Unsteady flow field reduced order prediction method with geometric prior weighting and related device
By introducing a geometric prior weight function for weighted orthogonal mode decomposition, the problem of insufficient representation of key flow regions in the traditional POD method is solved, and efficient reduced-order modeling and accurate prediction of unsteady flow fields are achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- XI AN JIAOTONG UNIV
- Filing Date
- 2026-03-13
- Publication Date
- 2026-06-05
AI Technical Summary
Traditional POD methods do not explicitly incorporate geometric information in order reduction modeling of unsteady flow fields, resulting in insufficient representation of key flow regions and decreased prediction accuracy.
By constructing a geometric prior weight function, weighted orthogonal mode decomposition is performed based on geometric structure information to enhance the expressive power of key flow regions, establish a weighted inner product space, and perform flow field order reduction modeling.
It improves the prediction accuracy and stability of key flow regions, reduces computational costs, and is applicable to a variety of engineering flow scenarios.
Smart Images
Figure CN122154551A_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of fluid dynamics numerical simulation and unsteady flow field prediction technology based on order reduction modeling, specifically involving an unsteady flow field order reduction prediction method and related apparatus that introduces geometric prior weighting. Background Technology
[0002] Unsteady flow field prediction has significant application value in engineering fields such as aerospace, energy and power, and fluid machinery. To reduce the computational cost of high-dimensional flow fields and improve prediction efficiency, flow field prediction methods based on order reduction modeling have attracted widespread attention.
[0003] Proper Orthogonal Decomposition (POD), a typical method for order reduction modeling, constructs spatial modes that characterize the main flow structures by performing eigenvalue decomposition on flow field snapshot data, thus achieving a mapping from high-dimensional flow fields to low-dimensional spaces. Traditional POD methods typically construct modes based on standard inner product spaces, aiming to maximize the energy share of the selected modes in a global sense.
[0004] Traditional POD methods rely on the assumption of equal-weighted inner products, with mode construction based on standard inner product space, assigning equal weights to all spatial locations during the mode construction process. However, in real-world unsteady flows, the influence of different spatial regions of the flow field on the evolution of the flow structure is not uniform. For example, near-wall regions, flow separation regions, or shear layer regions close to geometric boundaries often play a crucial role in the overall flow characteristics, but these regions account for a small proportion of the global energy distribution. The traditional equal-weighted assumption struggles to highlight the flow characteristics of these key regions, resulting in reduced-order modes that tend to characterize the globally dominant structure but lack the ability to express local key flow regions, thus reducing prediction accuracy in relevant areas. Summary of the Invention
[0005] This application addresses the technical problem that the traditional POD method fails to explicitly incorporate geometric structure information during the unsteady flow field order reduction modeling process, resulting in insufficient expressive power of key flow regions. It provides an unsteady flow field order reduction prediction method and related apparatus that introduces geometric prior weighting.
[0006] To achieve the above objectives, this application adopts the following technical solution: A method for order reduction prediction of unsteady flow fields by incorporating geometric prior weighting includes the following steps: Acquire geometric information and unsteady flow field snapshot data of the target flow system; Based on the aforementioned geometric structure information, a spatial distance function δ(x) is constructed; Based on the spatial distance function δ(x), a geometric prior weight function w(x) is constructed; Based on the geometric prior weight function w(x), a weighted inner product space is constructed, and weighted orthogonal mode decomposition is performed on the unsteady flow field snapshot data to obtain the weighted space modes and the corresponding reduced-order mode coefficients; A modal coefficient prediction model is established, and based on the reduced-order modal coefficients, the modal coefficients at the test time are predicted to obtain the predicted modal coefficients. Based on the predicted modal coefficients and the weighted spatial modes, the flow field is reconstructed by inverse transformation to obtain the unsteady flow field prediction result at the target time.
[0007] Furthermore, the construction of the spatial distance function δ(x) based on the geometric structure information includes: Based on the geometric structure information, the minimum distance function from any position x in the flow field space to the geometric boundary is defined as the spatial distance function δ(x); the spatial distance function δ(x) is used to characterize the relative spatial relationship between the spatial position of the flow field and the geometric structure.
[0008] Furthermore, the geometric prior weighting function w(x) is an inverse distance function, which achieves differentiated weighting of key flow regions in the target flow system by adjusting the weighting intensity parameter; The geometric prior weight function w(x) is:
[0009] Where α is the weighting intensity parameter, ε is the regularization parameter, and δ(x) is the spatial distance function.
[0010] Furthermore, the geometric prior weighting function is an exponentially decaying function, which achieves differentiated weighting of key flow regions in the target flow system by adjusting the weighting intensity parameter and the decay scale parameter. The geometric prior weight function w(x) is:
[0011] Where α is the weighted intensity parameter, β is the attenuation scale parameter, and δ(x) is the spatial distance function.
[0012] Furthermore, the weighted inner product space is:
[0013] Where Ω represents the computational domain of the unsteady flow field, and w(x) is the geometric prior weighting function. Let v(x) be the value of the flow field variable at spatial location x, representing another snapshot of the unsteady flow field. Let x be the value of the flow field variable at spatial location x, representing another snapshot of the unsteady flow field at the initial moment.
[0014] Furthermore, the modal coefficient prediction model is a linear regression model, a time series model, or a machine learning model.
[0015] Furthermore, the geometric structure information includes the geometric boundary position, structural outline information, and spatial coordinate data; The unsteady flow field data were obtained by numerical simulation software to perform numerical calculations on the target flow system.
[0016] A system for performing the above-described method for reducing the order of unsteady flow field prediction by incorporating geometric prior weights, comprising: The data acquisition module is used to acquire geometric structure information and unsteady flow field snapshot data of the target flow system; A spatial distance function construction module is used to construct a spatial distance function δ(x) based on the geometric structure information; The geometric prior weight function construction module is used to construct the geometric prior weight function w(x) based on the spatial distance function δ(x); The order reduction modeling module is used to construct a weighted inner product space based on the geometric prior weighting function w(x), and to perform weighted orthogonal modal decomposition on unsteady flow field snapshot data to obtain the weighted space modes and the corresponding reduced order modal coefficients; The modal coefficient prediction module is used to establish a modal coefficient prediction model, and based on the reduced-order modal coefficients, to predict the modal coefficients at the test time to obtain the predicted modal coefficients. The flow field reconstruction and prediction module performs inverse transformation reconstruction of the flow field based on the predicted modal coefficients and weighted spatial modes to obtain the unsteady flow field prediction results at the target time.
[0017] A computer device includes: a processor and a computer-readable storage medium; A processor, adapted to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, implements the unsteady flow field order reduction prediction method with geometric prior weighting as described above.
[0018] A computer-readable storage medium storing a computer program adapted to be loaded by a processor and executed as described above for the method of reducing the order of unsteady flow field prediction by incorporating geometric prior weights.
[0019] Compared with the prior art, this application has the following beneficial effects: This application first constructs a spatial distance function related to the geometric structure based on traditional orthogonal modal decomposition (POD), forming a geometric prior weight function to obtain geometric prior information. Then, it introduces the spatial weighting function into the inner product calculation process of POD, and completes flow field order reduction modeling in the weighted inner product space. That is, through a geometric distance-driven spatial weighting mechanism, it changes the global equal weight assumption of the traditional POD method, allowing key flow regions near the geometric boundary to receive higher weights during mode construction. Finally, weighted orthogonal modal decomposition is performed on unsteady flow field snapshot data to obtain weighted spatial modes and corresponding reduced-order modal coefficients. The weighted spatial modes can be used for low-dimensional representation of unsteady flow fields and can be further combined with modal coefficient prediction models to achieve rapid reconstruction and prediction of unsteady flow fields. This application introduces geometric prior information in the order reduction modeling stage to enhance the representation of key flow regions of the target flow system. While maintaining a low modal order and order reduction efficiency, it improves the prediction accuracy and stability of key flow regions, improves the flow field prediction error distribution, enhances the overall effect of unsteady flow field prediction, and reduces computational costs. It is applicable to various engineering flow scenarios and has good engineering application value.
[0020] The construction of the spatial distance function δ(x) based on the geometric structure information includes: Based on the aforementioned geometric information, the minimum distance function from any position x in the flow field space to the geometric boundary is defined as the spatial distance function δ(x). The spatial distance function δ(x) characterizes the relative spatial relationship between the spatial position in the flow field and the geometric structure. The spatial distance function δ(x) characterizes the relative importance of different spatial positions in the order reduction modeling process corresponding to the weighted inner product space, providing data support for the subsequent order reduction modeling process and enabling a more robust expression of the key flow regions of the target flow system.
[0021] Furthermore, the geometric prior weighting function w(x) is an inverse distance function, which achieves differentiated weighting of key flow regions in the target flow system by adjusting the weighting intensity parameter; The geometric prior weight function w(x) is:
[0022] Where α is the weighting intensity parameter, ε is the regularization parameter, and δ(x) is the spatial distance function. This step adjusts the spatial weight gradient by regulating the weighting intensity parameter, ensuring that key flow regions near the geometric boundary receive higher weights during mode construction, thereby enhancing the ability of the reduced-order model to express local flow structures.
[0023] Furthermore, the geometric prior weighting function is an exponentially decaying function, which achieves differentiated weighting of key flow regions by adjusting the weighting intensity parameter and the decay scale parameter; The geometric prior weight function w(x) is:
[0024] Where α is the weighting intensity parameter, β is the decay scale parameter, and δ(x) is the spatial distance function. This step adjusts the spatial weight gradient by regulating the weighting intensity parameter and the decay scale parameter, and controls the geometric influence range. This ensures that key flow regions near the geometric boundary receive higher weights during mode construction, while maintaining a smooth spatial distribution of the weight function, thereby enhancing the ability of the reduced-order mode to express the local flow structure. Attached Figure Description
[0025] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.
[0026] Figure 1 This is a flowchart of the unsteady flow field order reduction prediction method with geometric prior weighting introduced in this invention; Figure 2 This is a schematic diagram of the construction of the weighted inner product space in the unsteady flow field order reduction prediction method with geometric prior weighting of the present invention; Figure 3 The diagram shows a comparison between the spatial modal structure obtained by the traditional POD method and the spatial modal structure obtained by the unsteady flow field order reduction prediction method with geometric prior weighting of the present invention. In this diagram, (a) is the weighted spatial mode obtained by the traditional POD method, and (b) is the weighted spatial mode obtained by the present application. Figure 4 This is a schematic diagram comparing the overall flow field prediction error distribution at a certain test time between the traditional POD method and the unsteady flow field order reduction prediction method of the present invention, which introduces geometric prior weighting. Among them, (a) is the error distribution between the overall predicted flow field and the actual flow field reconstructed by the traditional POD method based on the predicted mode coefficients, and (b) is the error distribution between the overall predicted flow field and the actual flow field reconstructed by the method of the present application based on the predicted mode coefficients. Figure 5 for Figure 4 The diagram shows a magnified view of the overall flow field prediction error distribution in the key flow region at a certain test moment. (a) is a magnified view of the prediction error distribution in the key flow region using the traditional POD method, and (b) is a magnified view of the prediction error distribution in the key flow region using the method of the present invention. Figure 6This is a schematic diagram of the unsteady flow field order reduction prediction system with geometric prior weighting introduced in this invention. Figure 7 This is a schematic diagram of a computer device structure. Detailed Implementation
[0027] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0028] In the traditional POD method, mode construction is based on the standard inner product space, which assumes that each spatial location has the same weight in energy calculation. However, in actual engineering flows, near-wall regions, separation regions, or shear layer regions close to geometric boundaries often have a more significant impact on the overall flow structure, and the traditional equal weight assumption is insufficient to highlight the flow characteristics of these key regions.
[0029] Therefore, as Figure 1 As shown, this application proposes a method for order reduction prediction of unsteady flow fields by incorporating geometric prior weighting, comprising the following steps: S1, acquire the geometric structure information and unsteady flow field snapshot data of the target flow system.
[0030] The geometric structure information may include, but is not limited to, the location of geometric boundaries, structural outline information, and spatial coordinate data.
[0031] In some embodiments of this application, unsteady flow field data can be obtained through commercial numerical simulation software, such as using fluid simulation software like ANSYS Fluent to perform numerical calculations on the target flow system to obtain unsteady flow field snapshot data. In this embodiment, a flow around a cylinder is used for verification.
[0032] S2, Based on the geometric structure information, construct the spatial distance function δ(x).
[0033] Specifically, based on the geometric structure information, a spatial distance function δ(x) is constructed, including: Based on geometric structure information, the minimum distance function from any position x in the flow field space to the geometric boundary is defined as the spatial distance function δ(x); the spatial distance function δ(x) is used to characterize the relative spatial relationship between the spatial position of the flow field and the geometric structure.
[0034] In some embodiments of this application, the spatial distance function δ(x) can be obtained by Euclidean distance calculation, grid distance search or other spatial distance calculation methods, that is, the geometric distance is obtained.
[0035] S3. Based on the spatial distance function δ(x), construct the geometric prior weight function w(x).
[0036] Specifically, based on the geometric distance function δ(x), a spatial weighting function w(x) is constructed to characterize the relative importance of different spatial locations in the order reduction modeling process.
[0037] One possible implementation is that the geometric prior weight function w(x) is an inverse distance function, which achieves differentiated weighting of key flow regions in the target flow system by adjusting the weighting intensity parameter; The geometric prior weight function w(x) is:
[0038] Where α is the weighting intensity parameter used to adjust the spatial weight gradient, ε is the regularization parameter used to avoid the denominator being zero, and δ(x) is the spatial distance function.
[0039] Another possible implementation involves using an exponentially decaying geometric prior weighting function w(x), which differentiates the weighting of key flow regions by adjusting the weighting intensity parameter and the decay scale parameter. The geometric prior weight function w(x) is:
[0040] Where α is the weighting intensity parameter used to adjust the spatial weight gradient, β is the decay scale parameter used to control the geometric influence range, and δ(x) is the spatial distance function.
[0041] It should be understood that the geometric prior weight function w(x) can also take other functional forms based on the spatial distance function δ(x). As long as it can achieve the purpose of assigning higher weights to key flow regions, it should be considered to fall within the protection scope of this invention.
[0042] S4. Based on the geometric prior weighting function, a weighted inner product space is constructed, and weighted orthogonal mode decomposition is performed on the unsteady flow field snapshot data to obtain the weighted space modes and the corresponding weighted mode coefficients.
[0043] The weighted inner product space is:
[0044] Where Ω represents the computational domain of the unsteady flow field, and w(x) is the geometric prior weighting function. Let x be the value of the flow field variables at spatial location x, representing a snapshot of the unsteady flow field at a certain moment. Let x be the value of the flow field variable at spatial location x, representing another snapshot of the unsteady flow field at the initial moment.
[0045] One possible implementation is, such as Figure 2 As shown, the standard inner product space is constructed based on w(x)=1, where each spatial location has the same weight in the inner product calculation process. This application introduces a spatial weighting function w(x) into the inner product calculation process, giving higher weights to regions near the geometric boundaries, thus forming a weighted inner product space. Orthogonal mode decomposition is performed within this weighted inner product space to obtain weighted spatial modes, thereby enhancing the ability of the reduced-order modes to represent key flow regions.
[0046] like Figure 3 As shown, comparing the spatial modal structures obtained by the traditional POD method with those obtained by the unsteady flow field order reduction prediction method of the present invention with geometric prior weighting, it can be concluded that the modal structures obtained by the traditional POD method are more dispersed throughout the entire computational region, while the spatial modal structures obtained by the method of the present invention have more obvious flow structure characteristics near the geometric boundary and wake region, and the modal energy is more concentrated in the key flow region. This indicates that by introducing geometric prior weights, the order reduction mode can more effectively characterize the flow structure characteristics of the key flow region.
[0047] S5. Establish a modal coefficient prediction model. Based on the reduced-order modal coefficients, predict the modal coefficients at the test time to obtain the predicted modal coefficients.
[0048] Specifically, the modal coefficient prediction model can be a linear regression model, a time series model, or a machine learning model.
[0049] like Figure 4 As shown, a comparison of the overall flow field prediction error distribution at a certain test moment between the traditional POD method and the geometrically prior-weighted unsteady flow field order reduction prediction method of the present invention reveals a significant difference in the overall flow field prediction error distribution at a certain test moment. The method of the present invention exhibits a more concentrated overall prediction error distribution and a relatively smaller error amplitude near the geometric boundary and wake region, indicating that the geometrically prior-weighted order reduction modeling method proposed in this application can improve the prediction accuracy of key flow regions.
[0050] S6. Based on the predicted modal coefficients and the weighted spatial modes, perform inverse transformation and reconstruction of the flow field to obtain the unsteady flow field prediction result at the target time.
[0051] Among them, based on the predicted modal coefficients and weighted spatial modes obtained from the prediction, the unsteady flow field can be rapidly reconstructed, thereby realizing the rapid prediction of the unsteady flow field.
[0052] like Figure 5 As shown, Figure 4 The diagram shown is a magnified view of the overall flow field prediction error distribution in the key flow region at a certain test moment. It can be seen that in key flow regions such as the cylindrical wake, the prediction error amplitude of the traditional POD method is large and the distribution range is wide. However, the error amplitude of the method of the present invention is significantly reduced in the same region and the error distribution range is smaller. This indicates that the introduction of a geometric prior weighting mechanism can effectively improve the prediction accuracy of key flow regions.
[0053] In some embodiments of this application, in the geometric prior weighted unsteady flow field order reduction prediction method, after obtaining the unsteady flow field snapshot data, the geometric distance calculation, geometric prior weight function construction and weighted orthogonal mode decomposition process can be implemented by a programming language, such as using Python for algorithm implementation.
[0054] It should be understood that the ANSYS Fluent and Python languages used above are merely examples, and the methods of this invention can also be implemented in other fluid simulation software or other programming environments.
[0055] In one embodiment of this application, such as Figure 6 As shown, a method for order reduction prediction of unsteady flow fields by incorporating geometric prior weighting is provided, comprising: The data acquisition module is used to acquire geometric structure information and unsteady flow field snapshot data of the target flow system; A spatial distance function construction module is used to construct a spatial distance function δ(x) based on the geometric structure information; The geometric prior weight function construction module is used to construct the geometric prior weight function w(x) based on the spatial distance function δ(x); The order reduction modeling module is used to construct a weighted inner product space based on the geometric prior weighting function w(x), and to perform weighted orthogonal modal decomposition on unsteady flow field snapshot data to obtain the weighted space modes and the corresponding reduced order modal coefficients; The modal coefficient prediction module is used to establish a modal coefficient prediction model, and based on the reduced-order modal coefficients, to predict the modal coefficients at the test time to obtain the predicted modal coefficients. The reconstruction and prediction module performs inverse transformation reconstruction based on the predicted modal coefficients and weighted spatial modes to obtain the unsteady flow field prediction results at the target time.
[0056] In one embodiment, the data acquisition module includes an unsteady flow field snapshot data input module and a geometric information acquisition module. The unsteady flow field snapshot data input module is used to input unsteady flow field snapshot data of the target flow system; the geometric information acquisition module is used to acquire geometric structure information of the target flow system.
[0057] In another embodiment, the order reduction modeling module includes a weighted inner product space construction module and a weighted orthogonal mode decomposition module. The weighted inner product space construction module is used to construct a weighted inner product space based on the geometric prior weight function w(x); the weighted orthogonal mode decomposition module is used to perform weighted orthogonal mode decomposition on unsteady flow field snapshot data based on the weighted inner product space.
[0058] Specific limitations regarding the geometrically prior-weighted unsteady flow field order reduction prediction system can be found in the limitations outlined above for the geometrically prior-weighted unsteady flow field order reduction prediction method; the corresponding technical effects are equivalent and will not be repeated here. Each module in the aforementioned geometrically prior-weighted unsteady flow field order reduction prediction system can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the computer device's memory as software, allowing the processor to call and execute the corresponding operations of each module.
[0059] Figure 7 An internal structural diagram of a computer device is shown in one embodiment. This computer device may specifically be a terminal or a server. Figure 7 As shown, the computer device includes a processor, memory, network interface, display, camera, and input device connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When executed by the processor, the computer program implements a battery state prediction method. The display screen can be an LCD screen or an e-ink display. The input device can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.
[0060] As will be understood by those skilled in the art, computer equipment Figure 7The structure shown is merely a block diagram of a portion of the structure related to the present invention and does not constitute a limitation on the computer device to which the present invention is applied. A specific computing device may include more or fewer components than those shown in the figure, or combine certain components, or have the same component arrangement.
[0061] In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method described above.
[0062] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.
[0063] In summary, the embodiments of this application provide a method, system, computer device, and storage medium for predicting unsteady flow fields by introducing geometric prior weighting. By introducing a geometric distance-driven spatial weighting mechanism in the order reduction modeling stage, this invention changes the equal weight structure of traditional orthogonal mode decomposition, enabling key flow regions to obtain enhanced representation in mode construction, thereby improving the accuracy and stability of unsteady flow field prediction.
[0064] The various embodiments in this specification are described in a progressive manner. For directly identical or similar parts of the embodiments, refer to each other. Each embodiment focuses on its differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. It should be noted that the technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification.
[0065] The above-described embodiments are merely preferred embodiments of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various improvements and substitutions without departing from the principles of the present invention, and these improvements and substitutions should also be considered within the scope of protection of the present invention. Therefore, the scope of protection of this invention should be determined by the scope of the claims.
Claims
1. A method for order reduction prediction of unsteady flow fields by incorporating geometric prior weighting, characterized in that, Includes the following steps: Acquire geometric information and unsteady flow field snapshot data of the target flow system; Based on the aforementioned geometric structure information, a spatial distance function δ(x) is constructed; Based on the spatial distance function δ(x), a geometric prior weight function w(x) is constructed; Based on the geometric prior weight function w(x), a weighted inner product space is constructed, and weighted orthogonal mode decomposition is performed on the unsteady flow field snapshot data to obtain the weighted space modes and the corresponding reduced-order mode coefficients. A modal coefficient prediction model is established, and based on the reduced-order modal coefficients, the modal coefficients at the test time are predicted to obtain the predicted modal coefficients. Based on the predicted modal coefficients and the weighted spatial modes, the flow field is reconstructed by inverse transformation to obtain the unsteady flow field prediction result at the target time.
2. The unsteady flow field order reduction prediction method with geometric prior weighting as described in claim 1, characterized in that, The construction of the spatial distance function δ(x) based on the geometric structure information includes: Based on the geometric structure information, the minimum distance function from any position x in the flow field space to the geometric boundary is defined as the spatial distance function δ(x); the spatial distance function δ(x) is used to characterize the relative spatial relationship between the spatial position of the flow field and the geometric structure.
3. The method for order reduction prediction of unsteady flow fields by introducing geometric prior weighting as described in claim 1, characterized in that, The geometric prior weighting function w(x) is an inverse distance function, which achieves differentiated weighting of key flow regions in the target flow system by adjusting the weighting intensity parameter; The geometric prior weight function w(x) is: Where α is the weighting intensity parameter, ε is the regularization parameter, and δ(x) is the spatial distance function.
4. The unsteady flow field order reduction prediction method based on geometric prior weighting as described in claim 1, characterized in that, The geometric prior weighting function is an exponentially decaying function, which achieves differentiated weighting of key flow regions in the target flow system by adjusting the weighting intensity parameter and the decay scale parameter. The geometric prior weight function w(x) is: Where α is the weighted intensity parameter, β is the attenuation scale parameter, and δ(x) is the spatial distance function.
5. The unsteady flow field order reduction prediction method based on geometric prior weighting according to claim 1, characterized in that, The weighted inner product space is: Where Ω represents the computational domain of the unsteady flow field, and w(x) is the geometric prior weighting function. Let x be the value of the flow field variables at spatial location x, representing a snapshot of the unsteady flow field at a certain moment. Let x be the value of the flow field variable at spatial location x, representing another snapshot of the unsteady flow field at the initial moment.
6. The unsteady flow field order reduction prediction method based on geometric prior weighting according to claim 1, characterized in that, The modal coefficient prediction model is a linear regression model, a time series model, or a machine learning model.
7. The unsteady flow field order reduction prediction method based on geometric prior weighting as described in claim 1, characterized in that, The geometric structure information includes the geometric boundary position, structural outline information, and spatial coordinate data; The unsteady flow field data were obtained by numerical simulation software to perform numerical calculations on the target flow system.
8. A system for performing the unsteady flow field order reduction prediction method according to any one of claims 1-7, characterized in that, include: The data acquisition module is used to acquire geometric structure information and unsteady flow field snapshot data of the target flow system; A spatial distance function construction module is used to construct a spatial distance function δ(x) based on the geometric structure information; The geometric prior weight function construction module is used to construct the geometric prior weight function w(x) based on the spatial distance function δ(x); The order reduction modeling module is used to construct a weighted inner product space based on the geometric prior weighting function w(x), and to perform weighted orthogonal modal decomposition on unsteady flow field snapshot data to obtain the weighted space modes and the corresponding reduced order modal coefficients; The modal coefficient prediction module is used to establish a modal coefficient prediction model, and based on the reduced-order modal coefficients, to predict the modal coefficients at the test time to obtain the predicted modal coefficients. The flow field reconstruction and prediction module performs inverse transformation reconstruction of the flow field based on the predicted modal coefficients and weighted spatial modes to obtain the unsteady flow field prediction results at the target time.
9. A computer device, characterized in that, include: Processor and computer-readable storage media; A processor, adapted to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, implements the unsteady flow field order reduction prediction method with geometric prior weighting as described in any one of claims 1 to 7.
10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program adapted to be loaded by a processor and executed as described in any one of claims 1 to 7, the method for predicting unsteady flow fields by introducing geometric prior weights.