JP3692460B2 - Numerical analysis system using mixed grid type solution adaptive grid method - Google Patents

Description

  The present invention relates to a numerical analysis apparatus using a mixed lattice type solution-adapted lattice method, and more particularly, to a mixed lattice type in which a lattice combining a tetrahedron, a pentahedron (pyramid element, prism element), and a hexahedron is divided and deleted according to changes. The present invention relates to a numerical analysis apparatus that generates a transition element by using a solution-adapted grid method and performs calculation by a finite element method.

  In unsteady analysis of compressible high-speed fluids, discontinuities of physical quantities such as shock waves that change with time are handled. In such a case, a fine grid of elements is required to obtain a highly accurate result. However, if the entire analysis area is divided by a fine grid, a large amount of calculation memory is consumed and the calculation speed is also reduced. In order to save memory and speed up calculation, it is better to make the grid finer only in the part where the physical quantity changes drastically. As this method, there is a solution fitting lattice method. There are a p-method, an r-method, and an h-method as solution-matching grid methods, but the h-method of subdividing elements is most effective when dealing with discontinuous portions as in shock wave analysis. In particular, the h method is called the AMR (Adaptive Mesh Refinement) method, which not only subdivides elements, but also restores unnecessary elements to the initial elements, enabling high-precision analysis with a minimum of calculation memory. It can be carried out.

  In recent numerical analysis, the shape of the analysis object is complicated, and the efficiency of the grid generation work is required. It is important that even if the object to be analyzed is a complicated shape, a grid can be easily generated using high-quality elements with little distortion. In the three-dimensional analysis, tetrahedral elements and hexahedral elements are mainly used. Since the tetrahedron element has good shape adaptability, a lattice can be easily generated using an element with less distortion even for an object having a complicated shape, but the calculation efficiency is poor. Although the hexahedral element is efficient in calculation, it is difficult to generate a lattice for a target having a complicated shape, and the element is distorted. Other elements include a pyramid element and a prism element. The prism element has good shape compatibility and high accuracy.

  In the problem of handling an object having a complicated shape, a hybrid grid composed of these elements is used. It is most efficient to use a hexahedral element grid as much as possible in the analysis region, and to perform an analysis using a tetrahedral element grid only at a location where grid generation is difficult. A tetrahedron element and a prism element can satisfy shape conformity. The calculation efficiency can be satisfied by the hexahedral element and the prism element. Still another element is a pyramid element. By using a pyramid element between a tetrahedron element and a hexahedron element, a continuous lattice can be formed without difficulty. By using the hybrid grid, in particular, an element with less distortion can be generated around an object having a complicated shape, and a highly accurate analysis can be performed. A method of applying the AMR method to the hybrid grid is called a hybrid grid adaptation (HGA).

  However, when the AMR method is applied, intermediate nodes (incomplete vertices) are generated between the divided element and its neighboring elements or between the elements sharing the edge by dividing / deleting the element. The In general, if such intermediate nodes remain generated, the calculation cannot be performed. Therefore, it is necessary to take some measures. When the element center finite volume method is used, calculation can be performed by evaluating the flux by adjusting the number of boundary surfaces.

  Some conventional examples related to the AMR method will be briefly described. The present inventor has proposed a numerical analysis apparatus in Patent Document 1 that uses a mixed lattice type solution-matching lattice method to achieve both lattice freedom and calculation efficiency. It is a numerical analysis device that performs numerical analysis by the element center finite volume method. Initial lattice data created using a free combination of a tetrahedral element, a hexahedral element, and a pentahedral element (pyramid element, prism element) is used. A guideline value for division deletion is calculated based on the density for each element. If the element volume is larger than the minimum value, the lattice level (number of divisions) of the element is not the maximum, and the division deletion guide value is larger than the division threshold value, the triangular face of the element is changed to multiple triangles. The element is divided so that the quadrangular surface is divided into a plurality of quadrangles. If the element lattice level is not an initial lattice of zero and the division deletion guideline value is smaller than the deletion threshold value, the elements are deleted and merged and returned to the element before the division.

Non-Patent Document 1 discloses an adaptive mesh method. It formulates an adaptive subdivision method based on hierarchical element division. We analyzed a mesh that arbitrarily mixed tetrahedron, hexahedron, prism and pyramid. The necessary memory was reduced as much as possible. This method is used with an algebraic multi-lattice fluid analyzer that calculates on a mixed mesh. Both viscous and non-viscous flows can be calculated by adaptively subdividing the tetrahedron, hexahedron and mixed mesh.
Japanese Patent Application No. 2002-195688 Specification DJ Mavriplis; "Adaptive meshing techniques for viscous flowcalculations on mixed element unstructured meshes", Int. J. Numer. Meth. Fluids 2000; 34: 93-111.

  However, it is difficult to apply the conventional mixed grid type solution fitting grid method to the finite element method. In general, an element (transition element) that temporarily fills an intermediate node is used. However, when transition elements are used, the algorithm becomes complicated and the shape of the elements tends to be distorted. When only tetrahedral elements are used, a transition element may be created using tetrahedral elements, and the algorithm is simple. Further, the distortion of the element is eliminated to some extent. However, when only hexahedral elements are used, it is necessary to create transition elements using hexahedral elements, which complicates the algorithm. Furthermore, since the elements are easily distorted, the calculation becomes unstable.

  An object of the present invention is to solve these conventional problems so that even a finite element method can be calculated by a mixed lattice type solution fitting lattice method.

  In order to solve the above problem, in the present invention, a tetrahedral element, a hexahedral element, a pentahedral element (pyramid element, An initial lattice storage means for storing initial lattice data created using a free combination of prism elements), an element so that a triangular surface of the element is divided into a plurality of triangles and a quadrilateral surface is divided into a plurality of rectangles. Grid division means to divide the element into multiple elements, grid deletion means to delete the divided elements and return to the element before division, and to eliminate intermediate nodes that are incomplete nodes caused by element division deletion A transition element generating means for generating a transition element, a guideline value calculating means for calculating a guideline value for dividing and deleting each element of the lattice in which the transition element is generated, and dividing or deleting the element based on the guideline value And determining split deletion determining means Luke, a configuration that includes a transition element removal means for deleting a transition element.

  In addition, the transition element generation unit includes an individual division processing unit that divides the element by an individual division method according to the arrangement state of the intermediate nodes in the element, and a uniform standard division method when the element cannot be divided by the individual division processing unit And a standard division processing means for dividing the element.

  In the present invention, the configuration as described above enables stable calculation by the finite element method even when the mixed grid type solution-matching grid method is used. By making the AMR method compatible with the Hybrid grid, the transition element creation / deletion algorithm can be simplified to some extent, transition elements with less distortion can be created, and high-precision numerical fluid can be created with a low-capacity computer. Analysis is possible. Furthermore, since the hybrid lattice is used, the shape conformity and the calculation efficiency are excellent. In particular, even in fluid analysis around an analysis object having a complicated shape, a lattice can be easily generated, and highly accurate analysis can be performed.

  Hereinafter, the best mode for carrying out the present invention will be described in detail with reference to FIGS.

  The first embodiment of the present invention uses a tetrahedron element, a hexahedron element, and a pentahedron element (pyramid element, prism element), and if the division deletion guideline value is larger than the division threshold value, the triangular face of the element is determined. Divide an element into multiple triangles so that the quadrilateral surface is divided into multiple quadrilaterals.If the split deletion guideline value is smaller than the deletion threshold, delete the element and It is a numerical analysis device that performs numerical analysis by the finite element method by returning to an element, eliminating intermediate nodes caused by division deletion with a transition element.

  FIG. 1 is a functional block diagram showing the configuration of the numerical analysis device according to the first embodiment of the present invention. In FIG. 1, an input device 1 is means for inputting various data and parameters such as initial lattice data, division threshold data, deletion threshold data, and physical quantities. The initial lattice memory 2 is a memory that stores initial values of lattices. The division threshold memory 3 is a memory that holds a determination criterion for lattice division. The deletion threshold memory 4 is a memory that holds a determination criterion for lattice deletion. The finite element method computing device 5 is means for performing numerical analysis by the finite element method. The lattice dividing means 6 is means for dividing the elements of the lattice. The lattice deletion means 7 is means for deleting the lattice and returning the elements to the original size even if the elements are merged. The guide value calculation means 8 is a means for calculating the guide value based on a physical quantity such as density. The division determination means 9 is a means for comparing the division threshold value with the guideline value. The deletion determination means 10 is a means for comparing the deletion threshold value with the guideline value. The display device 11 is means for displaying the result of numerical analysis. The transition element generation means 12 is a means for generating a transition element. The transition element deletion means 13 is a means for deleting a transition element.

  FIG. 2 is a flowchart showing an operation procedure of the numerical analysis apparatus according to the first embodiment of the present invention. FIG. 3 is a flowchart showing a procedure related to the HGA method. FIG. 4 is a flowchart showing a dividing procedure and a deleting procedure of the numerical analysis device.

  FIG. 5 is a diagram showing a grid element dividing method used in the numerical analysis apparatus according to the first embodiment of the present invention. FIG. 5A is a diagram illustrating a tetrahedral eight-division method (Type 1). FIG. 5B is a diagram illustrating a tetrahedral six-division method (Type 2). FIG. 5C is a diagram showing a 10-division method for dividing a pyramid (quadrangular pyramid) element into six pyramids and four tetrahedrons. FIG. 5D is a diagram showing an eight-division method for prism (triangular prism) elements. FIG. 5 (e) is a diagram showing a hexahedral dividing method. FIG. 5F is a diagram illustrating a method of dividing a triangular surface. FIG. 5G is a diagram illustrating a method for dividing a quadrangular surface. FIG. 5H is a diagram for explaining the Family relationship of elements.

  FIG. 6A is a diagram illustrating a method of dividing an element having a lattice level difference of 0 in two dimensions. FIG. 6B is a diagram illustrating a method of dividing an element having a lattice level difference of 1 in two dimensions. FIG. 6C is a diagram illustrating a method for deleting an element having a lattice level difference of 1 in two dimensions. FIG. 6D is a diagram illustrating a method of deleting elements having a lattice level difference of 0 in two dimensions. FIG. 6E is an explanatory diagram of intermediate nodes and transition elements in two dimensions. FIG. 7A is a diagram for explaining a procedure for generating transition elements. FIG. 7B is a diagram for explaining the transition element deletion procedure. FIG. 7C is a diagram for explaining generation and deletion of transition elements. FIG. 8 is a diagram for explaining a transition element generation method. FIG. 9 is a diagram for explaining a case-classification method for correcting the data of adjacent elements at the time of generation / deletion of transition elements.

The operation of the numerical analysis apparatus according to the first embodiment of the present invention configured as described above will be described. First, an overview of the functions of the numerical analysis device will be described with reference to FIG. The basic configuration of the numerical analysis device is the same as that of the conventional device. HGA (Hybrid) so that it can be calculated by the finite element method.
Grid Adaptation) algorithm is a transition element generation / deletion procedure. Various data and parameters such as initial lattice data, division threshold data, deletion threshold data, and physical quantities are input from the input device 1. The initial value of the lattice is stored in the initial lattice memory 2. The determination criterion for lattice division is held in the division threshold memory 3. The determination criterion for lattice deletion is stored in the deletion threshold value memory 4. Based on these data, the finite element method computing device 5 performs numerical analysis by the finite element method.

  The guideline value calculation means 8 calculates the guideline value based on a physical quantity such as density. The division determination means 9 compares the division threshold value with the guideline value. The deletion determination means 10 compares the deletion threshold value with the guideline value. If the pointer value is equal to or greater than the division threshold value, the lattice dividing means 6 divides the elements of the lattice. If the guideline value is equal to or smaller than the deletion threshold value, the lattice deletion means 7 deletes the lattice and returns the element to the original size even if the elements are merged. The transition element creating means 12 creates a transition element for eliminating the intermediate node generated by the generation and deletion of the grid. The lattice from which the intermediate nodes are eliminated is subjected to numerical analysis by the finite element method computing device 5 using the finite element method. The guideline value calculation means 8 calculates the guideline value based on a physical quantity such as density. Thereafter, the transition element deletion means 13 deletes the transition element. Repeat this to proceed with numerical analysis. The result of the numerical analysis is displayed on the display device 11.

  Next, the outline of the overall operation procedure of the numerical analysis apparatus based on the HGA method will be described with reference to FIG. In step 1, the finite element method computing device 5 reads initial lattice data from the initial lattice memory 2. In step 2, calculation by the finite element method is executed. The number of time units executed here may be one or more. In step 3, it is checked whether the calculation has been completed for all time units. If completed, the result is displayed in step 4 and the process is terminated. If not completed, the guideline value is calculated in step 5, and the transition element is deleted and the lattice data is updated in step 6. The update of lattice data is correction of data such as adjacent elements. Update of the lattice data is executed after dividing and deleting elements, deleting and creating transition elements, respectively.

  In step 7, the guideline value is compared with the division threshold value. If the guideline value is equal to or greater than the division threshold value, the element is divided in step 8 and the lattice data is updated. The guideline value is compared with the deletion threshold value. If the guideline value is equal to or smaller than the deletion threshold value, the element is deleted in step 9 and the lattice data is updated. If the guideline value is between the division threshold and the deletion threshold, neither division nor deletion is performed. The comparison, division, and deletion processes are performed for all elements constituting the grid. Thereafter, in step 10, a transition element is generated and the lattice data is updated, and the process returns to step 2 to execute calculation by the finite element method.

Thirdly, an outline of an operation procedure particularly related to the HGA method of the numerical analysis apparatus will be described with reference to FIG. As shown in FIG. 3, the main part of the HGA method is roughly divided into the following steps.
(1) Calculation of guideline values for division / deletion, marking of elements (2) Deletion of transition elements (3) Division of elements (4) Deletion of elements (5) Marking of elements with intermediate nodes (6) Creating transition elements (7) Counting the number of elements and nodes

  In the procedure (1) of the HGA method, a guideline value is calculated for each element as a pre-stage for determining the element to be divided / deleted. The purpose of the HGA method is to concentrate elements at locations where the physical quantity changes rapidly. In order to detect such a location, usually density, pressure gradient, second-order differential of pressure, or the like is used. In the case of a compressible fluid, the density is used as a guide value for detecting a shock wave or a contact discontinuity surface. Therefore, the density is also used as a guide value for division / deletion. By using other physical quantities for this guideline value, the present invention can be applied to other numerical analysis fields.

  When the guideline value of each element is calculated and the guideline value is larger than the division threshold, the division / deletion flag is set to “division”. If it is smaller than the deletion threshold, the division / deletion flag is set to “delete”. If it is in the middle, the division / deletion flag is set to “no division / deletion”. Further, when the lattice level (number of divisions) of each element is equal to the preset maximum value, the element is not divided. If the element volume is smaller than a preset minimum value, the division / deletion flag is not set to “division” even if the lattice level is not maximum. If the lattice level is 0 (initial lattice), the deletion is not performed. In the procedure (2) of the HGA method, the transition element is deleted.

  In the procedure (3) of the HGA method, before the element is divided, the element is re-marked based on the information of the element of interest, its adjacent element, and the element sharing the side (edge). This operation is recursively repeated until the difference in lattice level between the element of interest and its adjacent elements and elements sharing the node is suppressed to within one. That is, only one intermediate node can be taken on one side (edge). Thereafter, a division routine corresponding to each element shape is executed. In step (4) of the HGA method, elements are deleted. The element is deleted by the reverse method of division. The element deletion is executed when a specific condition is satisfied. In the procedure (5) of the HGA method, an element having an intermediate node is marked. In the procedure (6) of the HGA method, a transition element is created. In step (7) of the HGA method, the number of elements and the number of nodes are counted. The detailed contents of each procedure of the HGA method will be described later.

  Fourth, the procedure for dividing and deleting elements will be described with reference to FIG. With reference to FIG. 4A, the element division processing procedure will be described. In step 11, the data is moved and the memory is secured. The element information before the division is transferred to the temporary memory of the temporary parent element. A new node and element memory are secured. In step 12, information on newly created elements is set. Set the memory of the nodes composing the elements newly created by the division and the memory of the adjacent elements, and give physical quantities. In step 13, the information of the element adjacent to the element before the division is corrected. The data of the node of the adjacent element, the adjacent element, and the number of element boundary faces is corrected. In step 14, the element data sharing the node is set and corrected. Set and modify the data of the node sharing element between the node newly generated by dividing the element and the existing node. In step 15, the data of the element sharing the edge with the element before the division is corrected. Search for elements that share a node, add the newly created node to the element information, and modify the element data. In step 16, the temporary parent memory is released.

  With reference to FIG. 4B, an element deletion processing procedure will be described. In step 21, provisional memory is secured and data is moved. Move parent element information before deletion to temporary parent element. In step 22, the element information after deletion is set. Set the cell data of the element after deletion and the element data of the adjacent element. In step 23, the information of the element adjacent to the previous element to be deleted is corrected. In step 24, the element data adjacent at the node is corrected. As the element is deleted, the adjacent element data of the node is corrected. In step 25, the element data of the element sharing the side with the previous element to be deleted is corrected. The element sharing the node is searched, the lattice level difference is taken into consideration, it is determined whether to delete the node, and the element data is corrected. When a node is deleted, the memory at that node is released. In step 26, the temporary parent memory and the deleted element memory are released.

  Fifth, an element dividing method and a deleting method will be described with reference to FIGS. The tetrahedron element is divided into eight tetrahedron elements (FIG. 5 (a) Type 1) and the method divided into four tetrahedron elements and two pyramid elements (FIG. 5 (b) Type 2). There are two types, which can be selected. Further, as shown in FIG. 5C, the pyramid element is divided into six pyramid elements and four tetrahedron elements. The prism element is divided into eight prism elements as shown in FIG. The hexahedral element is divided into eight hexahedral elements, as shown in FIG. Deletion is the opposite. By performing division deletion in this way, the triangular surface and the quadrangular surface on the element boundary surface become as shown in FIGS. 5 (f) and 5 (g), respectively. By doing so, the handling of the element boundary surface becomes easier to some extent, and the complication of the program can be prevented.

A specific procedure for dividing elements will be described.
(1) Data movement and memory allocation: The information of the element before the division is moved to the temporary parent element. A new node and element memory are secured.
(2) Setting of new element data: Data of elements newly created by division is set. Furthermore, a Family relationship as shown in FIG. In FIG. 5 (h), a two-dimensional triangular element is used for easy understanding. One element having the same shape as the element before the division is set as a parent element. However, the parent element of the parent element is itself. A sibling element is one of the elements generated by splitting together. Family-related data is arranged in an array and is set for each grid level. If there is no parent element or sibling element, a null character is entered as a value at the corresponding position in the array.

(3) Correction of information on adjacent elements: Since a new element is generated by dividing an element, various data of adjacent elements of the element before the division are corrected. When the grid level difference with the adjacent element is 0 (FIG. 6 (a)), various data of the element is corrected, and when the grid level difference is 1 (FIG. 6 (b)) Only correct the data. In addition, processing corresponding to each element shape is executed.
(4) Setting and correction of node data: Setting and correcting various data of nodes newly generated by dividing elements and existing nodes.
(5) Element data correction: Search for elements that share an edge with the previous element using the various data of the elements that share the nodes, add the newly created nodes to the element information, Correct it.
(6) Release memory: Release the temporary parent's memory.

A specific procedure for deleting an element will be described. The element is deleted by the reverse method of division. The element is deleted when the following condition is satisfied.
(Condition 1) The lattice level (number of divisions) of the parent element and all its sibling elements is the same (Condition 2) The parent element and all its sibling elements are marked for deletion (1) Memory reservation and data movement: Before deletion The data of the parent element is transferred to the temporary parent element.
(2) Element data setting: Various data of elements after deletion are set.
(3) Data correction of adjacent element: Since the element is deleted, various data of the adjacent element of the element before the deletion is corrected. When the grid level difference with the adjacent element is 1 (FIG. 6C), various data are corrected, and when the grid level difference is 0 (FIG. 6D), only the adjacent element information is corrected. To do. A processing function corresponding to the shape of each adjacent element is executed.

(4) Data setting and correction: Various data of nodes are corrected as elements are deleted.
(5) Element data correction: Searches for elements that share an edge with the previous element to be deleted using various data of elements that share nodes, and considers whether or not to delete the node considering the grid level difference. Determine and correct various data. When a node is deleted, the memory at that node is released.
(6) Release memory: Release the temporary parent memory and the deleted element memory.

  Sixth, the transition element generation method will be described with reference to FIG. Transition elements are as follows. When the AMR method is applied, an intermediate node that is an incomplete vertex is generated between an element divided by element division / deletion and an adjacent element (an element sharing an edge or edge). An element having an intermediate node will be referred to as an intermediate element. As shown in FIG. 6E, a temporary element is generated in order to eliminate this intermediate node. This temporary element is called a transition element. The part of the lattice composed of transition elements is called a transition lattice. Since it corresponds to the Hybrid lattice, a transition element can be created using a tetrahedral element, a pyramid element, a prism element, and a hexahedral element. Basically, a transition element is created by two processes (Process1 and Process2) as shown in FIG. Before creating a transition element, marking is performed on an intermediate element having an intermediate node. The types of transition elements are classified according to the shape of the intermediate element and the position of the intermediate node before the transition element is created, and are stored in the flag memory. By doing so, the algorithm is simplified to some extent.

In Process1, a temporary node Temporary node is created at the center (body center) of the intermediate element where the intermediate node exists, and a tetrahedral element or pyramid element is created. The tetrahedral element, pyramid element, prism element, and hexahedral element are as shown in FIG. The specific procedure of Process1 is as follows.
(1) Data movement and memory allocation: The data of the intermediate element before creating the transition element is moved to the temporary parent element. A memory for a new node (a node generated at the center of the intermediate element) and a memory for the new element are secured.
(2) New element data setting: Set the family data and the element data newly created by creating the transition element.
(3) Data setting and correction: By creating a transition element, a newly generated node (node generated at the element center) and various data of existing nodes are set and corrected.
(4) Release memory: Release the temporary parent's memory.

  In Process2, transition elements are created so as to eliminate the intermediate nodes of the tetrahedron and pyramid elements created by Process1. As the result of Process1 processing, the intermediate node now exists on only one surface, so the types of processing functions that create transition elements are the shape of the surface where the intermediate node exists (triangle or square), and the intermediate node. Depending on the location of the case. Specifically, it is as shown in FIG. When the shape of the surface on which the intermediate node exists is a triangle, the shape is as shown in FIG. When the shape of the surface where the intermediate node exists is a quadrangle, the shape is as shown in FIG. By creating transition elements in this way, the types of transition elements can be captured two-dimensionally, and the complexity of the algorithm can be prevented. However, the dotted circle in the figure represents both the presence and absence of the node.

The specific procedure of Process2 is as follows.
(1) Data movement and memory allocation: The data of the element before creating the transition element is moved to the temporary parent element. Allocate memory for newly created nodes (when creating a node at the center of the surface in caseB-6) and memory for new elements.
(2) New element data setting: Various family data and family relationships are set by creating a transition element.
(3) Adjacent element data correction: data of an adjacent element (when creating a node at the center of the surface) and data related to the adjacent element before the transition element is generated. The processing functions executed at this time are classified according to cases as shown in FIG.
(4) Data setting and correction: A newly generated node (when creating a node at the center of the surface) and various data of existing nodes are set and corrected.
(5) Release memory: Release the temporary parent's memory.

Seventh, the transition element deletion method will be described with reference to FIG. Since the transition element is a temporary element, all the transition elements are deleted after the calculation of the guideline value. As with creation, deletion is performed by the following two processes, following the reverse process of creation. In Process1, the transition element created by Process2 for creating the transition element is deleted and returned to the tetrahedral element and pyramid element created by Process1 for creating the transition element.
(1) Memory reservation and data movement: The data of one element among the elements before the transition element deletion is moved to the temporary parent element.
(2) Element data setting: Various element data after transition element deletion is set.
(3) Data correction of adjacent elements: Various data of adjacent elements are corrected. The processing functions executed at this time are classified according to cases as shown in FIG.
(4) Data setting and correction: As transition elements are deleted, various data of nodes are corrected.
(5) Release of memory: Release the memory of the temporary parent and the memory of the deleted element and node (when deleting the node at the center of the surface in Case B-6).

In Process2, the tetrahedron element and pyramid element created by Process1 of transition element creation are deleted.
(1) Memory reservation and data movement: The data of the parent element before the transition element deletion is moved to the temporary parent element.
(2) Element data setting: Various data of intermediate elements after transition elements are deleted are set.
(3) Data setting and correction: As transition elements are deleted, various data of nodes are corrected.
(4) Release of memory: The temporary parent memory, the deleted element memory, and the node center memory are released.

  Describe how to obtain the array element numbers of newly generated elements and nodes. As a method for obtaining the array numbers of elements and nodes newly generated by the division, if the array numbers that have been freed by the previous deletion are reused, the minimum array number is sufficient. However, searching for free sequence numbers should be avoided because it takes a significant amount of time. Keep as many array numbers as your computer allows. New numbers are required for new arrays required for division. When the maximum sequence number is used up, the sequence number is reused. In this way, the HGA method can be executed very quickly until the maximum sequence number is used.

  The HGA method is a method of performing analysis by dividing an analysis target into elements using a hybrid lattice composed of tetrahedral elements, pyramid elements, prism elements, and hexahedral elements. In the HGA method, in the Hybrid lattice, the element at the location where the change in the physical quantity is abrupt is divided, and the element at the location where the change is not abrupt and does not need to be a fine element is deleted and returned to the initial element. Do it. Since intermediate nodes are eliminated using transition elements, no other special processing is required. It can be easily incorporated by adding variables used in the HGA method to the conventional finite element method program compatible with Hybrid grid, and numerical analysis using a mixed grid type solution adaptive grid method A device can be realized.

  As described above, in the first embodiment of the present invention, the numerical analysis apparatus uses a tetrahedron element, a hexahedron element, and a pentahedron element (pyramid element, prism element). Is larger, the element's triangle face is divided into multiple triangles, and the quadrilateral face is divided into multiple squares. For example, the element is deleted and returned to the element before the division, the intermediate node generated by the division deletion is eliminated by the transition element, and the numerical analysis is performed by the finite element method. It can be calculated by the finite element method.

  Embodiment 2 of the present invention uses a tetrahedron element, a hexahedron element, and a pentahedron element (pyramid element, prism element), and if the division deletion guideline value is larger than the division threshold value, the triangular face of the element is determined. Divide an element into multiple triangles so that the quadrilateral surface is divided into multiple quadrilaterals.If the split deletion guideline value is smaller than the deletion threshold, delete the element and A numerical analysis device that performs numerical analysis by the finite element method by generating transition elements by using the method of applying the individual division method in preference to the standard division method to eliminate intermediate nodes that have been generated by dividing and deleting elements. is there.

  FIG. 10 is a diagram for explaining a method for generating the transition element by the individual division method in the numerical analysis apparatus according to the second embodiment of the present invention. FIG. 11 is a diagram for explaining a generation / deletion method based on an individual division method for tetrahedral transition elements. FIG. 12 is a diagram for explaining a generation / deletion method based on an individual division method of transition elements of a pyramid. FIG. 13 is a diagram for explaining a generation / deletion method based on the individual division method of the transition elements of the prism. FIG. 14 is a diagram for explaining a generation / deletion method based on an individual division method of hexahedral transition elements. FIG. 15 is a table for explaining a generation / deletion method based on the individual division method of transition elements. The basic configuration of the numerical analysis device according to the second embodiment is the same as that of the first embodiment. The difference is that the transition elements are generated in preference to the individual division method.

  The generation and deletion of transition elements by the individual division method will be described. If a transition element is generated only by the division method of the first embodiment (this is called a standard division method), the calculation time increases or the calculation becomes unstable due to an increase in the number of elements and distortion of the elements. There is a case. For example, when a tetrahedron with one intermediate node is divided by the standard division method, the tetrahedron is divided into four triangular pyramids (tetrahedrons) with the body center of the tetrahedron as the apex and each face of the tetrahedron as the bottom (Fig. 7 (c-1)), and further dividing on the plane passing through the intermediate node (FIG. 8 (a-2)), the number of elements increases to six, and the shape of the elements becomes flat. Therefore, an appropriate division method according to the position where the intermediate node exists is individually applied, and a transition element is generated by a method different from the standard division method.

  As shown in FIG. 10, the element is divided according to the position where the intermediate node exists by a method corresponding to FIG. 8 of the standard dividing method. For example, when a tetrahedron having one intermediate node is divided by the individual division method, it is only divided into two on a plane passing through the intermediate node (FIG. 11C). The shape of the element does not become flat. This transition element generation / deletion method by the individual division method is executed in preference to the standard method. Only when the transition element cannot be generated by the individual division method, the transition element is generated by the standard division method. When deleting a transition element generated by the individual division method, the transition element is deleted in the reverse procedure of the individual division method. Individual division methods of the individual division method can be added or deleted as appropriate.

The transition element creation procedure of the individual division method will be described.
(1) Data movement and memory reservation: The information of the element before creating the transition element is moved to the temporary parent element. Then, a new node (when a node is generated at the center of the surface) and an element memory are secured.
(2) Setting of new element information: Various data of a new element created by creating a transition element and a family relationship are set.
(3) Correction of information on adjacent elements: Various data of adjacent elements of elements before transition elements are generated are corrected. The processing functions executed at this time are classified according to cases as shown in FIG.
(4) Setting and correction of relational data: Setting and correction of relational data between a node newly generated by creating a transition element (when a node is generated at the center of the surface) and an existing node.
(5) Release memory: Release the temporary parent's memory.

A process at the time of transition element deletion in the individual division method will be described.
(1) Memory reservation and data movement: The parent element information before deletion of the transition element is moved to the temporary parent element.
(2) Element information setting after deletion: Various data of elements after transition element deletion is set.
(3) Correction of information on adjacent elements: Various data of adjacent elements of elements before transition elements are deleted are corrected. The processing functions executed at this time are classified according to cases as shown in FIG.
(4) Setting and correction of relational data: As the elements are deleted, the relational data of the nodes is corrected.
(5) Release of memory: Release the memory of the temporary parent, the deleted element, and the node (when deleting the node at the center of the surface).

  A specific method of generating / deleting transition elements by the individual division method will be described. As shown in FIG. 10, the boundary surface is divided according to the state of the intermediate node on the boundary surface of the element. This dividing method of the boundary surface is a method corresponding to the dividing method of the bottom surface of the standard dividing method shown in FIG. The elements are divided by combining the division methods to generate transition elements. For example, when there is one intermediate node in the tetrahedron, FIG. 10A and FIG. 10B are combined and divided as shown in FIG.

  In the case of a tetrahedron element, it is divided as shown in FIG. 11 and FIG. However, CaseC-1 and CaseC-2 are divided into tetrahedrons (CaseC-1) using the usual method of dividing elements of the lattice (CaseC-1), and into tetrahedrons and pyramids (CaseC-2). Is used. In the case of a pyramid element, it is divided as shown in FIG. 12 and FIG. However, CaseD-1 is divided into four tetrahedrons and six pyramids using the normal method of dividing the lattice elements. In the case of a prism element, it is divided as shown in FIG. 13 and FIG. However, CaseE-1 is divided into 8 prisms using a normal method of dividing the lattice elements. The hexahedral element is divided as shown in FIGS. 14 and 15 (d). However, CaseF-1 is divided into eight hexahedrons using a normal method of dividing the lattice elements.

  As described above, in the second embodiment of the present invention, the numerical analysis apparatus uses a tetrahedron element, a hexahedron element, and a pentahedron element (pyramid element, prism element). Is larger, the element's triangle face is divided into multiple triangles, and the quadrilateral face is divided into multiple squares. For example, the element is deleted and returned to the element before division, and the individual division method is preferentially executed, and the intermediate node caused by the division deletion is eliminated by the transition element, and the numerical analysis is performed by the finite element method Therefore, it is possible to perform highly accurate analysis with the minimum necessary calculation memory.

  The present invention is used for Computational Fluid Dynamics (CFD). It can also be incorporated into computer graphics and CAD.

FIG. 2 is a functional block diagram showing the configuration of the numerical analysis device according to the first embodiment of the present invention; The flowchart which shows the operation | movement procedure of the numerical analysis apparatus in Example 1 of this invention, The flowchart which shows the procedure regarding the HGA method of the numerical analyzer in Example 1 of this invention, The flowchart which shows the division | segmentation procedure and deletion procedure of the numerical analyzer in Example 1 of this invention, The figure which shows the division | segmentation method of the grating | lattice of the numerical analyzer in Example 1 of this invention, The figure which shows the method of dividing | segmenting the two-dimensional element of the numerical analyzer in Example 1 of this invention, The figure explaining the generation | occurrence | production deletion of the transition element of the numerical analysis apparatus in Example 1 of this invention, The figure explaining the production | generation of the transition element of the numerical analysis apparatus in Example 1 of this invention, The figure explaining the method of the case classification for correcting the data of an adjacent element in the case of the production | generation deletion of the transition element of the numerical analysis apparatus in Example 1 of this invention, The figure explaining the production | generation method of the transition element by the separate division | segmentation method of the numerical analysis apparatus in Example 2 of this invention, The figure explaining the production | generation of the transition element of the tetrahedron by the separate division | segmentation method of the numerical analysis apparatus in Example 2 of this invention, The figure explaining the generation | occurrence | production deletion of the transition element of a pyramid by the separate division | segmentation method of the numerical analysis apparatus in Example 2 of this invention, FIG. 5 is a diagram for explaining generation and deletion of a transition element of a prism by an individual division method of a numerical analysis device according to a second embodiment of the present invention; The figure explaining the generation | occurrence | production deletion of the transition element of the hexahedron by the separate division | segmentation method of the numerical analysis apparatus in Example 2 of this invention, It is a table | surface explaining the production | generation deletion of the transition element by the individual division method of the numerical analysis apparatus in Example 2 of this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Input device 2 Initial lattice memory 3 Division | segmentation threshold value memory 4 Deletion threshold value memory 5 Finite element method arithmetic unit 6 Lattice division means 7 Lattice deletion means 8 Guide value calculation means 9 Division determination means
10 Deletion judgment means
11 Display device
12 Transition element generation means
13 Transition element deletion method

Claims (2)

A numerical analysis device that applies solution-adapted lattice method (AMR) to a finite element method using a mixed lattice and performs physical quantity numerical analysis, and includes tetrahedral elements, hexahedral elements, and pentahedral elements (pyramid elements, prism elements). An initial lattice storage means for storing initial lattice data created using any combination, and an element is divided into a plurality of elements such that a triangular surface of the element is divided into a plurality of triangles and a quadrilateral surface is divided into a plurality of rectangles. A grid dividing means for dividing the element into two, a grid deleting means for deleting the divided element and returning it to the element before the division, and a transition element so as to eliminate the intermediate node that is an incomplete node caused by dividing and deleting the element. A transition element generating means for generating, a guideline value calculating means for calculating a guideline value for splitting and deleting each element of the lattice, and a split deletion determining means for determining whether to split or delete the element based on the guideline value Numerical analysis apparatus characterized by comprising a transition element removal means for deleting a transition element. The transition element generating means includes an individual division processing means for dividing an element by an individual division method according to an arrangement state of intermediate nodes in the element, and a tetrahedral element or a hexahedron when the element cannot be divided by the individual division processing means. A standard division that divides an element by a standard division method that divides the polyhedron element, which is an element or pentahedron element, into a polyhedron with the body center of the polyhedron element as the apex and each face of the polyhedron element as the base, and then dividing it into a plane passing through the intermediate nodes The numerical analysis apparatus according to claim 1, further comprising a processing unit.

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