Статті в журналах: "Unstructured meshe"

1

SCHNEIDERS, ROBERT. "OCTREE-BASED HEXAHEDRAL MESH GENERATION." International Journal of Computational Geometry & Applications 10, no. 04 (August 2000): 383–98. http://dx.doi.org/10.1142/s021819590000022x.

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An octree-based algorithm for the generation of hexahedral element meshes is presented. The algorithm works in three steps: (i) The geometry to be meshed is approximated by an octree structure. (ii) An unstructured hexahedral element mesh is derived from the octree. (iii) The mesh is adapted to the boundary of the geometry. We focus on step (ii) and describe an algorithm that constructs a hex mesh for a given octree structure.

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2

Noleto, Luciano Gonçalves, Manuel N. D. Barcelos, and Antonio C. P. Brasil. "A Pseudo-Stokes Mesh Motion Algorithm." Advances in Applied Mathematics and Mechanics 5, no. 2 (April 2013): 194–211. http://dx.doi.org/10.4208/aamm.11-m1186.

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AbstractThis work presents a moving mesh methodology based on the solution of a pseudo flow problem. The mesh motion is modeled as a pseudo Stokes problem solved by an explicit finite element projection method. The mesh quality requirements are satisfied by employing a null divergent velocity condition. This methodology is applied to triangular unstructured meshes and compared to well known approaches such as the ones based on diffusion and pseudo structural problems. One of the test cases is an airfoil with a fully meshed domain. A specific rotation velocity is imposed as the airfoil boundary condition. The other test is a set of two cylinders that move toward each other. A mesh quality criteria is employed to identify critically distorted elements and to evaluate the performance of each mesh motion approach. The results obtained for each test case show that the pseudo-flow methodology produces satisfactory meshes during the moving process.

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3

Cai, Jian, Lan Chen, and Umezuruike Linus Opara. "Numerical Simulation of Powder Dispersion Performance by Different Mesh Types." Key Engineering Materials 680 (February 2016): 82–85. http://dx.doi.org/10.4028/www.scientific.net/kem.680.82.

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OBJECTIVE To investigate the influence of mesh type on numerical simulating the dispersion performance of micro-powders through a home-made tube. METHODS With the computational fluid dynamics (CFD) method, a powder dispersion tube was meshed in three different types, namely, tetrahedral, unstructured hexahedral and prismatic-tetrahedral hybrid meshes. The inner flow field and the kinetic characteristics of the particles were investigated. Results of the numerical simulation were compared with literature evidences. RESULTS The results showed that using tetrahedral mesh had the highest computational efficiency, while employing the unstructured hexahedral mesh obtained more accurate outlet velocity. The simulation results of the inner flow field and the kinetic characteristics of the particles were slightly different among the three mesh types. The calculated particle velocity using the tetrahedral mesh had the best correlation with the changing trend of the fine particle mass in the first 4 stages of the new generation impactor (NGI) (R2 = 0.91 and 0.89 for powder A and B, respectively). Conclusions Mesh type affected computational time, accuracy of simulation results and the prediction abilities of fine particle deposition.

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4

Song, Tao, Jiarong Wang, Danya Xu, Wei Wei, Runsheng Han, Fan Meng, Ying Li, and Pengfei Xie. "Unsupervised Machine Learning for Improved Delaunay Triangulation." Journal of Marine Science and Engineering 9, no. 12 (December 7, 2021): 1398. http://dx.doi.org/10.3390/jmse9121398.

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Physical oceanography models rely heavily on grid discretization. It is known that unstructured grids perform well in dealing with boundary fitting problems in complex nearshore regions. However, it is time-consuming to find a set of unstructured grids in specific ocean areas, particularly in the case of land areas that are frequently changed by human construction. In this work, an attempt was made to use machine learning for the optimization of the unstructured triangular meshes formed with Delaunay triangulation in the global ocean field, so that the triangles in the triangular mesh were closer to equilateral triangles, the long, narrow triangles in the triangular mesh were reduced, and the mesh quality was improved. Specifically, we used Delaunay triangulation to generate the unstructured grid, and then developed a K-means clustering-based algorithm to optimize the unstructured grid. With the proposed method, unstructured meshes were generated and optimized for global oceans, small sea areas, and the South China Sea estuary to carry out data experiments. The results suggested that the proportion of triangles with a triangle shape factor greater than 0.7 amounted to 77.80%, 79.78%, and 79.78%, respectively, in the unstructured mesh. Meanwhile, the proportion of long, narrow triangles in the unstructured mesh was decreased to 8.99%, 3.46%, and 4.12%, respectively.

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5

Gustafsson, Tom. "simple technique for unstructured mesh generation via adaptive finite elements." Rakenteiden Mekaniikka 54, no. 2 (June 14, 2021): 69–79. http://dx.doi.org/10.23998/rm.99648.

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This work describes a concise algorithm for the generation of triangular meshes with the help of standard adaptive finite element methods. We demonstrate that a generic adaptive finite element solver can be repurposed into a triangular mesh generator if a robust mesh smoothing algorithm is applied between the mesh refinement steps. We present an implementation of the mesh generator and demonstrate the resulting meshes via examples.

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6

Schneider, Teseo, Yixin Hu, Xifeng Gao, Jérémie Dumas, Denis Zorin, and Daniele Panozzo. "A Large-Scale Comparison of Tetrahedral and Hexahedral Elements for Solving Elliptic PDEs with the Finite Element Method." ACM Transactions on Graphics 41, no. 3 (June 30, 2022): 1–14. http://dx.doi.org/10.1145/3508372.

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The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which require a tetrahedral or hexahedral mesh to construct the basis. While the theoretical properties of FEM basis (such as convergence rate, stability, etc.) are well understood under specific assumptions on the mesh quality, their practical performance, influenced both by the choice of the basis construction and quality of mesh generation, have not been systematically documented for large collections of automatically meshed 3D geometries. We introduce a set of benchmark problems involving most commonly solved elliptic PDEs, starting from simple cases with an analytical solution, moving to commonly used test problem setups, and using manufactured solutions for thousands of real-world, automatically meshed geometries. For all these cases, we use state-of-the-art meshing tools to create both tetrahedral and hexahedral meshes, and compare the performance of different element types for common elliptic PDEs. The goal of this benchmark is to enable comparison of complete FEM pipelines, from mesh generation to algebraic solver, and exploration of relative impact of different factors on the overall system performance. As a specific application of our geometry and benchmark dataset, we explore the question of relative advantages of unstructured (triangular/ tetrahedral) and structured (quadrilateral/hexahedral) discretizations. We observe that for Lagrange-type elements, while linear tetrahedral elements perform poorly, quadratic tetrahedral elements perform equally well or outperform hexahedral elements for our set of problems and currently available mesh generation algorithms. This observation suggests that for common problems in structural analysis, thermal analysis, and low Reynolds number flows, high-quality results can be obtained with unstructured tetrahedral meshes, which can be created robustly and automatically. We release the description of the benchmark problems, meshes, and reference implementation of our testing infrastructure to enable statistically significant comparisons between different FE methods, which we hope will be helpful in the development of new meshing and FEA techniques.

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7

Gruzintsev, I., M. Kornilina, and M. Yakobovskiy. "Adaptive 3D unstructured mesh refinement." E3S Web of Conferences 224 (2020): 01011. http://dx.doi.org/10.1051/e3sconf/202022401011.

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Algorithms for generating three-dimensional detailed computational meshes are considered. The algorithms are based on adaptive refinement of the original coarse meshes describing a 3D object. The purpose of adaptation is to form an accurate description of the volume and surface of a three-dimensional object for supercomputer modeling. Refinement of the boundary description is performed by projecting the cut elements of the coarse mesh onto the corresponding elements of the object’s surface.

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8

Peng, Biao, Chunhua Zhou, and Junqiang Ai. "Solution Reconstruction on Unstructured Tetrahedral Meshes Using P1-Conservative Interpolation." Advances in Applied Mathematics and Mechanics 8, no. 5 (July 8, 2016): 847–70. http://dx.doi.org/10.4208/aamm.2015.m1087.

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AbstractThis paper extends an algorithm of P1-conservative interpolation on triangular meshes to tetrahedral meshes and thus constructs an approach of solution reconstruction for three-dimensional problems. The conservation property is achieved by local mesh intersection and the mass of a tetrahedron of the current mesh is calculated by the integral on its intersection with the background mesh. For each current tetrahedron, the overlapped background tetrahedrons are detected efficiently. A mesh intersection algorithm is proposed to construct the intersection of a current tetrahedron with the overlapped background tetrahedron and mesh the intersection region by tetrahedrons. A localization algorithm is employed to search the host units in background mesh for each vertex of the current mesh. In order to enforce the maximum principle and avoid the loss of monotonicity, correction of nodal interpolated solution on tetrahedral meshes is given. The performance of the present solution reconstruction method is verified by numerical experiments on several analytic functions and the solution of the flow around a sphere.

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9

Gao, Song, Jory Seguin, Wagdi G. Habashi, Dario Isola, and Guido Baruzzi. "A finite element solver for hypersonic flows in thermo-chemical non-equilibrium, Part II." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 2 (August 19, 2019): 575–606. http://dx.doi.org/10.1108/hff-12-2018-0725.

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Purpose This work aims to describe the physical and numerical modeling of a CFD solver for hypersonic flows in thermo-chemical non-equilibrium. This paper is the second of a two-part series that concerns the application of the solver introduced in Part I to adaptive unstructured meshes. Design/methodology/approach The governing equations are discretized with an edge-based stabilized finite element method (FEM). Chemical non-equilibrium is simulated using a laminar finite-rate kinetics, while a two-temperature model is used to account for thermodynamic non-equilibrium. The equations for total quantities, species and vibrational-electronic energy conservation are loosely coupled to provide flexibility and ease of implementation. To accurately perform simulations on unstructured meshes, the non-equilibrium flow solver is coupled with an edge-based anisotropic mesh optimizer driven by the solution Hessian to carry out mesh refinement, coarsening, edge swapping and node movement. Findings The paper shows, through comparisons with experimental and other numerical results, how FEM + anisotropic mesh optimization are the natural choice to accurately simulate hypersonic non-equilibrium flows on unstructured meshes. Three-dimensional test cases demonstrate how, for high-speed flows, shocks resolution, and not necessarily boundary layers resolution, is the main driver of solution accuracy at walls. Equally distributing the error among all elements in a suitably defined Riemannian space yields highly anisotropic grids that feature well-resolved shock waves. The resulting high level of accuracy in the computation of the enthalpy jump translates into accurate wall heat flux predictions. At the opposite end, in all cases examined, high-quality but isotropic unstructured meshes gave very poor solutions with severely inadequate heat flux distributions not even featuring expected symmetries. The paper unequivocally demonstrates that unstructured anisotropically adapted meshes are the best, and may be the only, way for accurate and cost-effective hypersonic flow solutions. Originality/value Although many hypersonic flow solvers are developed for unstructured meshes, few numerical simulations on unstructured meshes are presented in the literature. This work demonstrates that the proposed approach can be used successfully for hypersonic flows on unstructured meshes.

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10

Knupp, Patrick M. "Algebraic mesh quality metrics for unstructured initial meshes." Finite Elements in Analysis and Design 39, no. 3 (January 2003): 217–41. http://dx.doi.org/10.1016/s0168-874x(02)00070-7.

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11

Wada, Yoshitaka, Takuji Hayashi, Masanori Kikuchi, and Fei Xu. "Improvement of Unstructured Quadrilateral Mesh Quality for Multigrid Analysis." Advanced Materials Research 33-37 (March 2008): 833–38. http://dx.doi.org/10.4028/www.scientific.net/amr.33-37.833.

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Due to more complex and severe design restrictions, more effective and faster finite element analyses are demanded. There are several ways to compute FE analysis efficiently: parallel computing, fast iterative or direct solvers, adaptive analysis and so on. One of the most effective analysis ways is the combination of adaptive analysis and multigrid iterative solver, because an adaptive analysis requires several meshes with difference resolutions and multigrid solver utilizes such meshes to accelerate its computation. However, convergence of multigrid solver is largely affected by initial shape of each element. An effective mesh improvement method is proposed here. It is the combination of mesh coarsening and refinement. A good mesh can be obtained by the method to be applied to an initial mesh, and better convergence is achieved by the improved initial mesh.

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12

Zheng, J., J. Zhu, Z. Wang, F. Fang, C. C. Pain, and J. Xiang. "A new multiscale air quality transport model (Fluidity, 4.1.9) using fully unstructured anisotropic adaptive mesh technology." Geoscientific Model Development Discussions 8, no. 6 (June 5, 2015): 4337–74. http://dx.doi.org/10.5194/gmdd-8-4337-2015.

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Abstract. A new anisotropic hr-adaptive mesh technique has been applied to modelling of multiscale transport phenomena, which is based on a discontinuous Galerkin/control volume discretization on unstructured meshes. Over existing air quality models typically based on static-structured grids using a locally nesting technique, the advantage of the anisotropic hr-adaptive model has the ability to adapt the mesh according to the evolving pollutant distribution and flow features. That is, the mesh resolution can be adjusted dynamically to simulate the pollutant transport process accurately and effectively. To illustrate the capability of the anisotropic adaptive unstructured mesh model, three benchmark numerical experiments have been setup for two-dimensional (2-D) transport phenomena. Comparisons have been made between the results obtained using uniform resolution meshes and anisotropic adaptive resolution meshes.

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13

Lewandowska, Natalia, and Jędrzej Mosiężny. "Meshing strategy for bifurcation arteries in the context of blood flow simulation accuracy." E3S Web of Conferences 128 (2019): 02003. http://dx.doi.org/10.1051/e3sconf/201912802003.

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The study presents a mesh dependency study for a carotid artery bifurcation geometry of a real-life specimen. The results of time-averaged velocity profiles at artery control surfaces and wall shear stresses are compared between a set of structured and unstructured meshes, with varying non–dimensional boundary layer first element thickness (y+) parameter. A set of four meshes in total is considered: a full–hexagonal structured mesh, an unstructured tetrahedral mesh with prism inflation layer, both created for y+=1 and y+=30. Apart from numerical results, overall mesh creation work time, overall analysisstability are compared with the mesh quality results: cell non–orthogonality, cell skew and aspect ratio. Numerical results are validated against results of real–life CT examination performed in Poznań Medical University.

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14

Narayan, Akil, and Tao Zhou. "Stochastic Collocation on Unstructured Multivariate Meshes." Communications in Computational Physics 18, no. 1 (July 2015): 1–36. http://dx.doi.org/10.4208/cicp.020215.070515a.

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AbstractCollocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification (UQ) community. Techniques for least-squares regularization, compressive sampling recovery, and interpolatory reconstruction are becoming standard tools used in a variety of applications. Selection of a collocation mesh is frequently a challenge, but methods that construct geometricallyunstructuredcollocation meshes have shown great potential due to attractive theoretical properties and direct, simple generation and implementation. We investigate properties of these meshes, presenting stability and accuracy results that can be used as guides for generating stochastic collocation grids in multiple dimensions.

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15

Zheng, Yao, Roland W. Lewis, and David T. Gethin. "Three-dimensional unstructured mesh generation: Part 2. Surface meshes." Computer Methods in Applied Mechanics and Engineering 134, no. 3-4 (August 1996): 269–84. http://dx.doi.org/10.1016/0045-7825(95)00917-5.

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16

Lewis, Roland W., Yao Zheng, and David T. Gethin. "Three-dimensional unstructured mesh generation: Part 3. Volume meshes." Computer Methods in Applied Mechanics and Engineering 134, no. 3-4 (August 1996): 285–310. http://dx.doi.org/10.1016/0045-7825(95)00918-3.

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17

Roberts, Keith J., William J. Pringle, and Joannes J. Westerink. "OceanMesh2D 1.0: MATLAB-based software for two-dimensional unstructured mesh generation in coastal ocean modeling." Geoscientific Model Development 12, no. 5 (May 10, 2019): 1847–68. http://dx.doi.org/10.5194/gmd-12-1847-2019.

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Abstract. OceanMesh2D is a set of MATLAB functions with preprocessing and post-processing utilities to generate two-dimensional (2-D) unstructured meshes for coastal ocean circulation models. Mesh resolution is controlled according to a variety of feature-driven geometric and topo-bathymetric functions. Mesh generation is achieved through a force balance algorithm to locate vertices and a number of topological improvement strategies aimed at improving the worst-case triangle quality. The placement of vertices along the mesh boundary is adapted automatically according to the mesh size function, eliminating the need for contour simplification algorithms. The software expresses the mesh design and generation process via an objected-oriented framework that facilitates efficient workflows that are flexible and automatic. This paper illustrates the various capabilities of the software and demonstrates its utility in realistic applications by producing high-quality, multiscale, unstructured meshes.

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18

Skamarock, William C., Michael G. Duda, Soyoung Ha, and Sang-Hun Park. "Limited-Area Atmospheric Modeling Using an Unstructured Mesh." Monthly Weather Review 146, no. 10 (September 26, 2018): 3445–60. http://dx.doi.org/10.1175/mwr-d-18-0155.1.

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Abstract A regional configuration of the atmospheric component of the Model for Prediction Across Scales (MPAS-A) is described and evaluated. It employs horizontally unstructured spherical centroidal Voronoi meshes (nominally hexagonal), and lateral boundary conditions used in rectangular grid regional models are adapted to the MPAS-A Voronoi mesh discretization. Test results using a perfect-model assumption show that the lateral boundary conditions are stable and robust. As found in other regional modeling studies, configurations using larger regional domains generally have smaller solution errors compared to configurations employing smaller regional domains. MPAS-A supports variable-resolution meshes, and when regional domains are expanded to include a coarser outer mesh, the variable-resolution configurations recover most of the error reduction compared to a configuration using uniform high resolution, and at much-reduced cost. The wider relaxation-zone region of the variable-resolution mesh also helps reconcile differences near the lateral boundary that evolve between the regional model solution and the driving solution, and the configuration is more stable than one using a uniform high-resolution regional mesh. At convection-permitting resolution, solutions produced using global variable-resolution MPAS-A configurations have smaller solution errors than the regional configurations after about 48 h.

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19

Li, Jinxi, Jie Zheng, Jiang Zhu, Fangxin Fang, Christopher Pain, Jürgen Steppeler, Michael Navon, and Hang Xiao. "Performance of Adaptive Unstructured Mesh Modelling in Idealized Advection Cases over Steep Terrains." Atmosphere 9, no. 11 (November 13, 2018): 444. http://dx.doi.org/10.3390/atmos9110444.

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Advection errors are common in basic terrain-following (TF) coordinates. Numerous methods, including the hybrid TF coordinate and smoothing vertical layers, have been proposed to reduce the advection errors. Advection errors are affected by the directions of velocity fields and the complexity of the terrain. In this study, an unstructured adaptive mesh together with the discontinuous Galerkin finite element method is employed to reduce advection errors over steep terrains. To test the capability of adaptive meshes, five two-dimensional (2D) idealized tests are conducted. Then, the results of adaptive meshes are compared with those of cut-cell and TF meshes. The results show that using adaptive meshes reduces the advection errors by one to two orders of magnitude compared to the cut-cell and TF meshes regardless of variations in velocity directions or terrain complexity. Furthermore, adaptive meshes can reduce the advection errors when the tracer moves tangentially along the terrain surface and allows the terrain to be represented without incurring in severe dispersion. Finally, the computational cost is analyzed. To achieve a given tagging criterion level, the adaptive mesh requires fewer nodes, smaller minimum mesh sizes, less runtime and lower proportion between the node numbers used for resolving the tracer and each wavelength than cut-cell and TF meshes, thus reducing the computational costs.

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20

Bercea, Gheorghe-Teodor, Andrew T. T. McRae, David A. Ham, Lawrence Mitchell, Florian Rathgeber, Luigi Nardi, Fabio Luporini, and Paul H. J. Kelly. "A structure-exploiting numbering algorithm for finite elements on extruded meshes, and its performance evaluation in Firedrake." Geoscientific Model Development 9, no. 10 (October 27, 2016): 3803–15. http://dx.doi.org/10.5194/gmd-9-3803-2016.

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Abstract. We present a generic algorithm for numbering and then efficiently iterating over the data values attached to an extruded mesh. An extruded mesh is formed by replicating an existing mesh, assumed to be unstructured, to form layers of prismatic cells. Applications of extruded meshes include, but are not limited to, the representation of three-dimensional high aspect ratio domains employed by geophysical finite element simulations. These meshes are structured in the extruded direction. The algorithm presented here exploits this structure to avoid the performance penalty traditionally associated with unstructured meshes. We evaluate the implementation of this algorithm in the Firedrake finite element system on a range of low compute intensity operations which constitute worst cases for data layout performance exploration. The experiments show that having structure along the extruded direction enables the cost of the indirect data accesses to be amortized after 10–20 layers as long as the underlying mesh is well ordered. We characterize the resulting spatial and temporal reuse in a representative set of both continuous-Galerkin and discontinuous-Galerkin discretizations. On meshes with realistic numbers of layers the performance achieved is between 70 and 90 % of a theoretical hardware-specific limit.

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21

Gansen, A., M. El Hachemi, S. Belouettar, O. Hassan, and K. Morgan. "A 3D Unstructured Mesh FDTD Scheme for EM Modelling." Archives of Computational Methods in Engineering 28, no. 1 (January 17, 2020): 181–213. http://dx.doi.org/10.1007/s11831-019-09395-z.

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AbstractThe Yee finite difference time domain (FDTD) algorithm is widely used in computational electromagnetics because of its simplicity, low computational costs and divergence free nature. The standard method uses a pair of staggered orthogonal cartesian meshes. However, accuracy losses result when it is used for modelling electromagnetic interactions with objects of arbitrary shape, because of the staircased representation of curved interfaces. For the solution of such problems, we generalise the approach and adopt an unstructured mesh FDTD method. This co-volume method is based upon the use of a Delaunay primal mesh and its high quality Voronoi dual. Computational efficiency is improved by employing a hybrid primal mesh, consisting of tetrahedral elements in the vicinity of curved interfaces and hexahedral elements elsewhere. Difficulties associated with ensuring the necessary quality of the generated meshes will be discussed. The power of the proposed solution approach is demonstrated by considering a range of scattering and/or transmission problems involving perfect electric conductors and isotropic lossy, anisotropic lossy and isotropic frequency dependent chiral materials.

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22

Wada, Yoshitaka, Jun'ichi Shinbori, and Masanori Kikuchi. "Adaptive FEM Analysis Technique Using Multigrid Method for Unstructured Hexahedral Meshes." Key Engineering Materials 306-308 (March 2006): 565–70. http://dx.doi.org/10.4028/www.scientific.net/kem.306-308.565.

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MG (multigrid) method is one of the most promising solvers for large scale problems. Hexahedral mesh generation and its adaptation are not enough to use for practical applications, because its mesh generation is very difficult and still labor intensive work by hand. We have developed hexahedral local refinement technique controlled by posterior error estimation. We have proposed a MG technique for unstructured hexahedral meshes with local mesh refinement. In this paper, the proposed technique is evaluated to check its performance and severe analyses of bending cantilevers. Performance of MG for unstructured hexahedral meshes is compared with that of the PCG (preconditioned conjugate gradient) through several benchmark examples of 3-D static elastic analysis. Proposed MG is faster than PCG for all problems as number of freedoms increases. Finally limitation of the proposed technique is presented.

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Zheng, J., J. Zhu, Z. Wang, F. Fang, C. C. Pain, and J. Xiang. "Towards a new multiscale air quality transport model using the fully unstructured anisotropic adaptive mesh technology of Fluidity (version 4.1.9)." Geoscientific Model Development 8, no. 10 (October 28, 2015): 3421–40. http://dx.doi.org/10.5194/gmd-8-3421-2015.

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Abstract. An integrated method of advanced anisotropic hr-adaptive mesh and discretization numerical techniques has been, for first time, applied to modelling of multiscale advection–diffusion problems, which is based on a discontinuous Galerkin/control volume discretization on unstructured meshes. Over existing air quality models typically based on static-structured grids using a locally nesting technique, the advantage of the anisotropic hr-adaptive model has the ability to adapt the mesh according to the evolving pollutant distribution and flow features. That is, the mesh resolution can be adjusted dynamically to simulate the pollutant transport process accurately and effectively. To illustrate the capability of the anisotropic adaptive unstructured mesh model, three benchmark numerical experiments have been set up for two-dimensional (2-D) advection phenomena. Comparisons have been made between the results obtained using uniform resolution meshes and anisotropic adaptive resolution meshes. Performance achieved in 3-D simulation of power plant plumes indicates that this new adaptive multiscale model has the potential to provide accurate air quality modelling solutions effectively.

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Sheng, Chunhua, and Christian B. Allen. "Efficient Mesh Deformation Using Radial Basis Functions on Unstructured Meshes." AIAA Journal 51, no. 3 (March 2013): 707–20. http://dx.doi.org/10.2514/1.j052126.

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25

Ray, Navamita, Iulian Grindeanu, Xinglin Zhao, Vijay Mahadevan, and Xiangmin Jiao. "Array-based, parallel hierarchical mesh refinement algorithms for unstructured meshes." Computer-Aided Design 85 (April 2017): 68–82. http://dx.doi.org/10.1016/j.cad.2016.07.011.

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Soner, Seren, and Can Ozturan. "Generating Multibillion Element Unstructured Meshes on Distributed Memory Parallel Machines." Scientific Programming 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/437480.

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We present a parallel mesh generator called PMSH that is developed as a wrapper code around the open source sequential Netgen mesh generator. Parallelization of the mesh generator is carried out in five stages: (i) generation of a coarse volume mesh; (ii) partitioning of the coarse mesh; (iii) refinement of coarse surface mesh to produce fine surface submeshes; (iv) remeshing of each fine surface submesh to get a final fine mesh; (v) matching of partition boundary vertices followed by global vertex numbering. A new integer based barycentric coordinate method is developed for matching distributed partition boundary vertices. This method does not have precision related problems of floating point coordinate based vertex matching. Test results obtained on an SGI Altix ICE X system with 8192 cores confirm that our approach does indeed enable us to generate multibillion element meshes in a scalable way.

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Benzley, Steven E., Nathan J. Harris, Michael Scott, Michael Borden, and Steven J. Owen. "Conformal Refinement and Coarsening of Unstructured Hexahedral Meshes." Journal of Computing and Information Science in Engineering 5, no. 4 (June 28, 2005): 330–37. http://dx.doi.org/10.1115/1.2052848.

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This paper describes recently developed procedures for local conformal refinement and coarsening of all-hexahedral unstructured meshes. Both refinement and coarsening procedures take advantage of properties found in the dual or “twist planes” of the mesh. A twist plane manifests itself as a conformal layer or sheet of hex elements within the global mesh. We suggest coarsening techniques that will identify and remove sheets to satisfy local mesh density criteria while not seriously degrading element quality after deletion. A two-dimensional local coarsening algorithm is introduced. We also explain local hexahedral refinement procedures that involve both the placement of new sheets, either between existing hex layers or within an individual layer. Hex elements earmarked for refinement may be defined to be as small as a single node or as large as a major group of existing elements. Combining both refinement and coarsening techniques allows for significant control over the density and quality of the resulting modified mesh.

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Wang, Q., S. Danilov, D. Sidorenko, R. Timmermann, C. Wekerle, X. Wang, T. Jung, and J. Schröter. "The Finite Element Sea Ice-Ocean Model (FESOM) v.1.4: formulation of an ocean general circulation model." Geoscientific Model Development 7, no. 2 (April 30, 2014): 663–93. http://dx.doi.org/10.5194/gmd-7-663-2014.

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Abstract. The Finite Element Sea Ice-Ocean Model (FESOM) is the first global ocean general circulation model based on unstructured-mesh methods that has been developed for the purpose of climate research. The advantage of unstructured-mesh models is their flexible multi-resolution modelling functionality. In this study, an overview of the main features of FESOM will be given; based on sensitivity experiments a number of specific parameter choices will be explained; and directions of future developments will be outlined. It is argued that FESOM is sufficiently mature to explore the benefits of multi-resolution climate modelling and that its applications will provide information useful for the advancement of climate modelling on unstructured meshes.

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Wang, Q., S. Danilov, D. Sidorenko, R. Timmermann, C. Wekerle, X. Wang, T. Jung, and J. Schröter. "The Finite Element Sea ice-Ocean Model (FESOM): formulation of an unstructured-mesh ocean general circulation model." Geoscientific Model Development Discussions 6, no. 3 (July 23, 2013): 3893–976. http://dx.doi.org/10.5194/gmdd-6-3893-2013.

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Abstract. The Finite Element Sea ice-Ocean Model (FESOM) is the first global ocean general circulation model based on unstructured-mesh methods that has been developed for the purpose of climate research. The advantage of unstructured-mesh models is their flexible multi-resolution modelling functionality. In this study, an overview of the main features of FESOM will be given; based on sensitivity experiments a number of specific parameter choices will be explained; and directions of future developments will be outlined. It is argued that FESOM is sufficiently mature to explore the benefits of multi-resolution climate modelling and that it provides an excellent platform for further developments required to advance the field of climate modelling on unstructured meshes.

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Liu, Hongbin, Hu Ren, Hanfeng Gu, Fei Gao, and Guangwen Yang. "UNAT: UNstructured Acceleration Toolkit on SW26010 many-core processor." Engineering Computations 37, no. 9 (May 1, 2020): 3187–208. http://dx.doi.org/10.1108/ec-09-2019-0401.

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Purpose The purpose of this paper is to provide an automatic parallelization toolkit for unstructured mesh-based computation. Among all kinds of mesh types, unstructured meshes are dominant in engineering simulation scenarios and play an essential role in scientific computations for their geometrical flexibility. However, the high-fidelity applications based on unstructured grids are still time-consuming, no matter for programming or running. Design/methodology/approach This study develops an efficient UNstructured Acceleration Toolkit (UNAT), which provides friendly high-level programming interfaces and elaborates lower level implementation on the target hardware to get nearly hand-optimized performance. At the present state, two efficient strategies, a multi-level blocks method and a row-subsections method, are designed and implemented on Sunway architecture. Random memory access and write–write conflict issues of unstructured meshes have been handled by partitioning, coloring and other hardware-specific techniques. Moreover, a data-reuse mechanism is developed to increase the computational intensity and alleviate the memory bandwidth bottleneck. Findings The authors select sparse matrix-vector multiplication as a performance benchmark of UNAT across different data layouts and different matrix formats. Experimental results show that the speed-ups reach up to 26× compared to single management processing element, and the utilization ratio tests indicate the capability of achieving nearly hand-optimized performance. Finally, the authors adopt UNAT to accelerate a well-tuned unstructured solver and obtain speed-ups of 19× and 10× on average for main kernels and overall solver, respectively. Originality/value The authors design an unstructured mesh toolkit, UNAT, to link the hardware and numerical algorithm, and then, engineers can focus on the algorithms and solvers rather than the parallel implementation. For the many-core processor SW26010 of the fastest supercomputer in China, UNAT yields up to 26× speed-ups and achieves nearly hand-optimized performance.

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Ansari, SeyedMasoud, Ernst Schetselaar, James Craven, and Colin Farquharson. "Three-dimensional magnetotelluric numerical simulation of realistic geologic models." GEOPHYSICS 85, no. 5 (July 28, 2020): E171—E190. http://dx.doi.org/10.1190/geo2019-0214.1.

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We have developed a workflow for constructing realistic mesh-based magnetotelluric (MT) models from 3D geologic models. The routine is developed for unstructured meshes that adapt to the complex shapes of geologic bodies including 3D surfaces and volumes in realistic modeling scenarios. The methodology is applied to the complexly altered Lalor volcanogenic massive sulfide deposit in Manitoba, Canada. The host rock envelope of the Lalor deposit is compartmentalized into lithostratigraphic units leading to a watertight model. This model then is meshed into unstructured tetrahedral meshes suitable for synthetic geophysical modeling of the MT method. Subsequently, two 3D resistivity models are generated from wireline logs: (1) a host rock background model in which each tetrahedral cell is attributed with the average resistivity of each lithostratigraphic unit and (2) a heterogeneous background-ore model in which the resistivity values of the cells are resampled from a 3D curvilinear grid model, generated by computing sequential Gaussian simulations from the resistivity data for each unit of a 3D lithofacies model produced by categorical kriging. To calculate the synthetic response of this model for MT, a numerical-modeling code is developed based on solving the vector-scalar potential formulation of the electromagnetic diffusion equation using the finite-element method on unstructured meshes. After validating the numerical method for the Commemi test model, the MT response of the Lalor model is investigated. A reasonable agreement is observed between the survey field data and the data synthesized from our constructed heterogeneous model. Using an investigation of the inductive and galvanic parts, we conclude with the ideal frequency range for detecting the ore deposit. We also conclude with and visualize the importance of regional-scale alteration zones around the ore deposits and model inhomogeneities in boosting the detectability of the ore formations through feeding electrical currents as a result of galvanic field dominance at depth.

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Androsov, Alexey, Vera Fofonova, Ivan Kuznetsov, Sergey Danilov, Natalja Rakowsky, Sven Harig, Holger Brix, and Karen Helen Wiltshire. "FESOM-C v.2: coastal dynamics on hybrid unstructured meshes." Geoscientific Model Development 12, no. 3 (March 21, 2019): 1009–28. http://dx.doi.org/10.5194/gmd-12-1009-2019.

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Abstract. We describe FESOM-C, the coastal branch of the Finite-volumE Sea ice – Ocean Model (FESOM2), which shares with FESOM2 many numerical aspects, in particular its finite-volume cell-vertex discretization. Its dynamical core differs in the implementation of time stepping, the use of a terrain-following vertical coordinate, and the formulation for hybrid meshes composed of triangles and quads. The first two distinctions were critical for coding FESOM-C as an independent branch. The hybrid mesh capability improves numerical efficiency, since quadrilateral cells have fewer edges than triangular cells. They do not suffer from spurious inertial modes of the triangular cell-vertex discretization and need less dissipation. The hybrid mesh capability allows one to use quasi-quadrilateral unstructured meshes, with triangular cells included only to join quadrilateral patches of different resolution or instead of strongly deformed quadrilateral cells. The description of the model numerical part is complemented by test cases illustrating the model performance.

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33

Zhang, Bo, Kim Wann Engebretsen, Gianluca Fiandaca, Hongzhu Cai, and Esben Auken. "3D inversion of time-domain electromagnetic data using finite elements and a triple mesh formulation." GEOPHYSICS 86, no. 3 (May 1, 2021): E257—E267. http://dx.doi.org/10.1190/geo2020-0079.1.

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Over several decades, much research has been done to develop 3D electromagnetic inversion algorithms. Due to the computational complexity and the memory requirements for 3D time-domain electromagnetic (TEM) inversion algorithms, many real-world surveys are inverted within one dimension. To speed up calculations and manage memory for 3D inversions of TEM data, we have developed an approach using three uncoupled meshes: an inversion mesh, a forward-model mesh, and a mesh for Jacobian calculations. The inversion mesh is a coarse regular and structured mesh, such that constraints are easily enforced between the model parameters. Forward responses are calculated on a dense unstructured mesh to obtain accurate electromagnetic fields, whereas the Jacobian is calculated on a coarse unstructured mesh. We found that using a coarse mesh for the Jacobian is sufficient for the inversion to converge and, equally important, that it provides a significant speed boost in the overall inversion process, compared to calculating it on the forward-modeling mesh. The unstructured meshes are made of tetrahedral elements, and the electromagnetic fields are calculated using the finite-element method. The inversion optimization uses a standard Gauss-Newton formulation. For further speed up and memory optimizing of the inversion, we use domain decomposition for calculating the responses for each transmitter separately and parallelize the problem over domains using OpenMP. Compared to a 1D solution, the accuracy for the Jacobian is 1%–5% for the dense mesh and 2%–7% for the coarse mesh, but the calculation time is approximately five times faster for the coarse mesh. We also examined the algorithm on a small ground-based TEM data set acquired in an area where a 3D earth distorts the electromagnetic fields to such a degree that a 1D inversion is not feasible.

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34

Bonfiglioli, Aldo, Renato Paciorri, and Andrea Di Mascio. "The Role of Mesh Generation, Adaptation, and Refinement on the Computation of Flows Featuring Strong Shocks." Modelling and Simulation in Engineering 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/631276.

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Within a continuum framework, flows featuring shock waves can be modelled by means of either shock capturing or shock fitting. Shock-capturing codes are algorithmically simple, but are plagued by a number of numerical troubles, particularly evident when shocks are strong and the grids unstructured. On the other hand, shock-fitting algorithms on structured grids allow to accurately compute solutions on coarse meshes, but tend to be algorithmically complex. We show how recent advances in computational mesh generation allow to relieve some of the difficulties encountered by shock capturing and contribute towards making shock fitting on unstructured meshes a versatile technique.

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35

Liu, Yutong, Kerem Pekkan, S. Casey Jones, and Ajit P. Yoganathan. "The Effects of Different Mesh Generation Methods on Computational Fluid Dynamic Analysis and Power Loss Assessment in Total Cavopulmonary Connection." Journal of Biomechanical Engineering 126, no. 5 (October 1, 2004): 594–603. http://dx.doi.org/10.1115/1.1800553.

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The flow field and energetic efficiency of total cavopulmonary connection (TCPC) models have been studied by both in vitro experiment and computational fluid dynamics (CFD). All the previous CFD studies have employed the structured mesh generation method to create the TCPC simulation model. In this study, a realistic TCPC model with complete anatomical features was numerically simulated using both structured and unstructured mesh generation methods. The flow fields and energy losses were compared in these two meshes. Two different energy loss calculation methods, the control volume and viscous dissipation methods, were investigated. The energy losses were also compared to the in vitro experimental results. The results demonstrated that: (1) the flow fields in the structured model were qualitatively similar to the unstructured model; (2) more vortices were present in the structured model than in the unstructured model; (3) both models had the least energy loss when flow was equally distributed to the left and right pulmonary arteries, while high losses occurred for extreme pulmonary arterial flow splits; (4) the energy loss results calculated using the same method were significantly different for different meshes; and (5) the energy loss results calculated using different methods were significantly different for the same mesh.

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36

Sidorenko, Dmitry, Sergey Danilov, Nikolay Koldunov, Patrick Scholz, and Qiang Wang. "Simple algorithms to compute meridional overturning and barotropic streamfunctions on unstructured meshes." Geoscientific Model Development 13, no. 7 (July 23, 2020): 3337–45. http://dx.doi.org/10.5194/gmd-13-3337-2020.

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Abstract. Computation of barotropic and meridional overturning streamfunctions for models formulated on unstructured meshes is commonly preceded by interpolation to a regular mesh. This operation destroys the original conservation, which can be then artificially imposed to make the computation possible. An elementary method is proposed that avoids interpolation and preserves conservation in a strict model sense. The method is described as applied to the discretization of the Finite volumE Sea ice – Ocean Model (FESOM2) on triangular meshes. It, however, is generalizable to colocated vertex-based discretization on triangular meshes and to both triangular and hexagonal C-grid discretizations.

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37

Yang, Zhi, and Dimitri J. Mavriplis. "Mesh Deformation Strategy Optimized by the Adjoint Method on Unstructured Meshes." AIAA Journal 45, no. 12 (December 2007): 2885–96. http://dx.doi.org/10.2514/1.30592.

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38

Zhang, Xia-ping, Dai Zhou, and Yan Bao. "Mesh motion approach based on spring analogy method for unstructured meshes." Journal of Shanghai Jiaotong University (Science) 15, no. 2 (April 2010): 138–46. http://dx.doi.org/10.1007/s12204-010-9547-y.

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39

Zhang, Bo, Changchun Yin, Yunhe Liu, Xiuyan Ren, Vikas C. Baranwal, and Bin Xiong. "3D inversion of large-scale frequency-domain airborne electromagnetic data using unstructured local mesh." GEOPHYSICS 86, no. 5 (August 4, 2021): E333—E342. http://dx.doi.org/10.1190/geo2020-0243.1.

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Airborne electromagnetic (AEM) methods have been more and more widely used in mineral exploration, environmental and engineering studies, and ground water investigation. However, compared with ground-based electromagnetic (EM) methods, such as magnetotelluric or controlled-source EM, AEM methods generally produce large amounts of data, which leads to very costly 3D EM inversions. We have developed a new 3D AEM inversion scheme based on the finite-element method and unstructured tetrahedral local meshes. This is different from the traditional local mesh method in that the traditional method uses regular cuboids for 3D AEM inversions, whereas our scheme uses irregular tetrahedral meshes that can easily accommodate the topography and complex underground structure. Moreover, because we create our local mesh by extracting from part of the global model mesh, the relationship between the local and global meshes is straightforward, so we can easily create a projection of the Jacobian matrix between global and local meshes and rapidly construct the global Jacobian matrix for 3D EM inversions. After formulating the boundary value problem based on the finite-element method, we verify the accuracy of our modeling algorithm by checking against the semianalytical solution for a homogeneous half-space model, and we test our inversion algorithm by running inversions on synthetic and survey data collected over Vesterålen, Norway. The numerical experiments demonstrate that our method can model the AEM responses at high accuracy and recover the subsurface main resistivity structures from synthetic and field data.

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40

YAO, JIANYAO, G. R. LIU, DONG QIAN, CHUNG-LUNG CHEN, and GEORGE X. XU. "A MOVING-MESH GRADIENT SMOOTHING METHOD FOR COMPRESSIBLE CFD PROBLEMS." Mathematical Models and Methods in Applied Sciences 23, no. 02 (January 8, 2013): 273–305. http://dx.doi.org/10.1142/s0218202513400046.

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A computational fluid dynamics (CFD) solver based on the gradient smoothing method (GSM) with moving mesh enabled is presented in this paper. The GSM uses unstructured meshes which could be generated and remeshed easily. The spatial derivatives of field variables at nodes and midpoints of cell edges are calculated using the gradient smoothing operations. The presented GSM codes use second-order Roes upwind flux difference splitting method and second-order 3-level backward differencing scheme for the compressible Navier–Stokes equations with moving mesh, and the second-order of accuracy for both the spatial and temporal discretization is ensured. The spatial discretization accuracy is verified using the method of manufactured solutions (MMS) on both structured and unstructured triangle meshes, and the results show that the observed order of accuracy achieves 2 even when highly distorted meshes are used. The temporal discretization accuracy is verified using the results with different time step lengths, and second-order accuracy is also obtained. Therefore, it is confirmed that the proposed GSM-CFD solver is a uniform second-order scheme.

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41

Shephard, Mark S. "Approaches to the Automatic Generation and Control of Finite Element Meshes." Applied Mechanics Reviews 41, no. 4 (April 1, 1988): 169–85. http://dx.doi.org/10.1115/1.3151889.

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This review paper discusses the algorithmic approaches being taken to the development of finite element mesh generators capable of automatically discretizing general domains without the need for user intervention. The paper demonstrates that because of the modeling demands placed on an automatic mesh generator, all the approaches taken to date produce unstructured meshes. Consideration is also given to both a priori and a posteriori mesh control devices for automatic mesh generators as well as their integration with geometric modeling and adaptive analysis procedures.

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42

Jayasinghe, Savithru, David L. Darmofal, Eric Dow, Marshall C. Galbraith, and Steven R. Allmaras. "A Discretization-Independent Distributed Well Model." SPE Journal 24, no. 06 (October 14, 2019): 2946–67. http://dx.doi.org/10.2118/198898-pa.

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Summary In this paper, we present a new well model for reservoir simulation. The proposed well model relates the volumetric flow rate and the bottomhole pressure (BHP) of the well to the reservoir pressure through a spatially distributed source term that is independent of the numerical method and the discrete mesh used to solve the flow problem. This is in contrast to the widely used Peaceman–type well models, which are inherently tied to a particular numerical discretization by the definition of an equivalent well radius. The proposed distributed well model does not require the calculation of an equivalent well radius. Hence, it can be readily applied to finite–difference, finite–volume (FV), or finite–element discretizations on arbitrarily unstructured meshes, which also makes it an attractive option for mesh–adaptation schemes. The new well model is demonstrated on a steady-state single-phase flow problem and an unsteady two-phase flow problem, using a conventional FV method and a high–order discontinuous Galerkin (DG) method. The distributed well model produces error–convergence behaviors that are very similar to the Peaceman well model on uniform structured meshes, but its applicability to high–order discretizations and mesh–adaptation schemes allows for higher convergence rates and more cost-efficient solutions, especially on adapted unstructured meshes.

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43

Stupak, Eugeniuš, and Romualdas Baušys. "GENERATION OF THE UNSTRUCTURED FE-GRIDS FOR COMPLEX 2D OBJECTS/NESTRUKTŪRINIŲ BE TINKLŲ GENERAVIMAS SUDĖTINGIEMS DVIMAČIAMS OBJEKTAMS." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 6, no. 1 (February 28, 2000): 17–24. http://dx.doi.org/10.3846/13921525.2000.10531559.

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For the numerical simulation of engineering problems, the finite element method (FEM) is among the most popular approaches. One of the main concerns in a finite element analysis is the adequacy of the finite element grid. The accuracy of the FEM depends on the size, shape and placement of the elements. On the other hand, the total computational cost is determined by the total number of elements in FE model. An increased accuracy can be obtained by the global reduction of the element size, but this can be characterised by drastically increased computational cost. Thus, in many engineering applications it is desirable to generate not regular FE mesh with finer grid in the regions where accuracy of numerical simulation is of most importance and with more coarse grid in the other regions. In this paper we present a new approach to the grid generation of the multimaterial or multidomain engineering systems by the advancing front technique. This technique has proved successful in generating unstructured meshes in two and three dimensions [1–9]. The algorithm of the technique is summarised in section 2. Common for all approaches of advancing front mesh generation is that the generation problem is divided into three parts. First, the specification of the mesh size attributes, second, the discretisation of the boundaries, and, third, the discretisation of the interior of the domain. In the advancing front technique the front is defined as the boundary between the gridded and ungridded region. The key algorithmic step that must be addressed to advancing front methods is the proper introduction of new elements into the ungridded region. For triangular and tetrahedral grids the elements are introduced sequentially one at a time. The most obvious advantage of the advancing front method is that it directly incorporates free form geometry. Direct implementation of the advancing front technique for multimaterial or multidomain engineering applications is still challenging. Grid generation in the place of few materials or domain contact must ensure the compatibility of nodes on common boundary segments (nodes on common boundary segments must be in the same positions). The advancing front technique does not include non-convex domain, so at the first step non-convex domain of discretisation is decomposed into few convex subdomains. The subdomain of interest must be defined by describing a course background mesh of triangle elements, covering the entire multidomain region, which forms the input for finite element analysis. In this work, a black box architecture expert system has been developed which incorporates the information about the object geometry as well as the boundary and loading conditions, distribution of materials characteristics to generate an a priori (before the finite element analysis is carried out) mesh which is more refined around the critical regions (singularities, re-entrant corners, regions with high-stress concentration, etc) of the problem domain. This system uses a new concept of subtracting to locate the critical regions in the domain and to assign priority and mesh size to them. This involves the decomposition of the original structure into substructures (or primitives) for which an initial and approximate analysis can be performed by using analytical solutions and heuristics. When incorporated into and compared with the traditional approach to the adaptive finite element analysis, it is expected that the proposed approach, which starts the process with near optimal meshes, will be more accurate and efficient. Several numerical examples are presented and discussed. Examples demonstrate that our approach enables to generate the compatible meshes for multimaterial or multidomain problems. The quality of meshes is good, there are no ill-shaped elements. By the proposed expert system we can generate the mesh for any complex structure. The generation of 2D meshes is only the first step using the proposed expert system; in future we shall extend it for 3D meshes. During the last decade a lot of research has been devoted to extension of the advancing front technique to the parallel computers [8, 10, 11]. But the application of the technique to parallel processors is still challenging. In fact, we have to solve how to minimise inter-processor communication during mesh generation of subdomains. The proposed expert system for complex structures grid generation enables to use it with parallel computers. At the first step the domain of discretisation is decomposed into subdomains and all the surfaces defining the boundaries of subdomains to be gridded are triangulated. Later all subdomains can be meshed concurrently and no more inter-processor communication is required. The master task sends to workers tasks information about dividing common boundaries and information of each subdomain. The workers tasks receive their subdomain data and mesh their subdomain. Later the master receives the information from the workers tasks and joins gridded subdomains to one structure, ensuring the compatibility of nodes on common boundaries. So this suggested expert system enables to minimise the communications and costs of computations. The implementation of the expert system to parallel processors is to be done in the future.

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44

Leyland, Pénélope, Angelo Casagrande, and Yannick Savoy. "Parallel Mesh Adaptive Techniques Illustrated with Complex Compressible Flow Simulations." Modelling and Simulation in Engineering 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/317359.

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The aim of this paper is to discuss efficient adaptive parallel solution techniques on unstructured 2D and 3D meshes. We concentrate on the aspect of parallel a posteriori mesh adaptation. One of the main advantages of unstructured grids is their capability to adapt dynamically by localised refinement and derefinement during the calculation to enhance the solution accuracy and to optimise the computational time. Grid adaption also involves optimisation of the grid quality, which will be described here for both structural and geometrical optimisation.

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45

CHAN (MAIAA), K. I., and E. Y. K. NG (MASME). "MODIFIED DISTRIBUTION-FORMULA SCHEME FOR UNSTRUCTURED ADAPTIVE NAVIER-STOKES SOLVERS." International Journal of Computational Methods 02, no. 03 (September 2005): 375–400. http://dx.doi.org/10.1142/s021987620500051x.

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The development and validation of an improved distribution-formula method is presented in this paper. The original technique, an explicit, cell-vertex, finite volume formulation, involves calculating the change in flow variables in each finite volume cell by integration of the governing equations, and then using distribution formulas to distribute such changes to the vertices. Its application has largely been in structured meshes without mesh adaptation. The present work introduces three improvements. Firstly, the extension of the method for use on unstructured adaptive meshes. This results in the additional advantages of mesh adaptation as well as the capability to simulate flows over arbitrarily complex geometries. Secondly, for the calculation of inviscid fluxes, the central differencing portion of the original method is replaced with a suitable higher-order upwind differencing scheme. This improves the accuracy and robustness of the distribution-formula method. Three different upwind techniques are evaluated through numerical investigations. The most promising among these techniques is selected for use in the development of the improved distribution-formula scheme for unstructured adaptive viscous solutions. Thirdly, the discretization of viscous fluxes is achieved through a method which requires less computational effort. The improved scheme is tested and found to be accurate, robust and computationally efficient.

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46

Brown, David A., Siva Nadarajah, Hong Yang, Patrice Castonguay, Hassan Raiesi, Kurt Sermeus, and Patrick Germain. "Quality-Preserving Linear Elasticity Mesh Movement Algorithm for Multi-Element Unstructured Meshes." AIAA Journal 57, no. 2 (February 2019): 521–31. http://dx.doi.org/10.2514/1.j057463.

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47

Karman, Steve L., W. Kyle Anderson, and Mandar Sahasrabudhe. "Mesh Generation Using Unstructured Computational Meshes and Elliptic Partial Differential Equation Smoothing." AIAA Journal 44, no. 6 (June 2006): 1277–86. http://dx.doi.org/10.2514/1.15929.

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48

Katz, Aaron, and Venkateswaran Sankaran. "Mesh quality effects on the accuracy of CFD solutions on unstructured meshes." Journal of Computational Physics 230, no. 20 (August 2011): 7670–86. http://dx.doi.org/10.1016/j.jcp.2011.06.023.

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49

Knupp, Patrick M. "Applications of mesh smoothing: copy, morph, and sweep on unstructured quadrilateral meshes." International Journal for Numerical Methods in Engineering 45, no. 1 (May 10, 1999): 37–45. http://dx.doi.org/10.1002/(sici)1097-0207(19990510)45:1<37::aid-nme577>3.0.co;2-f.

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50

Xu, He-Yong, Shi-Long Xing, Zheng-Yin Ye, and Ming-Sheng Ma. "A simple and conservative unstructured sliding-mesh approach for rotor–fuselage aerodynamic interaction simulation." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 231, no. 1 (October 2, 2016): 163–79. http://dx.doi.org/10.1177/0954410016664919.

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A conservative unstructured sliding-mesh technique is developed for the rotor–fuselage aerodynamic interaction simulation. The computational domain is decomposed into a rotational zone and a stationary zone. The rotational zone contains the rotor blades that rotate with the zone, while the stationary zone contains the fuselage which keeps stationary during the simulation. The two zones are connected via a sliding interface, which is designed to be a cylindrical surface consisting of the top, bottom, and side surfaces. The top and bottom surfaces are paved with arbitrary triangles and the side surface is meshed by triangularizing equal-sized and right-angled quadrilaterals. The intersection information between the rotational and stationary sliding interface meshes, such as the number of intersection triangles and the area of each intersection polygon, is the key to the present conservative computation. For the top and bottom surfaces, the point-on-line cases are first identified and the point perturbation operation is carried out to eliminate the potential error due to the presence of a point-on-line case. The neighbor-to-neighbor searching algorithm is applied for efficient determination of the intersection triangles, and the intersection polygon areas are determined by enumerating all the possible intersection cases. For the side surface, the intersection relations and polygon areas can be easily determined based on the enumeration method due to the special triangularization. The present method is validated by simulating the GIT (Georgia Institute of Technology) rotor–fuselage interaction model, and comparing numerical results with experiment measurements. It is demonstrated that the present conservative sliding-mesh method is simple to implement, and is efficient for the prediction of complicated unsteady rotor–fuselage aerodynamic interaction.

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