A multi-level multi-resolution MPS-FEM coupling calculation method suitable for thin-walled structures

Abstract

A multi-layer multi-resolution MPS-FEM coupling calculation method suitable for thin-walled structures, the coupling calculation method comprising the following steps: determining the physical parameters of the flow field and the solid structure; setting the grid model of the structure, the initial distribution of the particles and the range of high, medium and low precision areas according to the size of the flow field, the size of the structure and the thickness size of the thin-walled structure; using a layered contact search algorithm to determine the interacting particle pairs and the interacting particle and finite element contact pairs; the layered contact search algorithm is used to divide the range of high, medium and low precision areas into large, medium and small multi-layer lattices, and the corresponding positioning search is carried out on the large, medium and small particles respectively; performing finite element structure calculation and fluid MPS particle calculation; updating the kinematics information of the finite element nodes and the MPS particles to improve the overall calculation efficiency.

Description

Technical Field

[0001] This invention relates to a multi-level, multi-resolution MPS-FEM coupled calculation method applicable to thin-walled structures, and to the field of numerical simulation of fluid-solid coupling. Background Technology

[0002] Fluid-structure interaction phenomena are widespread in nature and engineering fields, such as hydrodynamic impaction, biomechanics, and offshore wind power. These complex physical phenomena typically involve structural deformation, fluid flow, and their interactions. Generally, these problems are solved through numerical simulation, primarily using mesh-based methods, meshless particle methods, and mesh-particle coupling methods.

[0003] Mesh-based methods have been widely used in the field of fluid-structure interaction (FSI). Among them, the pure Lagrangian mesh method has advantages in solid structure discretization and structural deformation modeling, but it still faces challenges in handling large displacement problems common in fluid simulation. The pure Eulerian mesh method (such as the finite element method FEM) can handle large deformations in the fluid domain relatively easily, but it is difficult to guarantee the computational accuracy of complex geometric boundaries and fluid-structure interaction interfaces. To overcome these limitations, coupled Lagrangian-Eulerian methods have been proposed in the prior art, but this method requires special techniques such as mesh reconstruction to ensure accuracy, which is computationally time-consuming. The particle finite element method based on Lagrangian description has received widespread attention in FSI modeling. Although this mesh method can effectively handle contact problems and free surface tracing, it suffers from low computational efficiency because the mesh needs to be reconstructed at each time step.

[0004] For meshless particle methods, the Smooth Particle Method (SPH) and Moving Particle Method (MPS) belong to the category of meshless methods. Their main advantage is that they can effectively describe the free surface and moving boundary of fluid flow, but they have difficulties in simulating solid structure deformation and discretizing complex geometric structures. Therefore, a coupled solution method of meshed and meshless methods can be adopted to give full play to their respective advantages and achieve accurate fluid-structure interaction simulation.

[0005] Traditional meshless particle methods discretize the fluid domain into a series of particles of the same size, each carrying corresponding dynamic information. When particle methods are coupled with mesh methods, the structural mesh is regarded as the boundary wall of the particles, applying boundary forces to the particle region, while the fluid particles apply pressure to the structural mesh. Due to the limitations of particle method computation theory, the thickness of the structural boundary interacting with the particles must be at least three times the interparticle spacing; otherwise, the calculation will be incorrect. When encountering thin-walled structures, the particle size must be small enough, which will result in a very large number of particles in the computational model, excessive overall computational load, and low computational efficiency. Summary of the Invention

[0006] This invention provides a multi-level, multi-resolution MPS-FEM coupled calculation method suitable for thin-walled structures. The method is rationally designed and, for thin-walled structures in the fluid domain, determines relevant physical parameters, sets the mesh model of the structure, the initial distribution of particles, and the range of high, medium, and low precision regions. Finite element calculation and MPS particle calculation are performed, and the fluid region is discretized into particles of different sizes, effectively reducing the amount of computation, improving the overall computational efficiency, and solving the problems existing in the prior art.

[0007] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0008] A multi-level, multi-resolution MPS-FEM coupled calculation method suitable for thin-walled structures, the coupled calculation method includes the following steps:

[0009] S1, determine the physical parameters of the flow field and solid structure, the physical parameters include size and material parameters, the size includes flow size and structural size, and the material parameters include density, Young's modulus, Poisson's ratio and viscosity;

[0010] S2 sets the mesh model of the structure, the initial distribution of particles, and the range of high, medium, and low precision regions based on the flow field size, structural size, and thickness of the thin-walled structure.

[0011] S3, a hierarchical contact search algorithm is used to determine the interacting particle pairs and the contact pairs between interacting particles and finite elements; the hierarchical contact search algorithm is used to divide the range of high, medium and low precision areas into large, medium and small multi-layer grids, and to perform corresponding positioning searches for large, medium and small particles respectively;

[0012] S4 is used for finite element structural calculations and fluid MPS particle calculations.

[0013] S5 updates the kinematic information of finite element nodes and MPS particles to improve overall computational efficiency.

[0014] Based on the flow field dimensions, structural dimensions, and the thickness of the thin-walled structure, the following steps are taken to define the mesh model of the structure, the initial particle distribution, and the range of high, medium, and low precision regions:

[0015] S2.1, set the thickness of the thin-walled structure to t, and set the interparticle spacing of the small particles to l. 小 =t / 3.0, setting the finite element size of the small grid to s. 小 =l 小 The fluid region within the range of motion of the thin-walled structure is set as a high-precision region, and the number of particle layers in each of the X, Y, and Z directions of the high-precision region is set to at least 8 layers.

[0016] S2.2, the outer layer of the high-precision region is set to the medium-precision region, and the particle gap of the medium particles is set to l. 中 =2*l 小 In the medium precision region, the number of particle layers in each of the X, Y, and Z directions is set to at least 8 layers;

[0017] S2.3, the outer layer of the medium-precision region is set to a low-precision region, and the interparticle gap of large particles is set to l. 大 =2*l 中 In the low-precision region, the number of particle layers in each of the X, Y, and Z directions is set to at least 8 layers;

[0018] S2.4 sets the remaining area to a low-precision area range, which can continue to expand outward to a multi-level, multi-resolution particle model when the number of particles is still large even with three layers of particles.

[0019] The steps involved in performing finite element structural calculations and fluid MPS particle calculations are as follows:

[0020] S4.1 For finite element structures, calculate the corresponding internal and external forces respectively;

[0021] S4.2 For fluid MPS particles, each precision region is calculated separately, and the velocity-viscosity force, gravity, pressure and pressure gradient force of the fluid MPS particles need to be calculated.

[0022] During the calculation, when a particle moves across a precision region, it needs to be split and merged. When a large particle enters a higher precision region, it is split into 8 medium particles. When a small particle enters a lower precision region, 8 adjacent small particles are merged into 1 medium particle.

[0023] S4.3 When fluid MPS particles interact with the finite element structure, the force exerted by the fluid MPS particles on the finite element is applied in the form of pressure to the integration points of the structural elements and distributed to each element section through shape functions; the force exerted by the finite element structure on the fluid MPS particles acts on the fluid particles in the form of interfacial forces.

[0024] The finite element size of the large grid is set to s. 大 =l 大 .

[0025] The finite element structure calculation provides wall boundaries for the fluid region, and the fluid MPS particle calculation provides external forces for the finite element structure.

[0026] This invention employs the aforementioned structure, providing a data foundation for defining and dividing the model region by determining the physical parameters of the flow field and the solid structure. Based on the flow field size, structural size, and the thickness of the thin-walled structure, the mesh model of the structure, the initial particle distribution, and the range of high, medium, and low precision regions are defined to ensure computational accuracy. A layered contact search algorithm is used to determine interacting particle pairs and the contact pairs between interacting particles and finite element units. When particles interact with the finite element structure, the force exerted by the fluid particles on the finite element is applied as pressure to the integration points of the structural elements and distributed to each element node through shape functions. The force exerted by the finite element structure on the particles acts on the fluid particles as interfacial forces, offering advantages of precision, efficiency, practicality, and reliability. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the process of the present invention.

[0028] Figure 2 This is a calculation diagram of the present invention.

[0029] Figure 3 for Figure 2 Enlarged view of the structure at point A in the middle. Detailed Implementation

[0030] To clearly illustrate the technical features of this solution, the invention will be described in detail below through specific implementation methods and in conjunction with the accompanying drawings.

[0031] like Figure 1-3 As shown, a multi-level, multi-resolution MPS-FEM coupled calculation method suitable for thin-walled structures is described. The coupled calculation method includes the following steps:

[0032] S1, determine the physical parameters of the flow field and solid structure, the physical parameters include size and material parameters, the size includes flow size and structural size, and the material parameters include density, Young's modulus, Poisson's ratio and viscosity;

[0033] S2 sets the mesh model of the structure, the initial distribution of particles, and the range of high, medium, and low precision regions based on the flow field size, structural size, and thickness of the thin-walled structure.

[0034] S3, a hierarchical contact search algorithm is used to determine the interacting particle pairs and the contact pairs between interacting particles and finite elements; the hierarchical contact search algorithm is used to divide the range of high, medium and low precision areas into large, medium and small multi-layer grids, and to perform corresponding positioning searches for large, medium and small particles respectively;

[0035] S4 is used for finite element structural calculations and fluid MPS particle calculations.

[0036] S5 updates the kinematic information of finite element nodes and MPS particles to improve overall computational efficiency.

[0037] Based on the flow field dimensions, structural dimensions, and the thickness of the thin-walled structure, the following steps are taken to define the mesh model of the structure, the initial particle distribution, and the range of high, medium, and low precision regions:

[0038] S2.1, set the thickness of the thin-walled structure to t, and set the interparticle spacing of the small particles to l. 小 =t / 3.0, setting the finite element size of the small grid to s. 小 =l 小 The fluid region within the range of motion of the thin-walled structure is set as a high-precision region, and the number of particle layers in each of the X, Y, and Z directions of the high-precision region is set to at least 8 layers.

[0039] S2.2, the outer layer of the high-precision region is set to the medium-precision region, and the particle gap of the medium particles is set to l. 中 =2*l 小 In the medium precision region, the number of particle layers in each of the X, Y, and Z directions is set to at least 8 layers;

[0040] S2.3, the outer layer of the medium-precision region is set to a low-precision region, and the interparticle gap of large particles is set to l. 大 =2*l 中 In the low-precision region, the number of particle layers in each of the X, Y, and Z directions is set to at least 8 layers;

[0041] S2.4 sets the remaining area to a low-precision area range, which can continue to expand outward to a multi-level, multi-resolution particle model when the number of particles is still large even with three layers of particles.

[0042] The steps involved in performing finite element structural calculations and fluid MPS particle calculations are as follows:

[0043] S4.1 For finite element structures, calculate the corresponding internal and external forces respectively;

[0044] S4.2 For fluid MPS particles, each precision region is calculated separately, and the velocity-viscosity force, gravity, pressure and pressure gradient force of the fluid MPS particles need to be calculated.

[0045] During the calculation, when a particle moves across a precision region, it needs to be split and merged. When a large particle enters a higher precision region, it is split into 8 medium particles. When a small particle enters a lower precision region, 8 adjacent small particles are merged into 1 medium particle.

[0046] S4.3 When fluid MPS particles interact with the finite element structure, the force exerted by the fluid MPS particles on the finite element is applied in the form of pressure to the integration points of the structural elements and distributed to each element section through shape functions; the force exerted by the finite element structure on the fluid MPS particles acts on the fluid particles in the form of interfacial forces.

[0047] The finite element size of the large grid is set to s. 大 =l 大 .

[0048] The finite element structure calculation provides wall boundaries for the fluid region, and the fluid MPS particle calculation provides external forces for the finite element structure.

[0049] The working principle of a multi-level, multi-resolution MPS-FEM coupled calculation method for thin-walled structures in this embodiment of the invention is as follows: For thin-walled structures in the fluid domain, relevant physical parameters are determined, the mesh model of the structure, the initial distribution of particles, and the range of high, medium, and low precision regions are set, finite element calculation and MPS particle calculation are performed, and the fluid region is discretized into particles of different sizes, which effectively reduces the amount of calculation and improves the overall calculation efficiency.

[0050] While the pure Eulerian mesh method can handle large deformations in the fluid domain relatively easily, it is difficult to guarantee the calculation accuracy of complex geometric boundaries and fluid-structure interaction interfaces. It is even more difficult to handle the accuracy of thin-walled structures. Therefore, it is necessary to couple the finite element algorithm and the moving particle algorithm for calculation.

[0051] Furthermore, this application mainly addresses the interaction problem between fluids and solids with thin-walled structures. It combines the finite element method and the moving particle method to simulate structural deformation and fluid flow, allowing the particle size near the thin-walled structure to be very small, and then expanding outward layer by layer, effectively reducing the overall number of particles and greatly improving computational efficiency.

[0052] In the overall scheme, the coupled calculation method includes the following steps: determining the physical parameters of the flow field and the solid structure, the physical parameters including size and material parameters, the size including flow rate size and structural size, and the material parameters including density, Young's modulus, Poisson's ratio, and viscosity; setting the mesh model of the structure, the initial distribution of particles, and the range of high, medium, and low precision regions based on the flow field size, structural size, and thickness of the thin-walled structure; using a layered contact search algorithm to determine the interacting particle pairs and the contact pairs between interacting particles and finite elements; the layered contact search algorithm is used to divide the range of high, medium, and low precision regions into large, medium, and small multi-layer grids, and to perform corresponding location searches for large, medium, and small particles respectively; performing finite element structural calculations and fluid MPS particle calculations; and updating the kinematic information of finite element nodes and MPS particles to improve overall computational efficiency.

[0053] Preferably, setting the mesh model of the structure, the initial distribution of particles, and the range of high, medium, and low precision regions based on the flow field size, structural size, and thickness of the thin-walled structure includes the following steps: setting the thickness of the thin-walled structure as t, and setting the particle spacing of the small particles as l. 小 =t / 3.0, setting the finite element size of the small grid to s. 小 =l 小 The fluid region within the motion range of the thin-walled structure is defined as a high-precision region, with at least 8 particle layers in each of the X, Y, and Z directions within this high-precision region. The outer layer of the high-precision region is defined as a medium-precision region, with the particle spacing of the medium-precision particles set to l. 中 =2*l 小 Within the medium-precision region, the number of particle layers in each of the X, Y, and Z directions is set to at least 8 layers; the outer layer of the medium-precision region is set to the low-precision region, and the particle gap of large particles is set to l. 大 =2*l 中 In the low-precision region, the number of particle layers in each direction X, Y and Z is set to at least 8; the remaining regions are set to the low-precision region range. When the number of particles is still large even with three layers of particles, it can continue to be expanded outward to a multi-level, multi-resolution particle model.

[0054] By referring to the content in the attached diagram, the specific settings and relationships between different particles and different grids can be clearly seen. For application scenarios with a large number of particles, the computation can be gradually expanded outwards.

[0055] Preferably, the calculation of finite element structure and fluid MPS particles includes the following steps: for the finite element structure, calculate its corresponding internal and external forces respectively; for the fluid MPS particles, perform separate calculations for each precision region, and calculate the velocity-viscosity force, gravity, pressure and pressure gradient force of the fluid MPS particles.

[0056] During the calculation, when a particle moves across a precision region, it needs to be split and merged. When a large particle enters a higher precision region, it is split into 8 medium particles. When a small particle enters a lower precision region, 8 adjacent small particles are merged into 1 medium particle.

[0057] When fluid MPS particles interact with the finite element structure, the force exerted by the fluid MPS particles on the finite element is applied in the form of pressure at the integration points of the structural elements and distributed to each element section through shape functions; the force exerted by the finite element structure on the fluid MPS particles acts on the fluid particles in the form of interfacial forces.

[0058] It should be noted that in this application, the finite element structure calculation provides the wall boundary for the fluid region, and the fluid MPS particle calculation provides the external force for the finite element structure. They are coupled to improve the overall calculation efficiency and achieve accurate calculation of a large number of particles in the fluid region in a simpler way.

[0059] In summary, the multi-level, multi-resolution MPS-FEM coupled calculation method for thin-walled structures in this embodiment of the invention targets thin-walled structures in the fluid domain. It determines relevant physical parameters, sets the mesh model of the structure, the initial distribution of particles, and the range of high, medium, and low precision regions, and performs finite element calculation and MPS particle calculation. By discretizing the fluid region into particles of different sizes, it effectively reduces the amount of calculation and improves the overall calculation efficiency.

[0060] The above specific embodiments should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, any alternative improvements or modifications made to the embodiments of the present invention shall fall within the scope of protection of the present invention.

[0061] Any aspects of this invention not described in detail are well-known to those skilled in the art.

Claims

1. A multi-level, multi-resolution MPS-FEM coupled calculation method suitable for thin-walled structures, characterized in that, The coupling calculation method includes the following steps: S1, determine the physical parameters of the flow field and solid structure, the physical parameters include size and material parameters, the size includes flow size and structural size, and the material parameters include density, Young's modulus, Poisson's ratio and viscosity; S2 sets the mesh model of the structure, the initial distribution of particles, and the range of high, medium, and low precision regions based on the flow field size, structural size, and thickness of the thin-walled structure. S3, a hierarchical contact search algorithm is used to determine the interacting particle pairs and the contact pairs between interacting particles and finite elements; the hierarchical contact search algorithm is used to divide the range of high, medium and low precision areas into large, medium and small multi-layer grids, and to perform corresponding positioning searches for large, medium and small particles respectively; S4 is used for finite element structural calculations and fluid MPS particle calculations. S5 updates the kinematic information of finite element nodes and MPS particles to improve overall computational efficiency.

2. The multi-level, multi-resolution MPS-FEM coupled calculation method for thin-walled structures according to claim 1, characterized in that, Based on the flow field dimensions, structural dimensions, and the thickness of the thin-walled structure, the following steps are taken to define the mesh model of the structure, the initial particle distribution, and the range of high, medium, and low precision regions: S2.1, set the thickness of the thin-walled structure to t, and set the interparticle spacing of the small particles to l. 小 =t / 3.0, setting the finite element size of the small grid to s. 小 =l 小 The fluid region within the range of motion of the thin-walled structure is set as a high-precision region, and the number of particle layers in each of the X, Y, and Z directions of the high-precision region is set to at least 8 layers. S2.2, the outer layer of the high-precision region is set to the medium-precision region, and the particle gap of the medium particles is set to l. 中 =2*l 小 In the medium precision region, the number of particle layers in each of the X, Y, and Z directions is set to at least 8 layers; S2.3, the outer layer of the medium-precision region is set to a low-precision region, and the interparticle gap of large particles is set to l. 大 =2*l 中 In the low-precision region, the number of particle layers in each of the X, Y, and Z directions is set to at least 8 layers; S2.4 sets the remaining area to a low-precision area range, which can continue to expand outward to a multi-level, multi-resolution particle model when the number of particles is still large even with three layers of particles.

3. The multi-level, multi-resolution MPS-FEM coupled calculation method for thin-walled structures according to claim 1, characterized in that, The steps involved in performing finite element structural calculations and fluid MPS particle calculations are as follows: S4.1 For finite element structures, calculate the corresponding internal and external forces respectively; S4.2 For fluid MPS particles, each precision region is calculated separately, which requires calculating the velocity-viscosity force, gravity, pressure, and pressure gradient force of the fluid MPS particles. During the calculation, when a particle moves across a precision region, it needs to be split and merged. When a large particle enters a higher precision region, it is split into 8 medium particles. When a small particle enters a lower precision region, 8 adjacent small particles are merged into 1 medium particle. S4.3 When fluid MPS particles interact with the finite element structure, the force exerted by the fluid MPS particles on the finite element is applied in the form of pressure to the integration points of the structural elements and distributed to each element section through shape functions; the force exerted by the finite element structure on the fluid MPS particles acts on the fluid particles in the form of interfacial forces.

4. The multi-level, multi-resolution MPS-FEM coupled calculation method for thin-walled structures according to claim 2, characterized in that: The finite element size of the large grid is set to s. 大 =l 大 .

5. The multi-level, multi-resolution MPS-FEM coupled calculation method for thin-walled structures according to claim 1, characterized in that: The finite element structure calculation provides wall boundaries for the fluid region, and the fluid MPS particle calculation provides external forces for the finite element structure.

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