3rd and 11th orders of accuracy of ‘linear’ and ‘quadratic’ elements for Poisson equation with irregular interfaces on Cartesian meshes

Purpose The purpose of this paper is as follows: to significantly reduce the computation time (by a factor of 1,000 and more) compared to known numerical techniques for real-world problems with complex interfaces; and to simplify the solution by using trivial unfitted Cartesian meshes (no need in complicated mesh generators for complex geometry). Design/methodology/approach This study extends the recently developed optimal local truncation error method (OLTEM) for the Poisson equation with constant coefficients to a much more general case of discontinuous coefficients that can be applied to domains with different material properties (e.g. different inclusions, multi-material structural components, etc.). This study develops OLTEM using compact 9-point and 25-point stencils that are similar to those for linear and quadratic finite elements. In contrast to finite elements and other known numerical techniques for interface problems with conformed and unfitted meshes, OLTEM with 9-point and 25-point stencils and unfitted Cartesian meshes provides the 3-rd and 11-th order of accuracy for irregular interfaces, respectively; i.e. a huge increase in accuracy by eight orders for the new 'quadratic' elements compared to known techniques at similar computational costs. There are no unknowns on interfaces between different materials; the structure of the global discrete system is the same for homogeneous and heterogeneous materials (the difference in the values of the stencil coefficients). The calculation of the unknown stencil coefficients is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy of OLTEM at a given stencil width. The numerical results with irregular interfaces show that at the same number of degrees of freedom, OLTEM with the 9-points stencils is even more accurate than the 4-th order finite elements; OLTEM with the 25-points stencils is much more accurate than the 7-th order finite elements with much wider stencils and conformed meshes. Findings The significant increase in accuracy for OLTEM by one order for 'linear' elements and by 8 orders for 'quadratic' elements compared to that for known techniques. This will lead to a huge reduction in the computation time for the problems with complex irregular interfaces. The use of trivial unfitted Cartesian meshes significantly simplifies the solution and reduces the time for the data preparation (no need in complicated mesh generators for complex geometry). Originality/value It has been never seen in the literature such a huge increase in accuracy for the proposed technique compared to existing methods. Due to a high accuracy, the proposed technique will allow the direct solution of multiscale problems without the scale separation.

MASK GENERATOR FOR ORTHOGONAL REGULAR MESH

Existing mesh generators are focused mainly on obtaining non-orthogonal irregular grids designed to describe the curved boundaries of streamlined bodies. However, the thickening of the grid leads to an increase in the calculation time, and the non-conformity of the grid leads to unphysical effects. The software package (SP) developed by the authors for the simulation of gas-thermodynamic processes is oriented toward a much simpler description of the geometry, i. e., uses a different principle of increasing the smoothness of the solution in places with a complex surface structure. This principle consists in superimposing on the flow such sources of momentum and energy, which are equivalent in their effect on the flow to the interaction with the solid wall. SP contains a mask generator of an orthogonal regular grid. The initial data for building the mask is a 3D model created in any CAD application, which is saved in the STL format and placed in the project directory. Each cell contains information about the presence of a three-dimensional solid, the permeability of each face of the hexahedron, and the direction of the normal vector to the streamlined surface. In this regard, the generator creates three types of masks: volumetric, surface full and incomplete permeability, as well as a mask of guiding cosines. To obtain a volume (solid) mask from the center of each cell along the axes, a straight line is drawn and its intersection is checked with each triangle approximating the surface of the body under study. An odd number of intersections of triangles and a straight line indicates the presence of a volume mask in the cells. A surface impermeable mask is formed in three directions at the free cell section and the occupied volume mask. If it is necessary to introduce a semipermeable mask, its localization and measure are assigned by the user. The mask of the guiding cosines is assigned in the cell, which is adjacent to the surface impermeable mask. The values of the guiding cosines are assigned equal to the corresponding values of the nearby triangle approximating the surface of the 3D model. The generated masks are formed as separate files. A SolidWorks application has been developed that allows for volumetric visualization. In the decisive program, the information about the presence of the volume mask is used as follows: the volume mask is excluded from the solution area, self-similar problems are solved near the surface, and if there are guiding properties, an isentropic flow rotation is performed.

Adaptive unstructured mesh generation methods for hydrogeological problems

Рассматриваются два сеточных генератора, внедренных в программный комплекс GeRa, предназначенный для решения задач геофильтрации и геомиграции радионуклидов. Это треугольно-призматический генератор с возможностью вырождения ячеек и генератор многогранных сеток с измельчением на основе восьмеричного дерева и возможностями скалывания ячеек. Генераторы позволяют автоматически строить конформные многогранные адаптивные сетки в трехмерных геологических областях с учетом сложной конфигурации внешних границ, кровель и подошв геологических пластов, выклинивания слоев и геологических неоднородностей. Two mesh generators embedded in the GeRa code for the solution of groundwater flow and radionuclide transport problems are discussed. The first one is a triangular-prismatic generator with the ability of cell degeneration; the second one is the polyhedral octree mesh generator implementing the cut-cell technology. These generators allow the user to automatically create conformal polyhedral adaptive grids in three-dimensional geological domains with consideration of complex boundaries, top and bottom geological layer surfaces, pinch-outs, and geological heterogeneities.

Stress Analysis of Air Compressor Crankshaft Based on ANSYS

The paper uses the preprocessor of ANSYS to generate the model of 3D entity and mesh generation on WW0.8/10 air compressor crankshaft. Mesh generators are transferred into data that will be used in finite element analysis. Passing by dealing with force and commitment, it calculates the forces of pressure working conditions of crankshaft. They are used in stress analysis. The stress data is calculated from the calculator of ANSYS. The static load safe coefficient and the fatigue safe coefficient of the crankshaft are tested from known stress. The result provides a high reference value for the optimization improvement of the crankshaft.

NUMERICAL SIMULATION OF AIRFOILS APPLIED TO UAVs

This essay aims the process optimization when referred to aeronautical projects. By using mesh generators softwares and simulations made in CFD, the article employs numerical techniques to simulate airfoils and shows that is possible to extract accurated and conservative outcomes when compared to wind tunnel results. The test cases studied were based on the Selig 1223 type of airfoil and developed into the ANSYS platform, whereas by using the ICEM mesh tool, structured meshs were generated and imported to the CFX enviroment, where they could be simulated and analyzed.

Hexahedral Meshing of Subject-Specific Anatomic Structures Using Registered Building Blocks

Generating high quality, subject-specific, 3D finite element anatomic models with minimal user-intervention remains a challenge. Numerous automated tetrahedral mesh generators are available, but hexahedral meshes are preferred due to their higher accuracy and faster computational time over tetrahedral meshes. Historically, the generation of hexahedral meshes for analysis is a tedious and time-consuming task. Therefore, the utilization of hexahedral meshes is often limited to baseline models that are powerful, but not patient-specific. Once a high quality mesh has been created, it would be ideal if it can be used to create meshes of similar surfaces from different subjects, without disrupting mesh quality.