Two-dimensional temperature field adaptive grid merging method
By estimating the continuity error of heat flux and using the independent cover manifold method, the accuracy problem of mesh merging judgment in the finite element method is solved, and efficient adaptive mesh merging of the two-dimensional temperature field is realized, improving the calculation accuracy and efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-31
- Publication Date
- 2026-03-10
AI Technical Summary
In the finite element method, existing technologies lack accurate error estimation for mesh merging, making it difficult to balance computational efficiency and local accuracy, and hindering adaptive analysis.
Using heat flow continuity as the basis for constructing the error estimator, global error estimation is achieved through absolute error estimation index and independent cover manifold method, and local mesh merging is performed to improve computational accuracy and efficiency.
It enhances the scientific rigor and accuracy of grid merging judgment, achieves high-precision local calculations, and balances computational efficiency and accuracy.
Smart Images
Figure CN121637867A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of numerical analysis of hydraulic structures, in particular to a two-dimensional temperature field adaptive grid merging method. BACKGROUND
[0002] The hydration reaction of concrete can produce a large amount of heat, and when the engineering structure is large, the heat is difficult to dissipate effectively. Once the temperature control is not in place, temperature cracks may occur, which can damage the integrity of the structure and reduce the durability of the structure. Therefore, the study of the temperature field of mass concrete has important practical significance. Through accurate temperature field analysis, scientific basis and theoretical support can be provided for temperature control and crack prevention of large-scale water conservancy projects.
[0003] The most widely used grid-based numerical method for temperature field analysis is the finite element method, but this method still has some problems in grid partitioning and calculation precision control. For example, the judgment basis for whether to perform grid merging often uses empirical formula, lacks accurate error estimation as a basis for judgment, and usually performs interlayer grid merging, lacks local grid merging means, and is difficult to balance calculation efficiency and local precision, making it difficult to achieve adaptive analysis. SUMMARY
[0004] In view of the above problems existing in the prior art, the purpose of the present application is to provide a two-dimensional temperature field adaptive grid merging method, which can achieve efficient balance of calculation precision and calculation efficiency in the whole calculation domain.
[0005] In order to solve the above problems, the technical scheme adopted by the present application is as follows: A two-dimensional temperature field adaptive grid merging method, characterized in that the method comprises the following steps: S1: setting the error threshold of grid merging according to the calculation precision requirement ; S2: taking heat flow continuity as the basis for constructing error estimators, using absolute error estimation index, the formula is: ; Wherein, is the calculated value of heat flow, is the relative accurate value, is the size of the partition interface; S3: reading the error estimation value between the two adjacent grids If , mark this strip and its corresponding two grids; S4: The following processing is performed on the two marked grids respectively, and the vectors of the sides surrounding the grid are calculated in turn in a counterclockwise direction, and it is determined whether there is an angle of 0° between two adjacent sides, if there is, the two original vectors are replaced by the resultant vector, and the grid vertex data represented by the least number of sides is obtained; if not, the next step is directly entered; S5: The feasibility of grid merging is determined ① Check whether the two processed marked grids are common sides, if they are, record the information of the common side and enter the next step, otherwise, it is determined that the two grids do not have the feasibility of merging; ② Check whether the common side of the two grids is completely coincident with the marked strip, if it is, it is determined that the feasibility of merging is met and the next step is entered, otherwise, it is determined that the feasibility of merging is not met; S6: The two grids determined to have the feasibility of merging are merged into one, and the merged grid is processed to be represented by the least number of sides; S7: The merged grid information is combined into a new grid file.
[0006] Further, in step S2, define two adjacent independent covers as cover one and cover two, and the heat flow calculation values of cover one and cover two are and , Take any one of and , as the arithmetic mean of the two.
[0007] Further, in step S4, the following steps are included: S4.1: In a polygonal grid, the vertex sequence is represented as , where each vertex is a two-dimensional coordinate point, and the sequence is arranged in counterclockwise order; S4.2: Calculate the edge vector sequence from the vertex sequence , where each edge vector is defined as the difference between adjacent vertices, i.e. , for ; S4.3: For the edge vector sequence , check each adjacent side pair , if the cross product of the edge vectors is zero and the dot product is positive, replace the original two vectors with the resultant vector ; S4.4: Iterate the above merging process for each vertex, and when the iteration is terminated, the final edge vector sequence is obtained, where ; S4.5: Reconstruct the vertex sequence from the simplified edge vector sequence ,in , ,for .
[0008] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention constructs an error estimator based on the continuity of heat flow between adjacent grids to replace conventional empirical formulas, thereby achieving automatic error estimation across the entire domain. This enhances the scientific rigor and accuracy of the decision on whether to merge grids, and enables high-precision local calculations. By merging local grids, it balances computational accuracy and efficiency. Attached Figure Description
[0009] Figure 1 This is a schematic diagram of the steps of the merging method described in this invention; Figure 2 A schematic diagram of an arbitrary-shaped covering system, exemplified in the independent covering popularization method; Figure 3 This is a schematic diagram of two independent coverages and their strip connection method; Figure 4 A schematic diagram of one-dimensional local coordinates along the thickness direction within a narrow strip region; Figure 5 This is a schematic diagram of the coverage distribution of two adjacent areas. Detailed Implementation
[0010] The present invention will be further described below with reference to specific embodiments.
[0011] like Figure 1 As shown, the two-dimensional temperature field adaptive mesh merging method of the present invention includes the following steps: S1: Set the error threshold for mesh merging according to the required computational accuracy. ; S2: Using heat flow continuity as the basis for constructing the error estimator, and employing the absolute error estimation index, the formula is as follows: ; in, This is the calculated value of heat flow. This is a relatively accurate value. The dimensions of the partition interface; S3: Read the error estimate between two adjacent grids. ,like Then mark this stripe and its two corresponding grids; S4: The following processing is performed on the two marked grids respectively, and the vectors of the sides surrounding the grid are calculated in turn counterclockwise, whether there is an angle of 0° between two adjacent sides is calculated, if there is, the two original vectors are replaced by the resultant vector, and the grid vertex data represented by the least side is obtained; if not, the next step is directly entered; S5: The feasibility of grid merging is determined ① Check whether the two processed marked grids are common edges, if they are common edges, record the information of the common edge and enter the next step, otherwise, it is determined that the two grids do not have merging feasibility; ② Check whether the common edge of the two grids is completely coincident with the marked strip, if it is completely coincident, it is determined that it has merging feasibility and enters the next step, otherwise, it is determined that it does not have merging feasibility; S6: The two grids determined to have merging feasibility are merged into one, and the merged grid is processed to be represented by the least side; S7: The merged grid information is combined into a new grid file.
[0012] In step S2, the absolute error estimation index adopted is based on the independent coverage flow method, which is, first, assume a calculation domain and divide it into several partitions, and use strips to connect between the partitions, as shown in Figure 2 Each partition forms an independent coverage, and each independent coverage and its surrounding strip form a coverage, and the independent coverage is an independent area of the coverage, and the strip is an overlapping area of multiple coverages.
[0013] Define a complete series (coverage series) such as polynomial series on each coverage: in the interior of the independent coverage , use the coverage series as an approximate function to directly approximate the real physical field function. At each strip, use the unit resolution function to connect the series in the adjacent partitions into an overall approximate function: ; In the above formula, is the number of coverages at the strip, is the unit resolution function, ; In the above manner, the linear transition of the approximate function is further realized, and the series coefficients in the overall approximate function are obtained by the Galerkin method to form the so-called "partition series solution".
[0014] Two arbitrary-shaped partitions (or coverages) are intercepted from Figure 2 , as shown in Figure 3 , and the convergence is analyzed. Let the true solution on coverage 1 be , and define the coverage series The true solution on the cover 2 is The cover series is defined as The true solution on the narrow strip of the overlap of two covers is As shown in Figure 4 , a one-dimensional local coordinate is established along the thickness direction of the strip The unit decomposition function is a linear shape function of one-dimensional finite element: ; ; Each cover uses a complete series. According to the classical function local approximation theory, any continuous function can be approximated by a complete series in the partition of a closed set. Therefore, with the increase of the number of series terms, it is obvious that the independent cover inside can obtain: ; ; In the narrow strip part of the overlap of the two: ; Considering the continuity of the true solution: ; It is concluded that: ; Thus, it verifies the convergence of the physical field function itself, and the overall approximate function satisfies continuity.
[0015] Further investigate the convergence and continuity of its derivative. Since a complete series is used, in each cover (taking the derivative in the direction as an example): ; ; Among them, in the narrow strip part of the overlap of the two covers: ; Since the convergence of the physical field itself and the continuity of the true solution have been verified, it is obtained: ; Considering the continuity of the derivative of the true solution: ; It is concluded that: ; Thus, it verifies the convergence of the derivative of the physical field, and the approximate function has continuity in the sense of convergence.
[0016] Extending the above analysis to Figure 2 In cases of multiple coverage connections, for the connection region of multiple coverages, the unit decomposition function can be the shape function of the polygon finite element method, or it can be decomposed into multiple finite elements, yielding the same conclusion. However, in general, since the area of the narrow strip in the connection region of multiple (more than 2) coverages is very small, the lack of a strictly defined unit decomposition function has little impact on the calculation results. Therefore, generally only the narrow strip between two coverages is considered. Moreover, in the calculation program, the strip is added automatically. At present, the principle for determining the strip width is, based on calculation experience, generally taking the strip area to be 1% of the total coverage area.
[0017] In summary, in the independent covering maneuver, as the covering series increases, not only is the physical field itself convergent, but its derivative also converges. Specifically, the global race function... Continuity, as a necessary condition for convergence, strictly reflects the accuracy of computation and can thus serve as an indicator for error estimation.
[0018] Meanwhile, the shape and size of each partition cover (hereinafter, both are equivalent) do not affect the final approximation result, but only the approximation speed; that is, each cover can have any shape. Furthermore, covers can be arbitrarily misaligned and connected, such as... Figure 2 As shown, it demonstrates a computational grid of arbitrary shape and arbitrary connection. Thus, the encryption of the overlay grid also has any property: no matter what encryption method is used, no matter what shape the independent overlay is refined into, and no matter how the refined overlays are connected, as long as each overlay is encrypted to an appropriate size, it is always possible to approximate the true solution with a complete series of appropriate order within each overlay.
[0019] Figure 1 In The variable representing the loop, assuming the number of label stripes is... Then, the processing method should be followed from the first marked bar to the second. Each marked stripe is processed individually.
[0020] In step S2, heat flux continuity is used as the basis for constructing the error estimator, including requirements for the continuity between two adjacent grids within the computational domain and the consistency of the computational domain boundary under the second type of boundary conditions. For example... Figure 5 Taking the one-dimensional problem shown as an example, we define two adjacent independent covers as Coverage 1 and Coverage 2, and the calculated heat flow values for Coverage 1 and Coverage 2 are... and , Pick and Any one of them, This is the arithmetic mean of the two.
[0021] Further, the step S4 comprises the following steps: S4.1: In a polygonal mesh, whose vertex sequence is denoted as where each vertex is a two-dimensional coordinate point, and the sequence is arranged in anticlockwise order; S4.2: Calculate the edge vector sequence from the vertex sequence where each edge vector is defined as the difference between two adjacent vertices, i.e. for ; S4.3: For the edge vector sequence , check each adjacent edge pair , if the cross product of the edge vectors is zero and the dot product is positive, replace the original two vectors with the sum vector ; S4.4: Iterate the above merging process for each vertex, and when the iteration is terminated, the final edge vector sequence is obtained, where ; S4.5: Reconstruct the vertex sequence from the simplified edge vector sequence where , for .
Claims
1. A two-dimensional temperature field adaptive grid merging method, characterized in that, The method comprises the following steps: S1: set the error threshold of grid merging according to the calculation accuracy requirement ; S2: Taking the heat flow continuity as the construction basis of the error estimator, an absolute error estimation index is adopted, and the formula is: ； wherein, is the heat flow calculated value, is the relative accuracy value, is the size of the partition interface; S3: read the error estimate value between the two adjacent grids , if , mark the strip and its corresponding two grids; S4: The following processing is performed on the two marked grids respectively, the edge vectors surrounding the grid are calculated in turn counterclockwise, whether the adjacent two edges exist the angle of 0° is calculated, if it exists, the sum vector is used to replace the original two vectors to obtain the grid vertex data represented by the least edges; if it does not exist, the next step is directly entered; S5: The feasibility of grid merging is judged: ①Check whether the two processed marked grids are common edges, if they are common edges, the information of the common edge is recorded and the next step is entered, otherwise it is judged that the two grids do not have the merging feasibility; ②Check whether the common edge of the two grids is completely coincided with the marked strip, if it is completely coincided, it is judged that it has the merging feasibility and the next step is entered, otherwise it is judged that it does not have the merging feasibility; S6: The two grids which are judged to have the merging feasibility are merged into one, and the merged grid is processed to be represented by the least edges; S7: The merged grid information is combined into a new grid file.
2. The two-dimensional temperature field adaptive grid merging method of claim 1, wherein, In step S2, define two adjacent independent covers as cover one and cover two, and the heat flow calculation values of cover one and cover two are and , take and any one of , as the arithmetic mean of the two.
3. The two-dimensional temperature field adaptive grid merging method of claim 1, wherein, In step S4, the following steps are included: S4.1: In a polygonal mesh, the sequence of vertices is denoted as where each vertex is a two-dimensional coordinate point, and the sequence is in counterclockwise order; S4.2: Compute edge vector sequence from vertex sequence where each edge vector is defined as the difference of adjacent vertices, i.e. , for ; S4.3: For the sequence of edge vectors check each pair of adjacent edges if the cross product of the edge vectors is zero and the dot product is positive, replace the two original vectors by the sum vector ; S4.4: For each vertex iteration, the above merging process is performed, and when the iteration is terminated, the final edge vector sequence is obtained wherein ; S4.5: Reconstructing the sequence of vertices from the simplified sequence of edge vectors wherein , for .