Journal articles: 'Unstructured grid'

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Mavriplis, D. J. "UNSTRUCTURED GRID TECHNIQUES." Annual Review of Fluid Mechanics 29, no. 1 (January 1997): 473–514. http://dx.doi.org/10.1146/annurev.fluid.29.1.473.

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Evazi, M., and H. Mahani. "Unstructured-Coarse-Grid Generation Using Background-Grid Approach." SPE Journal 15, no. 02 (March 3, 2010): 326–40. http://dx.doi.org/10.2118/120170-pa.

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Summary Reservoir flow simulation involves subdivision of the physical domain into a number of gridblocks. This is best accomplished with optimized gridpoint density and a minimized number of gridblocks, especially for coarse-grid generation from a fine-grid geological model. In any coarse-grid generation, proper distribution of gridpoints, which form the basis of numerical gridblocks, is a challenging task. We show that this can be achieved effectively by a novel grid-generation approach based on a background grid that stores gridpoint spacing parameters. Spacing parameter (L) can be described by Poisson's equation (∇2L = G), where the local density of gridpoints is controlled by a variable source term (G); see Eq. 1. This source term can be based on different gridpoint density indicators, such as permeability variations, fluid velocity, or their combination (e.g., vorticity) where they can be extracted from the reference fine grid. Once a background grid is generated, advancing-front triangulation (AFT) and then Delaunay tessellation are invoked to form the final (coarse) gridblocks. The algorithm produces grids varying smoothly from high- to low-density gridpoints, thus minimizing use of grid-smoothing and -optimization techniques. This algorithm is quite flexible, allowing choice of the gridding indicator, hence providing the possibility of comparing the grids generated with different indicators and selecting the best. In this paper, the capabilities of approach in generation of unstructured coarse grids from fine geological models are illustrated using 2D highly heterogeneous test cases. Flexibility of algorithm to gridding indicator is demonstrated using vorticity, permeability variation, and velocity. Quality of the coarse grids is evaluated by comparing their two-phase-flow simulation results to those of fine grid and uniform coarse grid. Results demonstrate the robustness and attractiveness of the approach, as well as relative quality/performance of grids generated by using different indicators.

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Suzuki, Masahiro. "Surface grid generation based on unstructured grids." AIAA Journal 29, no. 12 (December 1991): 2262–64. http://dx.doi.org/10.2514/3.10869.

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Petrov, I. B., A. V. Favorskaya, M. V. Muratov, V. A. Biryukov, and A. V. Sannikov. "Grid-characteristic method on unstructured tetrahedral grids." Doklady Mathematics 90, no. 3 (November 2014): 781–83. http://dx.doi.org/10.1134/s1064562414070254.

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Löhner, Rainald. "Automatic unstructured grid generators." Finite Elements in Analysis and Design 25, no. 1-2 (March 1997): 111–34. http://dx.doi.org/10.1016/s0168-874x(96)00038-8.

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Löhner, Rainald, Jose Camberos, and Marshal Merriam. "Parallel unstructured grid generation." Computer Methods in Applied Mechanics and Engineering 95, no. 3 (March 1992): 343–57. http://dx.doi.org/10.1016/0045-7825(92)90192-m.

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Lauritzen, P. H., J. T. Bacmeister, P. F. Callaghan, and M. A. Taylor. "NCAR_Topo (v1.0): NCAR global model topography generation software for unstructured grids." Geoscientific Model Development 8, no. 12 (December 14, 2015): 3975–86. http://dx.doi.org/10.5194/gmd-8-3975-2015.

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Abstract. It is the purpose of this paper to document the NCAR global model topography generation software for unstructured grids (NCAR_Topo (v1.0)). Given a model grid, the software computes the fraction of the grid box covered by land, the grid-box mean elevation (deviation from a geoid that defines nominal sea level surface), and associated sub-grid-scale variances commonly used for gravity wave and turbulent mountain stress parameterizations. The software supports regular latitude–longitude grids as well as unstructured grids, e.g., icosahedral, Voronoi, cubed-sphere and variable-resolution grids.

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Guo, Guang Dong, Song Sheng Deng, and Wei Xing Hua. "Comparison of Different Grid Structures for the Hydrocyclone Flow Field Simulation." Applied Mechanics and Materials 353-356 (August 2013): 3399–402. http://dx.doi.org/10.4028/www.scientific.net/amm.353-356.3399.

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In the CFD(computational fluid dynamics) study of hydrocyclones, the grid is a important factor to predicting the flow field. An attempt has been made in this study, in the same turbulence model and boundary conditions, three different structures of grid, the structured grid, the unstructured grid and the hybrid grid, are compared for the predictions of the axial, radial and tangential velocities. It has been observed that the memory space structured grid is large, and there are much number grid of the unstructured grid. The structured grid led to an improved turbulence field prediction and thereby to predict the velocity fields of single phase flow field more accurately. The unstructured grids is used to simulate the process of oil-water separation.

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Fung, L. S. K. S. K., X. Y. Y. Ding, and A. H. H. Dogru. "Unconstrained Voronoi Grids for Densely Spaced Complex Wells in Full-Field Reservoir Simulation." SPE Journal 19, no. 05 (January 30, 2014): 803–15. http://dx.doi.org/10.2118/163648-pa.

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Summary Accurate representation of near-well flow is an important subject matter in reservoir simulation. In today's field-scale reservoir simulation, cell-centered structured grids remain the predominant practice. Typically, well-inflow performance of the perforated cells is connected to the finite-volume solution by means of well indices that may not be well-defined when the wellbore intersects the finite-volume cells in a complex trajectory. Fine gridding is also required to resolve the flow dynamics in the near-well regions. Strong grid-orientation sensitivities can also contribute to the numerical errors and may require significant local grid refinement to alleviate. There are ongoing resesarch-and-development (R&D) efforts on applying unstructured grids to better represent the near-well flow in reservoir simulation, but their applications are mainly in single-well study or sector modeling with a few wells. Some of the reasons cited for this include (1) the lack of an effective, easy-to-use full-field complex well-gridding tool; (2) the lack of supporting unstructured workflow for full-cycle reservoir simulation; (3) the cost of unstructured-grid simulation; and (4) the availability of post-analysis and visualization tools for unstructured-grid simulation. The paper describes a novel method to automatically generate unstructured grids that conform to complex well paths in field-scale simulation. The method uses a multilevel approach to place cells optimally within the solution domain on the basis of the “regions of interests.” The wellbore geometry is honored by means of the construction of a near-well grid that is complemented with multilevel quad-tree (Fig. 1) refinements to achieve the desired resolution in grid transition zones. The method includes an algorithm to remove small cells and pinching cells on the basis of local grid quality measures and cell prioritization to honor well paths. The gridding process forms a component of a production-level reservoir-simulation workflow. The use of unstructured grid results in computational savings by placing cells where the resolution is needed. An in-house massively parallel simulator is used to run the unstructured-grid models. Simulation examples for full-field applications with hundreds of complex wells by use of both structured grids and unstructured grids will be used to compare results, accuracy, and performance of the gridding method for reservoir simulation.

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TIAN, SHULING, YIZHAO WU, and JIAN XIA. "NUMERICAL SIMULATION OF UNSTEADY FLOW FIELD AROUND HELICOPTER IN FORWARD FLIGHT USING A PARALLEL DYNAMIC OVERSET UNSTRUCTURED GRIDS METHOD." Modern Physics Letters B 23, no. 03 (January 30, 2009): 325–28. http://dx.doi.org/10.1142/s021798490901831x.

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A parallel Navier-Stokes solver based on dynamic overset unstructured grids method is presented to simulate the unsteady turbulent flow field around helicopter in forward flight. The grid method has the advantages of unstructured grid and Chimera grid and is suitable to deal with multiple bodies in relatively moving. Unsteady Navier-Stokes equations are solved on overset unstructured grids by an explicit dual time-stepping, finite volume method. Preconditioning method applied to inner iteration of the dual-time stepping is used to speed up the convergence of numerical simulation. The Spalart-Allmaras one-equation turbulence model is used to evaluate the turbulent viscosity. Parallel computation is based on the dynamic domain decomposition method in overset unstructured grids system at each physical time step. A generic helicopter Robin with a four-blade rotor in forward flight is considered to validate the method presented in this paper. Numerical simulation results show that the parallel dynamic overset unstructured grids method is very efficient for the simulation of helicopter flow field and the results are reliable.

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Riley, D. J., and C. D. Turner. "Interfacing unstructured tetrahedron grids to structured-grid FDTD." IEEE Microwave and Guided Wave Letters 5, no. 9 (1995): 284–86. http://dx.doi.org/10.1109/75.410398.

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Sun, Jianlei, David Schechter, and Chung-Kan Huang. "Grid-Sensitivity Analysis and Comparison Between Unstructured Perpendicular Bisector and Structured Tartan/Local-Grid-Refinement Grids for Hydraulically Fractured Horizontal Wells in Eagle Ford Formation With Complicated Natural Fractures." SPE Journal 21, no. 06 (July 15, 2016): 2260–75. http://dx.doi.org/10.2118/177480-pa.

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Summary In the context of modeling fractured horizontal wells, unstructured grids have been applied to generate simulation meshes for complex fracture networks. It is necessary to investigate how to choose an unstructured mesh to accurately simulate production performance. In this paper, a new unstructured gridding and discretization work flow is proposed to handle nonorthogonal and low-angle intersections of extensively clustered fractures with nonuniform apertures. The work flow is then validated with two models in terms of production behavior and central-processing-unit (CPU) performance: a synthetic model with one horizontal well and orthogonal intersected hydraulic fractures built by tartan grid, and a field-scale local-grid-refinement (LGR) model with three horizontal wells and irregular hydraulic fractures in a slightly dipping reservoir created by a commercial software plug-in. Good-quality matches are obtained between unstructured and structured grids in both pressure and production behavior. Sensitivity analysis of the meshing parameters suggests that refinement in the vicinity of fractures has improved both early and late production of a well, whereas background density has a dominant effect on the late production. Background-grid type and orientation have less influence as long as they have the same grid density. Fewer cells can be achieved by increasing reservoir-background size and size-progression ratio, replacing unstructured-background grids with structured grids, and reducing the complexity of the fracture networks without loss of the accuracy, resulting in improved CPU performance. This study applies unstructured grids to simulate multiple horizontal wells with complicated fracture networks, and provides detailed comparisons between unstructured and structured grids. Most importantly, it resolves the question regarding how to choose an appropriate mesh to yield both accurate results and high-quality CPU performance.

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Lauritzen, P. H., J. T. Bacmeister, P. F. Callaghan, and M. A. Taylor. "NCAR global model topography generation software for unstructured grids." Geoscientific Model Development Discussions 8, no. 6 (June 22, 2015): 4623–51. http://dx.doi.org/10.5194/gmdd-8-4623-2015.

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Abstract. It is the purpose of this paper to document the NCAR global model topography generation software for unstructured grids. Given a model grid, the software computes the fraction of the grid box covered by land, the gridbox mean elevation, and associated sub-grid scale variances commonly used for gravity wave and turbulent mountain stress parameterizations. The software supports regular latitude-longitude grids as well as unstructured grids; e.g. icosahedral, Voronoi, cubed-sphere and variable resolution grids. As an example application and in the spirit of documenting model development, exploratory simulations illustrating the impacts of topographic smoothing with the NCAR-DOE CESM (Community Earth System Model) CAM5.2-SE (Community Atmosphere Model version 5.2 – Spectral Elements dynamical core) are shown.

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Ghidoni, A., E. Pelizzari, S. Rebay, and V. Selmin. "3D anisotropic unstructured grid generation." International Journal for Numerical Methods in Fluids 51, no. 9-10 (2006): 1097–115. http://dx.doi.org/10.1002/fld.1151.

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Löhner, Rainald, Joseph D. Baum, Eric Mestreau, Dmitri Sharov, Charles Charman, and Daniele Pelessone. "Adaptive embedded unstructured grid methods." International Journal for Numerical Methods in Engineering 60, no. 3 (May 5, 2004): 641–60. http://dx.doi.org/10.1002/nme.978.

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Yang, Jue, and Baoshan Jia. "Unstructured grid and unstructured grid porous methods for numerical analysis of TACR moderator calandria." Advances in Engineering Software 39, no. 5 (May 2008): 407–15. http://dx.doi.org/10.1016/j.advengsoft.2007.03.007.

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Li, Zong Zhe, Zheng Hua Wang, Lu Yao, and Wei Cao. "A Combined Global Coarsening Method for 3D Multigrid Applications." Applied Mechanics and Materials 236-237 (November 2012): 1049–53. http://dx.doi.org/10.4028/www.scientific.net/amm.236-237.1049.

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An automatic agglomeration methodology to generate coarse grids for 3D flow solutions on anisotropic unstructured grids has been introduced in this paper. The algorithm combines isotropic octree based coarsening and anisotropic directional agglomeration to yield a desired coarsening ratio and high quality of coarse grids, which developed for cell-centered multigrid applications. This coarsening strategy developed is presented on an unstructured grid over 3D ONERA M6 wing. It is shown that the present method provides suitable coarsening ratio and well defined aspect ratio cells at all coarse grid levels.

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Henshaw, William D. "Automatic grid generation." Acta Numerica 5 (January 1996): 121–48. http://dx.doi.org/10.1017/s0962492900002634.

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Current methods for the automatic generation of grids are reviewed. The approaches to grid generation that are discussed include Cartesian, multi-block-structured, overlapping and unstructured. Emphasis is placed on those methods that can create high-quality grids appropriate for the solution of equations of a hyperbolic nature, such as those that arise in fluid dynamics. Numerous figures illustrate the different grid generation techniques.

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Özyıldırım, Özcan, Mehmet Emin Candansayar, İsmail Demirci, and Bülent Tezkan. "Two-dimensional inversion of magnetotelluric/radiomagnetotelluric data by using unstructured mesh." GEOPHYSICS 82, no. 4 (July 1, 2017): E197—E210. http://dx.doi.org/10.1190/geo2016-0378.1.

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We have compared structured and unstructured grid-based 2D inversion algorithms for magnetotelluric (MT) and radiomagnetotelluric (RMT) data in terms of speed and accuracy. We have developed a new 2D inversion algorithm for MT and RMT data by using a finite-element (FE) method that uses unstructured triangle grids. We compare the inversion results of our unstructured grid-based algorithm with those of the conventional algorithm, which uses either a structured FE or structured finite-difference (FD) numerical solution technique. The imaging of the surface topography and the underground resistivity structures by the new algorithm requires fewer elements than those that use FE and FD structured grids. We also find that when unstructured grids are used, the quality of the mesh is increased and the numerical errors are significantly reduced. Thus, the program runs faster and can simulate the complex surface topography in a more stable setting than the classic inversion algorithms. Furthermore, we implement a new smoothing matrix format for the unstructured triangle grids for the inversion procedure. We use two samples of synthetic data for the MT and RMT frequencies as well as a sample of field RMT data collected across a fault zone for comparison. In our synthetic data experiment, we find that the resistivity values and the boundaries obtained from the inversion of the unstructured mesh are closer to those of the true a priori synthetic model. Results of the synthetic and field data verify the computational advantages (speed and accuracy) of our inversion algorithm with respect to the conventional structured grid-based inversion algorithms.

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Li, Zong Zhe, Zheng Hua Wang, Wei Cao, and Lu Yao. "Directional Agglomeration with Quadtree Based Coarsening for 2D Anisotropic Unstructured Grids." Applied Mechanics and Materials 251 (December 2012): 10–14. http://dx.doi.org/10.4028/www.scientific.net/amm.251.10.

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This paper develops an automatic nested agglomeration methodology for 2D multigrid flow solutions over anisotropic unstructured grids. The algorithm combines isotropic quadtree based coarsening and anisotropic directional agglomeration method to yield a desired coarsening ratio and high quality of coarse grids, which works on cell-centered finite volume scheme. This coarsening strategy developed is presented on an unstructured grid over the RAE2822 airfoil. It is shown that the present method provides more suitable coarsening ratio and aspect ratio at all coarse grid levels than only quadtree based coarsening method.

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Abras, Jennifer N., C. Eric Lynch, and Marilyn J. Smith. "Computational Fluid Dynamics–Computational Structural Dynamics Rotor Coupling Using an Unstructured Reynolds-Averaged Navier–Stokes Methodology." Journal of the American Helicopter Society 57, no. 1 (January 1, 2012): 1–14. http://dx.doi.org/10.4050/jahs.57.012001.

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The focus of this paper is to discuss the unique challenges introduced through the use of unstructured grids in rotorcraft computational fluid dynamics (CFD)–computational structural dynamics (CSD) coupling. The use of unstructured grid methodology in CFD has been expanding because of the advantages in grid generation and modeling of complex configurations. However, the resulting amorphous distribution of the grid points on the rotor blade surface provides no information with regard to the orientation of the blade, in direct contrast to structured grid methodology that can take advantage of the ordered mapping of points to identify the orientation as well as simplifying airloads integration. A methodology has been developed and is described here, which now permits unstructured methods to be utilized for elastic rotary-wing simulations. This methodology is evaluated through comparison of the UH60A rotor with available flight test data for forward flight.

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Cui, Pengcheng, Bin Li, Jing Tang, Jiangtao Chen, and Youqi Deng. "A modified adjoint-based grid adaptation and error correction method for unstructured grid." Modern Physics Letters B 32, no. 12n13 (May 10, 2018): 1840020. http://dx.doi.org/10.1142/s0217984918400201.

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Grid adaptation is an important strategy to improve the accuracy of output functions (e.g. drag, lift, etc.) in computational fluid dynamics (CFD) analysis and design applications. This paper presents a modified robust grid adaptation and error correction method for reducing simulation errors in integral outputs. The procedure is based on discrete adjoint optimization theory in which the estimated global error of output functions can be directly related to the local residual error. According to this relationship, local residual error contribution can be used as an indicator in a grid adaptation strategy designed to generate refined grids for accurately estimating the output functions. This grid adaptation and error correction method is applied to subsonic and supersonic simulations around three-dimensional configurations. Numerical results demonstrate that the sensitive grids to output functions are detected and refined after grid adaptation, and the accuracy of output functions is obviously improved after error correction. The proposed grid adaptation and error correction method is shown to compare very favorably in terms of output accuracy and computational efficiency relative to the traditional featured-based grid adaptation.

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Engwirda, Darren. "JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere." Geoscientific Model Development 10, no. 6 (June 6, 2017): 2117–40. http://dx.doi.org/10.5194/gmd-10-2117-2017.

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Abstract. An algorithm for the generation of non-uniform, locally orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate very high-quality staggered Voronoi–Delaunay meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather prediction. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of high-quality unstructured spheroidal Delaunay triangulations is introduced. A locally orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. It is shown that use of the Frontal-Delaunay refinement technique allows for the generation of very high-quality unstructured triangulations, satisfying a priori bounds on element size and shape. Grid quality is further improved through the application of hill-climbing-type optimisation techniques. Overall, the algorithm is shown to produce grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. A selection of uniform and non-uniform spheroidal grids appropriate for high-resolution, multi-scale general circulation modelling are presented. These grids are shown to satisfy the geometric constraints associated with contemporary unstructured C-grid-type finite-volume models, including the Model for Prediction Across Scales (MPAS-O). The use of user-defined mesh-spacing functions to generate smoothly graded, non-uniform grids for multi-resolution-type studies is discussed in detail.

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Wang, Bing, and Hai Qing Si. "An Unstructured Moving Grid Scheme for Shock Impacting on Material Interface." Applied Mechanics and Materials 275-277 (January 2013): 138–51. http://dx.doi.org/10.4028/www.scientific.net/amm.275-277.138.

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An unstructured moving grid scheme is applied to track the real-time motion state of the material interface with large-scale deformation induced by shock in the compressible multi-material flow. The material interface is denoted as a special internal boundary which is made up of unstructured grid edges, and on both sides of that there exist grids used for the two different materials. Riemann problem is solved in order to track the motion of the grid points on the material interface, and the local re-meshing technique is also applied to cope with the large-scale deformation of the moving grids near the interface, especially for the case of strong shocks existing in the multi-material flows. Simultaneously, the material interface is also defined as a kind of grid-deforming boundary in case grid volumes are negative. To obtain the resolution of the whole multi-material flow domain, the arbitrary Lagrangian-Eulerian (ALE) is discretized using Harten-Lax-van Leer-Contact (HLLC) scheme. Several numerical calculations from shock-interface examples demonstrate that this moving grid technique is feasible and effective in tracking the real-time motion state of the material interface.

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Falsafioon, Mehdi, Sina Arabi, Ricardo Camarero, and François Guibault. "Unstructured Grid Smoothing for Turbomachinery Applications." International Journal of Fluid Machinery and Systems 10, no. 4 (December 31, 2017): 421–31. http://dx.doi.org/10.5293/ijfms.2017.10.4.421.

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ITO, Yasushi, and Kazuhiro NAKAHASHI. "Unstructured Surface Grid Generation Using GUI." Journal of the Japan Society for Aeronautical and Space Sciences 48, no. 554 (2000): 75–81. http://dx.doi.org/10.2322/jjsass.48.75.

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LI, Zong-Zhe, Zheng-Hua WANG, Lu YAO, and Wei CAO. "Parallel Multigrid Solver for Unstructured Grid." Journal of Software 24, no. 2 (December 27, 2013): 391–404. http://dx.doi.org/10.3724/sp.j.1001.2013.04241.

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Galbraith, Marshall C., Philip C. Caplan, Hugh A. Carson, Michael A. Park, Aravind Balan, W. Kyle Anderson, Todd Michal, et al. "Verification of Unstructured Grid Adaptation Components." AIAA Journal 58, no. 9 (September 2020): 3947–62. http://dx.doi.org/10.2514/1.j058783.

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Thomas, James L., Boris Diskin, and Christopher L. Rumsey. "Towards Verification of Unstructured-Grid Solvers." AIAA Journal 46, no. 12 (December 2008): 3070–79. http://dx.doi.org/10.2514/1.36655.

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Venkatakrishnan, V. "Parallel implicit unstructured grid Euler solvers." AIAA Journal 32, no. 10 (October 1994): 1985–91. http://dx.doi.org/10.2514/3.12242.

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Pakmor, Ruediger, Andreas Bauer, and Volker Springel. "Magnetohydrodynamics on an unstructured moving grid." Monthly Notices of the Royal Astronomical Society 418, no. 2 (September 23, 2011): 1392–401. http://dx.doi.org/10.1111/j.1365-2966.2011.19591.x.

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Venkatakrishnan, V. "Perspective on unstructured grid flow solvers." AIAA Journal 34, no. 3 (March 1996): 533–47. http://dx.doi.org/10.2514/3.13101.

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Shostko, Alexander, and Rainald Löhner. "Three-dimensional parallel unstructured grid generation." International Journal for Numerical Methods in Engineering 38, no. 6 (March 30, 1995): 905–25. http://dx.doi.org/10.1002/nme.1620380603.

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Löhner, Rainald, Juan R. Cebral, Fernando F. Camelli, Joseph D. Baum, Eric L. Mestreau, and Orlando A. Soto. "Adaptive Embedded/Immersed Unstructured Grid Techniques." Archives of Computational Methods in Engineering 14, no. 3 (July 19, 2007): 279–301. http://dx.doi.org/10.1007/s11831-007-9008-4.

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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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Mallison, Brad, Charles Sword, Thomas Viard, William Milliken, and Amy Cheng. "Unstructured Cut-Cell Grids for Modeling Complex Reservoirs." SPE Journal 19, no. 02 (January 30, 2014): 340–52. http://dx.doi.org/10.2118/163642-pa.

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Summary Effective workflows for translating Earth models into simulation models require grids that preserve geologic accuracy, offer flexible resolution control, integrate tightly with upscaling, and can be generated easily. Corner-point grids and pillar-based unstructured grids fail to satisfy these objectives; hence, a truly 3D unstructured approach is required. This paper describes unstructured cut-cell gridding tools that address these needs and improve the integration of our overall reservoir-modeling workflows. The construction of simulation grids begins with the geologic model: a numerical representation of the reservoir structure, stratigraphy, and properties. Our gridding uses a geochronological (GeoChron) map from physical coordinates to an unfaulted and unfolded depositional coordinate system. The mapping is represented implicitly on a tetrahedral mesh that conforms to faults, and it facilitates accurate geostatistical modeling of static depositional properties. In the simplest use case, we create an explicit representation of the geologic model as an unstructured polyhedral grid. Away from faults and other discontinuities, the cells are hexahedral, highly orthogonal, and arranged in a structured manner. Geometric cutting operations create general polyhedra adjacent to faults and explicit contact polygons across faults. The conversion of implicit models to explicit grids is conceptually straightforward, but the implementation is nontrivial because of the limitations of finite precision arithmetic and the need to remove small cells formed in the cutting process. In practice, simulation grids are often constructed at coarser resolutions than Earth models. Our implementation of local grid coarsening and refinement exploits the flexibility of unstructured grids to minimize upscaling errors and to preserve critical geologic features. Because the simulation grid and the geologic model are constructed by use of the same mapping, fine cells can be nested exactly inside coarse cells. Therefore, flow-based upscaling can be applied efficiently without resampling onto temporary local grids. This paper describes algorithms and data structures for constructing, storing, and simulating cut-cell grids. Examples illustrate the accurate modeling of normal faults, y-faults, overturned layers, and complex stratigraphy. Flow results, including a field-sector model, show the suitability of cut-cell grids for simulation.

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Qiu, Zihua, Min Xu, Bin Zhang, and Chunlei Liang. "High-Order Spectral Difference Method on 3D Unstructured Grids via Mixed Elements." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 37, no. 5 (October 2019): 968–76. http://dx.doi.org/10.1051/jnwpu/20193750968.

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The high-order methods is difficultly applied in various elements. The development of a 3D solver by using the spectral difference method of unstructured grids via mixed elements is presented. A mixed tri-prism and tetrahedral grid is firstly refined using one-level h-refinement to generate a hexahedral grid while keeping the curvature of wall boundaries. The SD method designed for hexahedral elements can subsequently be applied for refining the unstructured grid. Through a series of numerical tests, the present method is high-order accurate for both inviscid and viscous flows is demonstrated; the results obtained for inviscid and viscous compressible flows compare well with other published results.

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Li, Zong Zhe, Zheng Hua Wang, Wei Cao, and Lu Yao. "A New Agglomeration Method for Isotropic Unstructured Grids." Applied Mechanics and Materials 241-244 (December 2012): 2957–61. http://dx.doi.org/10.4028/www.scientific.net/amm.241-244.2957.

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A robust aspect ratio based agglomeration algorithm to generate high quality coarse grids for unstructured grid is proposed in this paper. The algorithm focuses on multigrid techniques for the numerical solution of Euler equations, which conform to cell-centered finite volume scheme, combines isotropic vertex-based agglomeration to yield large increases in convergence rates. Aspect ratio is used as fusing weight to capture the degree of cell convexity and give an indication of cell quality, agglomerating isotropic cells sharing a common vertex. Consequently, we conduct agglomeration multigrid method to solve Euler equations on 2D isotropic unstructured grid, and compare the results with MGridGen

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Theler, German. "Unstructured Grids and the Multigroup Neutron Diffusion Equation." Science and Technology of Nuclear Installations 2013 (2013): 1–26. http://dx.doi.org/10.1155/2013/641863.

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The neutron diffusion equation is often used to perform core-level neutronic calculations. It consists of a set of second-order partial differential equations over the spatial coordinates that are, both in the academia and in the industry, usually solved by discretizing the neutron leakage term using a structured grid. This work introduces the alternatives that unstructured grids can provide to aid the engineers to solve the neutron diffusion problem and gives a brief overview of the variety of possibilities they offer. It is by understanding the basic mathematics that lie beneath the equations that model real physical systems; better technical decisions can be made. It is in this spirit that this paper is written, giving a first introduction to the basic concepts which can be incorporated into core-level neutron flux computations. A simple two-dimensional homogeneous circular reactor is solved using a coarse unstructured grid in order to illustrate some basic differences between the finite volumes and the finite elements method. Also, the classic 2D IAEA PWR benchmark problem is solved for eighty combinations of symmetries, meshing algorithms, basic geometric entities, discretization schemes, and characteristic grid lengths, giving even more insight into the peculiarities that arise when solving the neutron diffusion equation using unstructured grids.

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KÄSER, MARTIN, HEINER IGEL, MALCOLM SAMBRIDGE, and JEAN BRAUN. "A COMPARATIVE STUDY OF EXPLICIT DIFFERENTIAL OPERATORS ON ARBITRARY GRIDS." Journal of Computational Acoustics 09, no. 03 (September 2001): 1111–25. http://dx.doi.org/10.1142/s0218396x01000838.

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We compare explicit differential operators for unstructured grids and their accuracy with the aim of solving time-dependent partial differential equations in geophysical applications. As many problems suggest the use of staggered grids we investigate different schemes for the calculation of space derivatives on two separate grids. The differential operators are explicit and local in the sense that they use only information of the function in their nearest neighborhood, so that no matrix inversion is necessary. This makes this approach well-suited for parallelization. Differential weights are obtained either with the finite-volume method or using natural neighbor coordinates. Unstructured grids have advantages concerning the simulation of complex geometries and boundaries. Our results show that while in general triangular (hexagonal) grids perform worse than standard finite-difference approaches, the effects of grid irregularities on the accuracy of the space derivatives are comparably small for realistic grids. This suggests that such a finite-difference-like approach to unstructured grids may be an alternative to other irregular grid methods such as the finite-element technique.

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Yousefifard, Mahdi, Parviz Ghadimi, and Rahim Zamanian. "Unstructured Grid Solutions for Incompressible Laminar Flow over a Circular Cylinder Using a Particular Finite Volume-Finite Element Method." Journal of Engineering 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/795237.

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A numerical modeling of a 2D Navier-Stokes equation by a particular vertex centered control volume framework on an unstructured grid is presented in this paper. Triangular elements are applied with an effective high performance fully coupled algorithm, to simulate incompressible laminar flow over a circular cylinder. The cell face velocities in the discretization of the continuity and momentum equations are calculated by a combined linear and momentum interpolation scheme, respectively, and their performances are compared. Flow analyses have been conducted based on various Reynolds numbers up to 200 for the steady and unsteady flows using structured and unstructured grids. The robustness and accuracy of the scheme in the unstructured mesh are proved using the benchmark problems of incompressible laminar flow over a circular cylinder at low and medium Reynolds numbers. Results have been compared with the structured grid results, both cases with equal cell numbers and same strategy for the mesh refinement. Current results display good agreement with the experimental values. Overall, it is shown that, using the suggested method for the current problem, unstructured grids are highly competitive with the structured grids.

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YAMAKAWA, Masashi, and Kenichi MATSUNO. "Unstructured Moving Patched-Grid Method Using Concept of Overset Grid." Transactions of the Japan Society of Mechanical Engineers Series B 73, no. 734 (2007): 2070–76. http://dx.doi.org/10.1299/kikaib.73.2070.

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Kuprat, Andrew, David Cartwright, J. Tinka Gammel, Denise George, Brian Kendrick, David Kilcrease, Harold Trease, and Robert Walker. "X3D Moving Grid Methods for Semiconductor Applications." VLSI Design 8, no. 1-4 (January 1, 1998): 117–21. http://dx.doi.org/10.1155/1998/47283.

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The Los Alamos 3D grid toolbox handles grid maintenance chores and provides access to a sophisticated set of optimization algorithms for unstructured grids. The application of these tools to semiconductor problems is illustrated in three examples: grain growth, topographic deposition and electrostatics. These examples demonstrate adaptive smoothing, front tracking, and automatic, adaptive refinement/derefinement.

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PETROVSKAYA, N. B., and A. V. WOLKOV. "THE ISSUES OF SOLUTION APPROXIMATION IN HIGHER-ORDER SCHEMES ON DISTORTED GRIDS." International Journal of Computational Methods 04, no. 02 (June 2007): 367–82. http://dx.doi.org/10.1142/s0219876207001084.

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The impact of grid cell geometry on the accuracy of a high order discretization is studied. The issues of solution approximation are investigated on unstructured grids where grid cells are present that are almost degenerate. It will be demonstrated that high-order discretization schemes which employ compact discretization stencil are less sensitive to the geometry of a distorted grid in comparison with those over expanded stencils.

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Khokhlov, Nikolay, and Polina Stognii. "Novel Approach to Modeling the Seismic Waves in the Areas with Complex Fractured Geological Structures." Minerals 10, no. 2 (January 30, 2020): 122. http://dx.doi.org/10.3390/min10020122.

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This paper presents a novel approach to modeling the propagation of seismic waves in a medium containing subvertical fractured inhomogeneities, typical for mineralization zones. The developed method allows us to perform calculations on a structural computational grid, which avoids the construction of unstructured grids. For the calculations, the grid-characteristic method is used. We also present a comparison of the proposed method with the one described at earlier works and discuss the areas of its practical application. As an example, the numerical results for a cluster of subvertical fractures are given. A new approach for modeling fractures makes it quite easy to incorporate fractured objects into the seismic models and perform calculations without using algorithms on unstructured and curved grids.

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Yamakawa, Masashi, and Kenichi Matsuno. "Unstructured Adaptively-Moving-Grid Finite-Volume Method." JOURNAL OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES 52, no. 607 (2004): 348–54. http://dx.doi.org/10.2322/jjsass.52.348.

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Hanert, E., D. Y. Le Roux, V. Legat, and E. Deleersnijder. "Advection schemes for unstructured grid ocean modelling." Ocean Modelling 7, no. 1-2 (January 2004): 39–58. http://dx.doi.org/10.1016/s1463-5003(03)00029-5.

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Wackers, J., M. Visonneau, and Z. Ali. "Automatic grid adaptation for unstructured finite volumes." International Journal of Engineering Systems Modelling and Simulation 2, no. 1/2 (2010): 2. http://dx.doi.org/10.1504/ijesms.2010.031866.

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Muratov, M. V., I. B. Petrov, I. V. Sannikov, and A. V. Favorskaya. "Grid-characteristic method on unstructured tetrahedral meshes." Computational Mathematics and Mathematical Physics 54, no. 5 (May 2014): 837–47. http://dx.doi.org/10.1134/s096554251405011x.

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Muigg, Philipp, Markus Hadwiger, Helmut Doleisch, and Helwig Hauser. "Scalable Hybrid Unstructured and Structured Grid Raycasting." IEEE Transactions on Visualization and Computer Graphics 13, no. 6 (November 2007): 1592–99. http://dx.doi.org/10.1109/tvcg.2007.70588.

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Journal articles on the topic 'Unstructured grid'

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