13f The umbrella canopy deformation at a typical moment is shown. Figure 14a , Figure 14b , Figure 14c , Figure 14d , Figure 14e , Figure 14f The velocity field around the parachute canopy at typical moments is shown. The calculated steady-state drag coefficient for a circular parachute is 1.2, which is close to the reference result. These results demonstrate that the multiphysics coupling calculation method for parachutes based on sharp-interface immersion boundaries proposed in this invention can accurately and reliably simulate the inflation process of various parachutes.
[0088] This invention provides a multiphysics coupling calculation method for parachutes based on sharp interface immersion boundaries. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment of the invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.
Claims
1. A multiphysics coupling calculation method for parachutes based on sharp interface immersion boundaries, characterized in that, Includes the following steps: Step 1: Establish the governing equations for the fluid; Step 2: Establish the governing equations for the structural dynamics of the parachute; Step 3: Use the open-source multiphysics coupling library preCICE to connect the IB solver with CalculiX; Step 3 includes: Step 3-1, Data mapping between fluid and solid interfaces: For a circular parachute canopy, the data mapping method between the fluid and solid interfaces includes: On the solid side, the canopy surface is discretized using second-order triangular shell elements in CalculiX. The nodes of each element are numbered in a counterclockwise direction as 1, 2, 3, 4, 5, 6. Then, using the nodes, each shell element is further divided into four triangular elements to discretize the canopy surface on the fluid side. Step 3-2, Select the coupling method: Use a tight coupling method with under-relaxed iteration, the expression is: （5）， in, This represents the pressure, velocity, or displacement at the fluid-structure interface during the k-th iteration at the n-th time step. These are the predicted values from the structure solver. The number of inner iterations. The under-relaxation factor is dynamically determined using the Aitken acceleration technique. The value; Step 3-3, Data transfer method: Throughout the simulation process, the communication between the fluid and solid domains is handled through the preCICE library; Steps 3-4 yield the following implicit coupling process between the IB solver based on the preCICE library and CalculiX: Step 3-4-1, at each time step The forces in the fluid domain are calculated using the IB solver. Step 3-4-2: Map the forces onto the solid surface mesh; Step 3-4-3: preCICE transmits the force data to CalculiX; Step 3-4-4: CalculiX uses mapped boundary conditions on the solid domain to calculate the displacement of the structure; In steps 3-4-5, preCICE transmits the displacement back to the IB solver; Steps 3-4-6 are repeated using the Aitken adaptive under-relaxation acceleration technique, from steps 3-4-1 to 3-4-5, until the results between two adjacent sub-iteration steps converge. Then, the IB solver receives the displacement field mapped back from the solid domain and, according to... The fluid-structure interface obtained from the time-step update calculates new forces; when the number of time steps exceeds a threshold... When the time is right, the entire simulation process ends; Step 4: Configure the calculation settings for the fluid domain; Step 5: Configure the calculation settings for the solid domain; Step 6: Conduct a numerical experiment on the typical parachute inflation process.
2. The method according to claim 1, characterized in that, Step 1 includes: The governing equations for the fluid are the following three-dimensional unsteady incompressible Navier-Stokes equations: （1）， （2）， in, , , , These represent the velocity, density, pressure, and kinematic viscosity of the fluid in the i-direction, respectively; i and j take values of 1, 2, and 3, corresponding to the x, y, and z directions, respectively. Cartesian coordinates; ; Cartesian coordinates; The governing equations are discretized using the sharp interface IB method. The numerical discretization process and the embedding of boundary conditions are independent of each other. The governing equations are discretized for all grid points within the solution domain, while the Navier-Stokes equations are discretized on a fixed Cartesian grid. Flow variables are spatially discretized by storing them in a non-interleaved manner at the cell centers, and time integration uses a fractional-step method: First, the modified momentum equation is solved to obtain intermediate velocities. The convection term uses a second-order Adams-Bashforth scheme, and the diffusion term uses an implicit Crank-Nicholson scheme to eliminate viscous stability constraints. Next, the pressure correction equation is solved using a geometric multigrid method. Once the pressure field is obtained, the final velocity field is updated. For the sharp interface IB method, a virtual thickness is introduced around the canopy. .
3. The method according to claim 2, characterized in that, Step 2 includes: The structural dynamics of the parachute are governed by the Navier equations, which characterize the linear stress-strain relationship. （3）， in, For the density of the structure, For the displacement of the structure, Represents the stress tensor. Represents physical strength, Nabla operator; The expression for the stress tensor is: （4）， in, For the Green-Lagrange strain tensor, Lamé's constant, For unit tensors, Indicates trace; The finite element method in CalculiX is used to solve equation (3) discretely; the direct integration dynamic analysis method is selected to perform numerical integration of equation (3).
4. The method according to claim 3, characterized in that, Step 4 includes: setting the computation domain to... A cuboid, in which The characteristic length of the umbrella canopy is given; the left side of the computational domain is set as a Dirichlet velocity inlet boundary condition, and the incoming flow velocity is... The right side is set as the Neumann velocity exit boundary condition, and the other four sides are set as free slip boundary conditions; Reynolds number Set as air density , The viscosity coefficient of air; a uniform grid is used around the canopy and gradually thins out towards the far field; the uniform grid size near the canopy is... The calculation time is .
5. The method according to claim 4, characterized in that, Step 5 includes: setting the thickness of each component of the parachute; each component of the parachute is discretized using the corresponding element type, specifically: the canopy is discretized using shell elements, and the parachute lines and reinforcing strips are discretized using beam elements; CalculiX automatically expands the two-dimensional elements into three dimensions during the calculation process; and specifying material properties for each component of the parachute. Two types of displacement boundary conditions are specified for the parachute system: one imposes fixed constraints on the six degrees of freedom at the junction of the parachute lines, and the other imposes binding constraints on the six degrees of freedom at the nodes connecting the canopy, parachute lines, and reinforcing strips.
6. The method according to claim 5, characterized in that, Step 6 includes: analyzing the breathing process of different parachutes, vortex shedding near the canopy, canopy displacement, and drag coefficient, where the drag coefficient of the parachute is... Represented as: （6）， in and These represent the drag force experienced by the parachute canopy and the nominal area of the parachute canopy, respectively. Indicates the velocity of the free flow.
7. A storage medium, characterized in that, It stores a computer program or instructions that, when executed, implement the method as described in any one of claims 1 to 6.