Multi-physics collaborative heterogeneous model simulation data space-time interpolation mapping method

Abstract

The present application belongs to the field of multi-physical field coupling modeling and simulation, and relates to a kind of multi-physical field collaborative heterogeneous model simulation data space-time interpolation mapping method.In the aspect of space interpolation, based on Shepard interpolation, target point data is calculated through source point data, thereby ensuring the boundedness of physical quantity.In the space-time mapping of physical quantities such as load and heat flow, based on the principle of virtual work, the equivalent physical quantity of element node of another physical field B is calculated using the physical quantity data of each discrete time of a physical field A, thereby ensuring the equivalence of node physical quantity;then, according to the law of conservation of momentum or energy, the equivalent physical quantity of element node at each discrete time of physical field B is obtained by calculating the change of momentum within the time step of physical field B, thereby ensuring the conservation of node physical quantity.The present application is suitable for data interpolation and space-time mapping in the process of collaborative analysis and optimization design of multi-specialty and multi-physical field heterogeneous models.

Description

Technical Field

[0001] This invention belongs to the field of multiphysics coupling modeling and simulation, and relates to a spatiotemporal interpolation and mapping method for multiphysics co-simulation data with boundedness, conservation and equivalence. Specifically, it is a spatiotemporal interpolation and mapping method for multiphysics co-simulation heterogeneous model simulation data, which is applicable to simulation data interpolation and mapping at different time and space scales. Background Technology

[0002] In the design and analysis of complex engineering systems in fields such as aviation, aerospace, shipbuilding, energy, and machinery, the coupling of multiple physical fields, including solids, fluids, heat, and electricity, is often involved. With the continuous improvement of product performance requirements, multidisciplinary collaborative simulation has become an important tool in engineering design. Different disciplines often rely on different simulation platforms and numerical methods, and their models differ in geometric description, mesh type, and time step. This makes achieving accurate simulation data transfer and coupled analysis between heterogeneous multiphysics models a key challenge in engineering applications.

[0003] Existing data transfer methods employing spatial or temporal interpolation techniques, while capable of achieving coupling between different models to some extent, still have significant shortcomings: First, data exchange between different grid systems lacks strict boundedness (e.g., fluid density, turbulent kinetic energy, pressure), conservation (e.g., momentum and energy conservation), and equivalence (e.g., resultant force and resultant torque equivalence), easily introducing additional errors and thus affecting the reliability of multiphysics coupling calculations; second, existing methods are mostly designed for single physics fields or isomorphic models, making it difficult to adapt to the common needs of multidisciplinary and heterogeneous models; third, existing interpolation methods are not sufficiently applicable to data at different time and spatial scales, limiting the transfer and fusion of simulation data. Summary of the Invention

[0004] To address the issues that existing multiphysics heterogeneous models struggle to strictly satisfy boundedness, conservation, and equivalence in data transfer during co-simulation, and are difficult to adapt to different time and spatial scales, this invention provides a spatiotemporal interpolation mapping method for simulation data of multiphysics heterogeneous collaborative models, in order to support co-simulation of multiphysics heterogeneous models and multiphysics coupled modeling.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] The spatiotemporal interpolation mapping method for simulation data of multiphysics collaborative heterogeneous models includes the following steps:

[0007] Step (1) Spatial interpolation:

[0008] 1-1): Input the coordinates of the source point and variable values, the coordinates of the target point and the cutoff radius.

[0009] 1-2): Calculate the variable values ​​for each target point based on Shepard interpolation; the variable values ​​include density, turbulent kinetic energy, pressure, etc.

[0010] Step (2) Spatiotemporal mapping:

[0011] 2-1): Input the physical quantity information corresponding to the time step of physical field A, the geometric characteristics of the interface between physical field A and physical field B, and the solution time steps of physical field A and physical field B; the physical quantities include surface load, heat flux density, etc.

[0012] 2-2): Based on the principle of virtual work, calculate the equivalent physical quantity at the node of physical field B at each discrete moment of physical field A.

[0013] 2-3): Based on the principle of virtual work, calculate the nodal equivalent physical quantities at the nodes of the physical field B unit at each discrete time of the physical field B; the nodal equivalent physical quantities include nodal equivalent load, nodal heat flux density, etc.

[0014] The beneficial effects of this invention are:

[0015] This invention proposes a spatiotemporal interpolation and mapping method for simulation data based on Shepard interpolation, the principle of virtual work, and conservation laws. This method possesses boundedness, conservation, and equivalence, and is applicable to different time and spatial scales. For spatial interpolation of simulation data such as density, turbulent kinetic energy, and pressure, Shepard interpolation is used to calculate target point data from source point data, thus ensuring the boundedness of physical quantities. For spatiotemporal mapping of physical quantities such as surface load and heat flux density, the principle of virtual work is used to calculate the equivalent physical quantities of unit nodes in another physical field B using physical quantity data from each discrete moment of one physical field A, ensuring the equivalence of nodal physical quantities. Subsequently, based on the law of conservation of momentum or energy, the equivalent physical quantities of unit nodes in physical field B at each discrete moment are obtained by calculating the change in momentum within the time step of physical field B, thus ensuring the conservation of nodal physical quantities. This invention is applicable to the data interpolation and spatiotemporal mapping stages in the collaborative analysis and optimization design of heterogeneous models involving multiple disciplines and multiple physical fields. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the interface between physical field A and physical field B;

[0017] Figure 2 This is a schematic diagram showing the changes of physical quantities of discrete unit nodes in the physical field B over time at different time steps;

[0018] Figure 3 This is a schematic diagram of a three-dimensional fluid-structure interaction problem;

[0019] Figure 4 This is a flowchart of the spatial interpolation algorithm;

[0020] Figure 5 This is a flowchart of the spacetime mapping algorithm;

[0021] Figure 6 This is a schematic diagram of the overall process of the present invention. Detailed Implementation

[0022] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0023] To address the challenges of existing multiphysics heterogeneous models in collaborative simulations where data transfer fails to strictly satisfy boundedness, conservation, and equivalence, and is ill-suited to different temporal and spatial scales, this invention proposes a spatiotemporal mapping method for simulation data in multiphysics collaborative heterogeneous models. The overall process is as follows: Figure 6 As shown.

[0024] For spatial interpolation, Shepard interpolation is used to calculate the variable values ​​for each target point. The specific calculation formula is as follows:

[0025]

[0026]

[0027] in, The variable value for the target point. The variable value of the source point, These are the interpolation coefficients. It is the distance between the target point and the source point (obtained using the coordinates of the source point and the target point). It is the number of source points within the cutoff radius of the target point.

[0028] This interpolation satisfies the Kronecker Delta property (strict interpolation) and has a boundedness, i.e. Data mapping is independent of the element type and distribution of the finite element model.

[0029] Regarding spatiotemporal mapping, firstly, based on the principle of virtual work, the discrete time intervals of the physical field A are calculated. The physical field B unit node Equivalent physical quantity Suppose that a unit surface of physical field B has an affinity with physical field A. Some units have overlapping surfaces, such as Figure 1 As shown. The surface physical quantity exerted by physical field A on physical field B is... (That is, the physical quantity information corresponding to the time step of physical field A).

[0030] If node It is the physical field B unit. A node whose local node number is The corresponding shape function is Using the principle of virtual work, surface physical quantities Converted into nodal equivalent physical quantities The calculation formula is:

[0031]

[0032] in, It is the set of all discrete elements of physical field A that have surfaces that coincide with the discrete elements of physical field B. It is a set The j-th element in the [node]. If node […]. Belonging to multiple elements, the nodal equivalent physical quantities calculated for each element are... The final equivalent physical quantity of the node can be obtained by summing them up. Otherwise, the calculated nodal physical quantities of a single unit That is, the final nodal equivalent physical quantity .

[0033] Consider the sum of the equivalent physical quantities at all nodes on a discrete element of a physical field B. Assume that a discrete element of a physical field B has... For each node, since the sum of the shape functions of a single element is 1, that is... Then the sum of the equivalent physical quantities of the nodes can be derived in the following form:

[0034]

[0035] Equation (4) shows that the calculated unit node physical quantities satisfy the equivalence.

[0036] Then, based on the conservation law, the discrete time intervals of physical field B are calculated. Physical field B unit node Equivalent physical quantity Assume the discrete time step of physical field A is... The discrete time step of physical field B is The specific steps are as follows:

[0037] At the discrete time of obtaining physical field A Physical quantities of unit B in the physical field Then, it is necessary to further calculate the physical field B at its own discrete time. Physical quantities of the lower unit node Since physical quantity data are only obtained at discrete moments, linear interpolation is used to describe the continuous change of conserved quantities over time and to calculate the changes in conserved quantities: physical quantities at two adjacent moments are connected by a straight line, thus obtaining the physical quantity at any moment within that time period. For example... Figure 2 As shown.

[0038] According to the law of conservation, within the time interval Within this context, it is necessary to ensure that the changes in conserved quantities are equal. Therefore, it is necessary to guarantee the equivalent physical quantities of the nodes in element B of physical field A at discrete moments. The area under the line graph is equivalent to the physical quantity of the element node of physical field B at the discrete time of physical field B. The areas under the resulting line graphs are equal, as shown in the following formula:

[0039]

[0040] Right now

[0041]

[0042] in, Indicates the time interval Within, the physical quantities of the element nodes of physical field B at the discrete time of physical field A. The area under the line graph that forms the structure. yes The physical quantities at the node at time t are known quantities. for The physical quantity at time t is the quantity to be determined.

[0043] We will now use a three-dimensional fluid-structure interaction problem as an example for verification. First, we use a spatial interpolation algorithm to interpolate the fluid load data (pressure) from the centroid of the fluid mesh to the fluid-structure boundary; then, we use a spatiotemporal mapping algorithm to calculate the nodal equivalent loads of the solid at discrete time points. Figure 3 The geometric dimensions and boundary conditions of the fluid-structure interaction problem in this embodiment are given. Figure 4 A flowchart of the spatial interpolation algorithm is provided. Figure 5 A flowchart of the spatiotemporal mapping algorithm is provided.

[0044] First, we will introduce the specific implementation steps of the spatial interpolation algorithm:

[0045] S1-1: Information required by the input space interpolation algorithm, specifically including: all source points Coordinates and their pressure values, all target points Coordinates and their cutoff radius, the dimensions of the interpolation problem.

[0046] In this example, the source point is the centroid of all fluid elements, numbering 275200. The pressure value at the element centroid is calculated using OpenFOAM. The target point is the centroid of the fluid element boundary surface at the fluid-solid interface, numbering 2960. The cutoff radius is taken as... .

[0047] S1-2: Using Shepard interpolation, the pressure value at each target point was calculated, and the results are shown in Table 1. The results show that the pressure at all target points lies between the minimum and maximum pressure at the source point, satisfying the boundedness property.

[0048] Table 1

[0049]

[0050] Note: Time unit is The pressure unit is .

[0051] The specific implementation steps of the spacetime mapping algorithm are described below:

[0052] S2-1: Input the discrete time steps for the fluid and solid interfaces, the load information corresponding to the fluid discrete time step, and the geometric features of the fluid-solid interface. Specifically, the geometric features of the fluid-solid interface include: the overall node number for which nodal forces need to be calculated, the overall and local node numbers of each solid element located at the fluid-solid boundary, the physical coordinates of all solid element nodes on the fluid-solid boundary, the fluid element numbers coinciding with the surfaces of each solid element, and the geometric information of the surfaces coinciding with the solid elements for each fluid element. In this example, the fluid discrete time step is... The unit size is The discrete time step for solids is The unit size is There are 196 solid nodes, 185 solid elements, and 2960 fluid elements at the fluid-solid interface. The load information is the pressure value obtained from S1-2.

[0053] S2-2: Calculate the equivalent load at the nodes of the solid element at each discrete fluid time step. For a solid element, the global numbering is... The node, its equivalent load The specific calculation method is as follows

[0054]

[0055] in, It is the element surface of the solid element located at the fluid-solid boundary. For nodes shape function, For load distribution. If the node If it belongs to multiple units, then include all connected units. Global equivalent load accumulated to this node .

[0056] The resultant force calculated from pressure data, relative to The resultant moment at the point, and the corresponding values ​​and errors calculated through the equivalent loads at the nodes, are shown in Table 2. The results show that the error between the resultant force and the resultant moment is less than 0.01%, satisfying the equivalence requirement.

[0057] Table 2

[0058]

[0059]

[0060] Note: Time unit is The unit of resultant force is The unit of resultant torque is The relative error is a dimensionless quantity.

[0061] S2-3: Calculate the equivalent load at the nodes of the solid element at each discrete time step. Since it is assumed that the load change is linear within each time step, the equivalent load at the solid element node under the fluid time step calculated in step S2-2 is used. The time step of each solid can be obtained. Changes in conserved quantities (momentum) Based on the change in momentum and the force at the previous discrete moment of the solid... Then the equivalent load at the node of the solid element at the discrete time can be obtained. The specific calculation method is as follows:

[0062]

[0063] The momentum change calculated from the pressure data, and the corresponding values ​​and errors calculated from the nodal equivalent loads, are shown in Table 3. The results show that the impulse error is less than 0.01%, satisfying the conservation property.

[0064] Table 3

[0065]

[0066] Note: Time unit is The unit of impulse is The relative error is a dimensionless quantity.

[0067] The essence of this invention is to propose a spatiotemporal interpolation mapping method for multiphysics collaborative heterogeneous model simulation data. It provides a systematic solution to the problems of existing methods in multiphysics simulations, such as the lack of boundedness, conservation, and equivalence in data transfer, as well as insufficient applicability to different time and spatial scales. In the spatial interpolation part, this invention uses Shepard interpolation to achieve the transfer of physical quantities between different grid systems, ensuring the boundedness of the interpolation results. In the spatiotemporal mapping part, this invention combines the principle of virtual work and conservation laws to achieve the transfer of physical quantities from physics field A to physics field B at different time and spatial scales, guaranteeing the conservation and equivalence of nodal physical quantities. Through the above methods, this invention can establish a bounded, equivalent, and conservation data interpolation mapping mechanism between heterogeneous models, suitable for multi-disciplinary, multiphysics coupled modeling and collaborative simulation, and can be widely applied to complex engineering design and analysis in fields such as aviation, aerospace, shipbuilding, energy, and machinery.

Claims

1. A spatiotemporal interpolation mapping method for simulation data of a multiphysics collaborative heterogeneous model, characterized in that, Includes the following steps: Step (1) Spatial interpolation: 1-1): Input the coordinates of the source point and variable values, the coordinates of the target point and the cutoff radius; 1-2): Calculate the variable values ​​for each target point based on Shepard interpolation; the variable values ​​include density, turbulent kinetic energy, and pressure; Step (2) Spatiotemporal mapping: 2-1): Input the physical quantity information corresponding to the time step of physical field A, the geometric characteristics of the interface between physical field A and physical field B, and the solution time steps of physical field A and physical field B; the physical quantities include surface load and heat flux density; 2-2): Based on the principle of virtual work, calculate the equivalent physical quantity at the node of physical field B at each discrete moment of physical field A; 2-3): Based on the conservation law, calculate the nodal equivalent physical quantities at the nodes of the physical field B element at each discrete time; the nodal equivalent physical quantities include the nodal equivalent load and the nodal heat flux density; In step (2), the discrete time steps of the physical field A are first calculated based on the principle of virtual work. The physical field B unit node Equivalent physical quantity Assume that a unit surface of physical field B has a relationship with physical field A. There are overlapping surfaces in each unit; the surface physical quantity applied by physical field A to physical field B is: ; If node It is the physical field B unit. A node whose local node number is The corresponding shape function is Using the principle of virtual work, surface physical quantities Converted into nodal equivalent physical quantities The calculation formula is: in, It is the set of all discrete elements of physical field A that have surfaces that coincide with the discrete elements of physical field B. It is a set The first in j Units; if node Belonging to multiple elements, the nodal equivalent physical quantities calculated for each element are... The final equivalent physical quantity of the node can be obtained by summing them up. Otherwise, the calculated nodal physical quantities of a single unit That is, the final nodal equivalent physical quantity ; The sum of the equivalent physical quantities at all nodes on a discrete element of a physical field B. Let a discrete element of a physical field B have... For each node, since the sum of the shape functions of a single element is 1, that is... The sum of the equivalent physical quantities of the nodes is derived as follows: Then, based on the conservation law, the discrete time intervals of physical field B are calculated. Physical field B unit node Equivalent physical quantity Assume the discrete time step of physical field A is... The discrete time step of physical field B is The specific steps are as follows: Since physical quantity data are only obtained at discrete moments, linear interpolation is used to describe the continuous change of the conserved quantity over time and to calculate the change of the conserved quantity: the physical quantities at two adjacent moments are connected by a straight line. According to the law of conservation, within the time interval Within this context, to ensure that the changes in conserved quantities are equal, it is necessary to guarantee that the equivalent physical quantities of the nodes in physical field B at the discrete time of physical field A are equal. The area under the line graph is equivalent to the physical quantity of the element node of physical field B at the discrete time of physical field B. The areas under the resulting line graphs are equal, as shown in the following formula: Right now in, Indicates the time interval Within, the physical quantities of the element nodes of physical field B at the discrete time of physical field A. The area under the line graph. yes The physical quantities at the node at time t are known quantities. for The physical quantity at time t is the quantity to be determined.

2. The spatiotemporal interpolation mapping method for simulation data of a multiphysics collaborative heterogeneous model according to claim 1, characterized in that, In step (1), the variable value of each target point is calculated based on Shepard interpolation; the specific calculation formula is as follows: in, The variable value for the target point. The variable value of the source point, These are the interpolation coefficients. It is the distance between the target point and the source point. It is the number of source points within the cutoff radius of the target point.

Images