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Journal articles on the topic 'Numerical grid generation (Numerical analysis) Tides'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Vasilev, Eugene, Dmitry Lachinov, Anton Grishin, and Vadim Turlapov. "Fast tetrahedral mesh generation and segmentation of an atlas-based heart model using a periodic uniform grid." Russian Journal of Numerical Analysis and Mathematical Modelling 33, no. 5 (November 27, 2018): 315–23. http://dx.doi.org/10.1515/rnam-2018-0026.

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Abstract A fast procedure for generation of regular tetrahedral finite element mesh for objects with complex shape cavities is proposed. The procedure like LBIE-Mesher can generate tetrahedral meshes for the volume interior to a polygonal surface, or for an interval volume between two surfaces having a complex shape and defined in STL-format. This procedure consists of several stages: generation of a regular tetrahedral mesh that fills the volume of the required object; generation of clipping for the uniform grid parts by a boundary surface; shifting vertices of the boundary layer to align onto the surface.We present a sequential and parallel implementation of the algorithm and compare their performance with existing generators of tetrahedral grids such as TetGen, NETGEN, and CGAL. The current version of the algorithm using the mobile GPU is about 5 times faster than NETGEN. The source code of the developed software is available on GitHub.

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Li, Guodong, Guoding Chen, Pengfeng Li, and Haixiao Jing. "Efficient and Accurate 3-D Numerical Modelling of Landslide Tsunami." Water 11, no. 10 (September 29, 2019): 2033. http://dx.doi.org/10.3390/w11102033.

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High-speed and accurate simulations of landslide-generated tsunamis are of great importance for the understanding of generation and propagation of water waves and for prediction of these natural disasters. A three-dimensional numerical model, based on Reynolds-averaged Navier–Stokes equations, is developed to simulate the landslide-generated tsunami. Available experiment data is used to validate the numerical model and to investigate the scale effect of numerical model according to the Froude similarity criterion. Based on grid convergence index (GCI) analysis, fourteen cases are arranged to study the sensitivity of numerical results to mesh resolution. Results show that numerical results are more sensitive to mesh resolution in near field than that in the propagation field. Nonuniform meshes can be used to balance the computational efficiency and accuracy. A mesh generation strategy is proposed and validated, achieving an accurate prediction and nearly 22 times reduction of computational cost. Further, this strategy of mesh generation is applied to simulate the Laxiwa Reservoir landslide tsunami. The results of this study provide an important guide for the establishment of a numerical model of the real-world problem of landslide tsunami.

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Tokunaga, Shogo, and Taro Arikawa. "STUDY ON SCOURING IN PILE OF OFFSHORE WIND FARMING BY NUMERICAL ANALYSIS USING BUILDING-CUBE METHOD." Coastal Engineering Proceedings, no. 36v (December 28, 2020): 42. http://dx.doi.org/10.9753/icce.v36v.sediment.42.

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In recent years, offshore wind farming has spread all over the world, and there has been rapid growth of not only conventional onshore wind farming but also offshore wind farming in the sea. However, there are many problems to be solved in offshore wind farming. Among them, the scour of the ocean floor caused by wave and tide has a great influence on the support structure. The purpose of this study is to clarify the scour phenomenon from the flow field and vortex generation conditions by numerical simulation using Building Cube Method. We conducted the simulation of the experiment which handles scouring around the monopile performed by Chen et al. (2018). The Building Cube Method was developed by Nakahashi and Kim (2004). In this study, we used CADMAS-BCM (developed by Arikawa et al.) that 3-D Navier-Stokes simulation model using the Building Cube Method. In this model, the 3-D Building Cube Method was applied using multiple roots. Moreover, because the calculation area is divided according to simple rules, it has features such as good compatibility with parallel computers, and grid generation by a simple method is useful for calculating the flow around objects with complex shapes. Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/OlJK_Qw_TwY

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De Basabe, Jonás D., and Mrinal K. Sen. "Grid dispersion and stability criteria of some common finite-element methods for acoustic and elastic wave equations." GEOPHYSICS 72, no. 6 (November 2007): T81—T95. http://dx.doi.org/10.1190/1.2785046.

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Purely numerical methods based on finite-element approximation of the acoustic or elastic wave equation are becoming increasingly popular for the generation of synthetic seismograms. We present formulas for the grid dispersion and stability criteria for some popular finite-element methods (FEM) for wave propagation, namely, classical and spectral FEM. We develop an approach based on a generalized eigenvalue formulation to analyze the dispersive behavior of these FEMs for acoustic or elastic wave propagation that overcomes difficulties caused by irregular node spacing within the element and the use of high-order polynomials, as is the case for spectral FEM. Analysis reveals that for spectral FEM of order four or greater, dispersion is less than 0.2% at four to five nodes per wavelength, and dispersion is not angle dependent. New results can be compared with grid-dispersion results of some classical finite-difference methods (FDM) used for acoustic or elastic wave propagation. Analysis reveals that FDM and classical FEM require a larger sampling ratio than a spectral FEM to obtain results with the same degree of accuracy. The staggered-grid FDM is an efficient scheme, but the dispersion is angle dependent with larger values along the grid axes. On the other hand, spectral FEM of order four or greater is isotropic with small dispersion, making it attractive for simulations with long propagation times.

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Müller, Andreas, Michal A. Kopera, Simone Marras, Lucas C. Wilcox, Tobin Isaac, and Francis X. Giraldo. "Strong scaling for numerical weather prediction at petascale with the atmospheric model NUMA." International Journal of High Performance Computing Applications 33, no. 2 (April 5, 2018): 411–26. http://dx.doi.org/10.1177/1094342018763966.

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Numerical weather prediction (NWP) has proven to be computationally challenging due to its inherent multiscale nature. Currently, the highest resolution global NWP models use a horizontal resolution of 9 km. At this resolution, many important processes in the atmosphere are not resolved. Needless to say, this introduces errors. In order to increase the resolution of NWP models, highly scalable atmospheric models are needed. The non-hydrostatic unified model of the atmosphere (NUMA), developed by the authors at the Naval Postgraduate School, was designed to achieve this purpose. NUMA is used by the Naval Research Laboratory, Monterey as the engine inside its next generation weather prediction system NEPTUNE. NUMA solves the fully compressible Navier–Stokes equations by means of high-order Galerkin methods (both spectral element as well as discontinuous Galerkin methods can be used). NUMA is capable of running middle and upper atmosphere simulations since it does not make use of the shallow-atmosphere approximation. This article presents the performance analysis and optimization of the spectral element version of NUMA. The performance at different optimization stages is analyzed using a theoretical performance model as well as measurements via hardware counters. Machine-independent optimization is compared to machine-specific optimization using Blue Gene (BG)/Q vector intrinsics. The best portable version of the main computations was found to be about two times slower than the best non-portable version. By using vector intrinsics, the main computations reach 1.2 PFlops on the entire IBM Blue Gene supercomputer Mira (12% of the theoretical peak performance). The article also presents scalability studies for two idealized test cases that are relevant for NWP applications. The atmospheric model NUMA delivers an excellent strong scaling efficiency of 99% on the entire supercomputer Mira using a mesh with 1.8 billion grid points. This allows running a global forecast of a baroclinic wave test case at a 3-km uniform horizontal resolution and double precision within the time frame required for operational weather prediction.

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Kadasch, Eckhard, Matthias Sühring, Tobias Gronemeier, and Siegfried Raasch. "Mesoscale nesting interface of the PALM model system 6.0." Geoscientific Model Development 14, no. 9 (September 3, 2021): 5435–65. http://dx.doi.org/10.5194/gmd-14-5435-2021.

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Abstract. In this paper, we present a newly developed mesoscale nesting interface for the PALM model system 6.0, which enables PALM to simulate the atmospheric boundary layer under spatially heterogeneous and non-stationary synoptic conditions. The implemented nesting interface, which is currently tailored to the mesoscale model COSMO, consists of two major parts: (i) the preprocessor INIFOR (initialization and forcing), which provides initial and time-dependent boundary conditions from mesoscale model output, and (ii) PALM's internal routines for reading the provided forcing data and superimposing synthetic turbulence to accelerate the transition to a fully developed turbulent atmospheric boundary layer. We describe in detail the conversion between the sets of prognostic variables, transformations between model coordinate systems, as well as data interpolation onto PALM's grid, which are carried out by INIFOR. Furthermore, we describe PALM's internal usage of the provided forcing data, which, besides the temporal interpolation of boundary conditions and removal of any residual divergence, includes the generation of stability-dependent synthetic turbulence at the inflow boundaries in order to accelerate the transition from the turbulence-free mesoscale solution to a resolved turbulent flow. We demonstrate and evaluate the nesting interface by means of a semi-idealized benchmark case. We carried out a large-eddy simulation (LES) of an evolving convective boundary layer on a clear-sky spring day. Besides verifying that changes in the inflow conditions enter into and successively propagate through the PALM domain, we focus our analysis on the effectiveness of the synthetic turbulence generation. By analysing various turbulence statistics, we show that the inflow in the present case is fully adjusted after having propagated for about two to three eddy-turnover times downstream, which corresponds well to other state-of-the-art methods for turbulence generation. Furthermore, we observe that numerical artefacts in the form of grid-scale convective structures in the mesoscale model enter the PALM domain, biasing the location of the turbulent up- and downdrafts in the LES. With these findings presented, we aim to verify the mesoscale nesting approach implemented in PALM, point out specific shortcomings, and build a baseline for future improvements and developments.

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Holt, Jason, Patrick Hyder, Mike Ashworth, James Harle, Helene T. Hewitt, Hedong Liu, Adrian L. New, et al. "Prospects for improving the representation of coastal and shelf seas in global ocean models." Geoscientific Model Development 10, no. 1 (February 1, 2017): 499–523. http://dx.doi.org/10.5194/gmd-10-499-2017.

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Abstract. Accurately representing coastal and shelf seas in global ocean models represents one of the grand challenges of Earth system science. They are regions of immense societal importance through the goods and services they provide, hazards they pose and their role in global-scale processes and cycles, e.g. carbon fluxes and dense water formation. However, they are poorly represented in the current generation of global ocean models. In this contribution, we aim to briefly characterise the problem, and then to identify the important physical processes, and their scales, needed to address this issue in the context of the options available to resolve these scales globally and the evolving computational landscape.We find barotropic and topographic scales are well resolved by the current state-of-the-art model resolutions, e.g. nominal 1∕12°, and still reasonably well resolved at 1∕4°; here, the focus is on process representation. We identify tides, vertical coordinates, river inflows and mixing schemes as four areas where modelling approaches can readily be transferred from regional to global modelling with substantial benefit. In terms of finer-scale processes, we find that a 1∕12° global model resolves the first baroclinic Rossby radius for only ∼ 8 % of regions < 500 m deep, but this increases to ∼ 70 % for a 1∕72° model, so resolving scales globally requires substantially finer resolution than the current state of the art.We quantify the benefit of improved resolution and process representation using 1∕12° global- and basin-scale northern North Atlantic nucleus for a European model of the ocean (NEMO) simulations; the latter includes tides and a k-ε vertical mixing scheme. These are compared with global stratification observations and 19 models from CMIP5. In terms of correlation and basin-wide rms error, the high-resolution models outperform all these CMIP5 models. The model with tides shows improved seasonal cycles compared to the high-resolution model without tides. The benefits of resolution are particularly apparent in eastern boundary upwelling zones.To explore the balance between the size of a globally refined model and that of multiscale modelling options (e.g. finite element, finite volume or a two-way nesting approach), we consider a simple scale analysis and a conceptual grid refining approach. We put this analysis in the context of evolving computer systems, discussing model turnaround time, scalability and resource costs. Using a simple cost model compared to a reference configuration (taken to be a 1∕4° global model in 2011) and the increasing performance of the UK Research Councils' computer facility, we estimate an unstructured mesh multiscale approach, resolving process scales down to 1.5 km, would use a comparable share of the computer resource by 2021, the two-way nested multiscale approach by 2022, and a 1∕72° global model by 2026. However, we also note that a 1∕12° global model would not have a comparable computational cost to a 1° global model in 2017 until 2027. Hence, we conclude that for computationally expensive models (e.g. for oceanographic research or operational oceanography), resolving scales to ∼ 1.5 km would be routinely practical in about a decade given substantial effort on numerical and computational development. For complex Earth system models, this extends to about 2 decades, suggesting the focus here needs to be on improved process parameterisation to meet these challenges.

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8

TSAY, TING-KUEI, and FU-SENG HSU. "NUMERICAL GRID GENERATION OF AN IRREGULAR REGION." International Journal for Numerical Methods in Engineering 40, no. 2 (January 30, 1997): 343–56. http://dx.doi.org/10.1002/(sici)1097-0207(19970130)40:2<343::aid-nme68>3.0.co;2-c.

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9

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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10

Steinberg, Stanly, and Patrick J. Roache. "Variational grid generation." Numerical Methods for Partial Differential Equations 2, no. 1 (1986): 71–96. http://dx.doi.org/10.1002/num.1690020107.

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11

Codd, A. L., T. A. Manteuffel, S. F. McCormick, and J. W. Ruge. "Multilevel First-Order System Least Squares for Elliptic Grid Generation." SIAM Journal on Numerical Analysis 41, no. 6 (January 2003): 2210–32. http://dx.doi.org/10.1137/s0036142902404418.

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12

Goto, Daisuke, Yousuke Sato, Hisashi Yashiro, Kentaroh Suzuki, Eiji Oikawa, Rei Kudo, Takashi M. Nagao, and Teruyuki Nakajima. "Global aerosol simulations using NICAM.16 on a 14 km grid spacing for a climate study: improved and remaining issues relative to a lower-resolution model." Geoscientific Model Development 13, no. 8 (August 25, 2020): 3731–68. http://dx.doi.org/10.5194/gmd-13-3731-2020.

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Abstract. High-performance computing resources allow us to conduct numerical simulations with a horizontal grid spacing that is sufficiently high to resolve cloud systems on a global scale, and high-resolution models (HRMs) generally provide better simulation performance than low-resolution models (LRMs). In this study, we execute a next-generation model that is capable of simulating global aerosols using version 16 of the Nonhydrostatic Icosahedral Atmospheric Model (NICAM.16). The simulated aerosol distributions are obtained for 3 years with an HRM using a global 14 km grid spacing, an unprecedentedly high horizontal resolution and long integration period. For comparison, a NICAM with a 56 km grid spacing is also run as an LRM, although this horizontal resolution is still high among current global aerosol climate models. The comparison elucidated that the differences in the various variables of meteorological fields, including the wind speed, precipitation, clouds, radiation fluxes and total aerosols, are generally within 10 % of their annual averages, but most of the variables related to aerosols simulated by the HRM are slightly closer to the observations than are those simulated by the LRM. Upon investigating the aerosol components, the differences in the water-insoluble black carbon and sulfate concentrations between the HRM and LRM are large (up to 32 %), even in the annual averages. This finding is attributed to the differences in the aerosol wet deposition flux, which is determined by the conversion rate of cloud to precipitation, and the difference between the HRM and LRM is approximately 20 %. Additionally, the differences in the simulated aerosol concentrations at polluted sites during polluted months between the HRM and LRM are estimated with normalized mean biases of −19 % for black carbon (BC), −5 % for sulfate and −3 % for the aerosol optical thickness (AOT). These findings indicate that the impacts of higher horizontal grid spacings on model performance for secondary products such as sulfate, and complex products such as the AOT, are weaker than those for primary products, such as BC. On a global scale, the subgrid variabilities in the simulated AOT and cloud optical thickness (COT) in the 1∘×1∘ domain using 6-hourly data are estimated to be 28.5 % and 80.0 %, respectively, in the HRM, whereas the corresponding differences are 16.6 % and 22.9 % in the LRM. Over the Arctic, both the HRM and the LRM generally reproduce the observed aerosols, but the largest difference in the surface BC mass concentrations between the HRM and LRM reaches 30 % in spring (the HRM-simulated results are closer to the observations). The vertical distributions of the HRM- and LRM-simulated aerosols are generally close to the measurements, but the differences between the HRM and LRM results are large above a height of approximately 3 km, mainly due to differences in the wet deposition of aerosols. The global annual averages of the effective radiative forcings due to aerosol–radiation and aerosol–cloud interactions (ERFari and ERFaci) attributed to anthropogenic aerosols in the HRM are estimated to be -0.293±0.001 and -0.919±0.004 W m−2, respectively, whereas those in the LRM are -0.239±0.002 and -1.101±0.013 W m−2. The differences in the ERFari between the HRM and LRM are primarily caused by those in the aerosol burden, whereas the differences in the ERFaci are primarily caused by those in the cloud expression and performance, which are attributed to the grid spacing. The analysis of interannual variability revealed that the difference in reproducibility of both sulfate and carbonaceous aerosols at different horizontal resolution is greater than their interannual variability over 3 years, but those of dust and sea salt AOT and possibly clouds were the opposite. Because at least 10 times the computer resources are required for the HRM (14 km grid) compared to the LRM (56 km grid), these findings in this study help modelers decide whether the objectives can be achieved using such higher resolution or not under the limitation of available computational resources.

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Lehtim�ki, Reijo. "On planar harmonic grid generation." Numerical Methods for Partial Differential Equations 15, no. 3 (May 1999): 305–15. http://dx.doi.org/10.1002/(sici)1098-2426(199905)15:3<305::aid-num3>3.0.co;2-3.

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14

Liao, G. "Variational approach to grid generation." Numerical Methods for Partial Differential Equations 8, no. 2 (March 1992): 143–47. http://dx.doi.org/10.1002/num.1690080205.

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15

Pistella, Francesca, and Rosa Maria Spitaleri. "Applied Scientific Computing VI: Numerical Grid Generation, Approximation and Visualization." Mathematics and Computers in Simulation 79, no. 8 (April 2009): 2333. http://dx.doi.org/10.1016/j.matcom.2009.01.014.

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16

Daripa, Prabir. "A New Theory for One-Dimensional Adaptive Grid Generation and Its Applications." SIAM Journal on Numerical Analysis 28, no. 6 (December 1991): 1635–60. http://dx.doi.org/10.1137/0728082.

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17

Conti, C., and R. Morandi. "Re-parameterisation technique in algebraic numerical grid generation via subdivision schemes." Applied Numerical Mathematics 51, no. 4 (December 2004): 487–96. http://dx.doi.org/10.1016/j.apnum.2004.06.005.

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18

Azarenok, Boris N. "Variational Barrier Method of Adaptive Grid Generation in Hyperbolic Problems of Gas Dynamics." SIAM Journal on Numerical Analysis 40, no. 2 (January 2002): 651–82. http://dx.doi.org/10.1137/s0036142900382727.

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19

Zhang, Y. G., Y. G. Bai, X. C. Yu, and Y. F. Liu. "Numerical Analysis of Active Cooling Structure of Engine Combustion Chamber." Advanced Materials Research 629 (December 2012): 564–69. http://dx.doi.org/10.4028/www.scientific.net/amr.629.564.

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With the convective heat transfer theory, numerical analysis of fluid-solid-heat coupling is implemented for the engine combustion chamber cooling structure based on finite element method and computational fluid dynamic method, thus to obtain valuable simulation results. Different components of the mesh generation method used which have different influences on the computational results are thought over during this analysis process, including different grid type, grid density and boundary layer meshes. Moreover, MPI parallel technique is also used to resolve the computation demands. The temperature distributions of the key parts in the cooling structure are investigated, which can be used as a significant reference for the thermal protection design of the engine combustion chamber.

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20

Arina, Renzo. "Orthogonal and conformal surface grid generation." Applied Numerical Mathematics 46, no. 3-4 (September 2003): 249–62. http://dx.doi.org/10.1016/s0168-9274(03)00045-x.

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21

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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22

Rane, S., and A. Kovačević. "Application of numerical grid generation for improved CFD analysis of multiphase screw machines." IOP Conference Series: Materials Science and Engineering 232 (August 2017): 012017. http://dx.doi.org/10.1088/1757-899x/232/1/012017.

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23

Pistella, Francesca, and Rosa Maria Spitaleri. "Applied Scientific Computing VII. Forward Numerical Grid Generation, Approximation and Simulation." Mathematics and Computers in Simulation 81, no. 3 (November 2010): 589. http://dx.doi.org/10.1016/j.matcom.2010.11.001.

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24

Athanasiadis, A. N., and H. Deconinck. "Object-oriented three-dimensional hybrid grid generation." International Journal for Numerical Methods in Engineering 58, no. 2 (2003): 301–18. http://dx.doi.org/10.1002/nme.764.

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Löhner, Rainald. "A parallel advancing front grid generation scheme." International Journal for Numerical Methods in Engineering 51, no. 6 (June 30, 2001): 663–78. http://dx.doi.org/10.1002/nme.175.abs.

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26

Hamimid, Sabar, and Messaoud Guellal. "Numerical analysis of combined natural convection-internal heat generation source-surface radiation." Thermal Science 20, no. 6 (2016): 1879–89. http://dx.doi.org/10.2298/tsci140315115h.

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Numerical study of combined laminar natural convection and surface radiation with internal heat generation is presented in this paper and computations are performed for an air-filled square cavity whose four walls have the same emissivity. Finite volume method through the concepts of staggered grid and SIMPLER algorithm has been applied, and the view factors are determined by analytical formula. A power scheme is also used in approximating advection-diffusion terms. Representative results illustrating the effects of emissivity and the internal heat generation on the streamlines and temperature contours within the enclosure are reported. In addition, obtained results for local and average convective and radiative Nusselt, for various parametric conditions, show that internal heat generation modifies significantly the flow and temperature fields.

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27

Andallan, Laek S. "On the Generation of a Hexagonal Collision Model for the Boltzmann equation." Computational Methods in Applied Mathematics 4, no. 3 (2004): 271–89. http://dx.doi.org/10.2478/cmam-2004-0016.

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AbstractIn this article we prove the existence of two different classes of regular hexagons in the hexagonal grid. We develop a generalized layer-wise construction of a hexagonal discrete velocity model and derive general formulae to identify all regular hexagons belonging to the grid. We also present some numerical results based on the hexagonal grid.

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Knupp, P., and R. Luczak. "Truncation error in grid generation: A case study." Numerical Methods for Partial Differential Equations 11, no. 6 (November 1995): 561–71. http://dx.doi.org/10.1002/num.1690110603.

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29

ECHEVERRI, P., T. YOKOSSI, N. J. BALMFORTH, and T. PEACOCK. "Tidally generated internal-wave attractors between double ridges." Journal of Fluid Mechanics 669 (January 11, 2011): 354–74. http://dx.doi.org/10.1017/s0022112010005069.

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A study is presented of the generation of internal tides by barotropic tidal flow over topography in the shape of a double ridge. An iterative map is constructed to expedite the search for the closed ray paths that form wave attractors in this geometry. The map connects the positions along a ray path of consecutive reflections from the surface, which is double-valued owing to the presence of both left- and right-going waves, but which can be made into a genuine one-dimensional map using a checkerboarding algorithm. Calculations are then presented for the steady-state scattering of internal tides from the barotropic tide above the double ridges. The calculations exploit a Green function technique that distributes sources along the topography to generate the scattering, and discretizes in space to calculate the source density via a standard matrix inversion. When attractors are present, the numerical procedure appears to fail, displaying no convergence with the number of grid points used in the spatial discretizations, indicating a failure of the Green function solution. With the addition of dissipation into the problem, these difficulties are avoided, leading to convergent numerical solutions. The paper concludes with a comparison between theory and a laboratory experiment.

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Khawaja, Aly, and Yannis Kallinderis. "Hybrid grid generation for turbomachinery and aerospace applications." International Journal for Numerical Methods in Engineering 49, no. 1-2 (2000): 145–66. http://dx.doi.org/10.1002/1097-0207(20000910/20)49:1/2<145::aid-nme927>3.0.co;2-w.

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31

Kovacevic, Ahmed. "Boundary adaptation in grid generation for CFD analysis of screw compressors." International Journal for Numerical Methods in Engineering 64, no. 3 (2005): 401–26. http://dx.doi.org/10.1002/nme.1376.

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32

Tsay, Ting-Kuei, John Wang, and Yung-Te Huang. "Numerical generation and grid controls of boundary-fitted conformal grids in multiply connected regions." International Journal for Numerical Methods in Engineering 67, no. 8 (2006): 1045–62. http://dx.doi.org/10.1002/nme.1618.

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Egidi, N., and P. Maponi. "A linearly constrained optimization problem for planar grid generation." Applied Numerical Mathematics 55, no. 3 (November 2005): 283–94. http://dx.doi.org/10.1016/j.apnum.2005.04.031.

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34

Basson, A., and B. Lakshminarayana. "Numerical Simulation of Tip Clearance Effects in Turbomachinery." Journal of Turbomachinery 117, no. 3 (July 1, 1995): 348–59. http://dx.doi.org/10.1115/1.2835668.

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The numerical formulation developed here includes an efficient grid generation scheme, particularly suited to computational grids for the analysis of turbulent turbo-machinery flows and tip clearance flows, and a semi-implicit, pressure-based computational fluid dynamics scheme that directly includes artificial dissipation, and is applicable to both viscous and inviscid flows. The value of this artificial dissipation is optimized to achieve accuracy and convergency in the solution. The numerical model is used to investigate the structure of tip clearance flows in a turbine nozzle. The structure of leakage flow is captured accurately, including blade-to-blade variation of all three velocity components, pitch and yaw angles, losses and blade static pressures in the tip clearance region. The simulation also includes evaluation of such quantities as leakage mass flow, vortex strength, losses, dominant leakage flow regions, and the spanwise extent affected by the leakage flow. It is demonstrated, through optimization of grid size and artificial dissipation, that the tip clearance flow field can be captured accurately.

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35

Polevikov, Victor K. "Methods for Numerical Modeling of Two-Dimensional Capillary Surfaces." Computational Methods in Applied Mathematics 4, no. 1 (2004): 66–93. http://dx.doi.org/10.2478/cmam-2004-0005.

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Abstract Certain methods for numerical solving plane and axially symmetric problems on equilibrium shapes of a capillary surface are presented. The methods possess a high order of approximation on a nonuniform grid. They are easy to realize, fairly universal and suitable for constructing not only simply connected but also doubly connected and disconnected surfaces, including strongly curved ones. It is shown that the iterative algorithms constructed are absolutely stable at each iteration. The condition for convergence of iterations is obtained within the framework of a linear theory. To describe peak-shaped configurations of a magnetic uid in a high magnetic field, an algorithm of generation of adaptive grid nodes in accordance with the surface curvature is proposed. The methods have been tested for the well-known problems of capillary hydrostatics on equilibrium shapes of a drop adjacent to the horizontal rotating plate under gravity, and of an isolated magneticuid drop in a high uniform magnetic field. It has been established that they adequately respond to the physical phenomenon of a crisis of equilibrium shapes, i.e., they can be adopted to investigate the stability of equilibrium states of a capillary surface.

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36

Zhu, J. "A hybrid differential-algebraic method for three-dimensional grid generation." International Journal for Numerical Methods in Engineering 29, no. 6 (May 1990): 1271–79. http://dx.doi.org/10.1002/nme.1620290611.

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37

Egidi, N., and P. Maponi. "A class of network optimization methods for planar grid generation." Applied Numerical Mathematics 52, no. 4 (March 2005): 363–79. http://dx.doi.org/10.1016/j.apnum.2004.08.004.

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38

Tao, Du, Fang Guo-hong, and Fang Xin-hua. "A layered numerical model for simulating the generation and propagation of internal tides over continental slope II stability analysis." Chinese Journal of Oceanology and Limnology 17, no. 3 (September 1999): 252–57. http://dx.doi.org/10.1007/bf02842603.

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39

Mathur, J. S., and S. K. Chakrabartty. "An approximate factorization scheme for elliptic grid generation with control functions." Numerical Methods for Partial Differential Equations 10, no. 6 (November 1994): 703–13. http://dx.doi.org/10.1002/num.1690100606.

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40

Barrera-Sánchez, Pablo, Longina Castellanos Noda, Francisco J. Domínguez-Mota, Guilmer F. González Flores, and Angel Pérez Domínguez. "Adaptive discrete harmonic grid generation." Mathematics and Computers in Simulation 79, no. 6 (February 2009): 1792–809. http://dx.doi.org/10.1016/j.matcom.2007.04.015.

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41

Kim, Hyun-Goo, and Wan-Ho Jeon. "Experimental and Numerical Analysis of a Seawall’s Effect on Wind Turbine Performance." Energies 12, no. 20 (October 14, 2019): 3877. http://dx.doi.org/10.3390/en12203877.

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For the purposes of this study, a wind tunnel experiment and a numerical analysis during ebb and high tides were conducted to determine the positive and negative effects of wind flow influenced by a seawall structure on the performance of wind turbines installed along a coastal seawall. The comparison of the wind flow field between a wind tunnel experiment performed with a 1/100 scale model and a computational fluid dynamics (CFD) analysis confirmed that the MP k-turbulence model estimated flow separation on the leeside of the seawall the most accurately. The CFD analysis verified that wind speed-up occurred due to the virtual hill effect caused by the seawall’s windward slope and the recirculation zone of its rear face, which created a positive effect by mitigating wind shear while increasing the mean wind speed in the wind turbine’s rotor plane. In contrast, the turbulence effect of flow separation on the seawall’s leeside was limited to the area below the wind turbine rotor, and had no negative effect. The use of the CFD verified with the comparison with the wind tunnel experiment was extended to the full-scale seawall, and the results of the analysis based on the wind turbine Supervisory Control and Data Acquisition (SCADA) data of a wind farm confirmed that the seawall effect was equivalent to a 1.5% increase in power generation as a result of a mitigation of the wind profile.

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42

Montgomery, Matthew, and Sanford Fleeter. "A locally analytic technique applied to grid generation by elliptic equations." International Journal for Numerical Methods in Engineering 38, no. 3 (February 15, 1995): 421–32. http://dx.doi.org/10.1002/nme.1620380305.

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43

ZAKHARIAN, A. R., M. BRIO, J. K. HUNTER, and G. M. WEBB. "The von Neumann paradox in weak shock reflection." Journal of Fluid Mechanics 422 (November 3, 2000): 193–205. http://dx.doi.org/10.1017/s0022112000001609.

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We present a numerical solution of the Euler equations of gas dynamics for a weak-shock Mach reflection in a half-space. In our numerical solutions, the incident, reflected, and Mach shocks meet at a triple point, and there is a supersonic patch behind the triple point, as proposed by Guderley. A theoretical analysis supports the existence of an expansion fan at the triple point, in addition to the three shocks. This solution is in complete agreement with the numerical solution of the unsteady transonic small-disturbance equations obtained by Hunter & Brio (2000), which provides an asymptotic description of a weak-shock Mach reflection. The supersonic patch is extremely small, and this work is the first time it has been resolved in a numerical solution of the Euler equations. The numerical solution uses six levels of grid refinement around the triple point. A delicate combination of numerical techniques is required to minimize both the effects of numerical diffusion and the generation of numerical oscillations at grid interfaces and shocks.

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44

Chiu, Cheng Ping, and Tser Son Wu. "STUDY OF AIR MOTION IN RECIPROCATING ENGINE USING AN ALGEBRAIC GRID GENERATION TECHNIQUE." Numerical Heat Transfer, Part A: Applications 17, no. 3 (April 1990): 309–27. http://dx.doi.org/10.1080/10407789008944745.

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45

Mei, L., Y. Xue, G. de Leeuw, T. Holzer-Popp, J. Guang, Y. Li, L. Yang, et al. "Retrieval of aerosol optical depth over land based on a time series technique using MSG/SEVIRI data." Atmospheric Chemistry and Physics 12, no. 19 (October 10, 2012): 9167–85. http://dx.doi.org/10.5194/acp-12-9167-2012.

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Abstract. A novel approach for the joint retrieval of aerosol optical depth (AOD) and aerosol type, using Meteosat Second Generation – Spinning Enhanced Visible and Infrared Imagers (MSG/SEVIRI) observations in two solar channels, is presented. The retrieval is based on a Time Series (TS) technique, which makes use of the two visible bands at 0.6 μm and 0.8 μm in three orderly scan times (15 min interval between two scans) to retrieve the AOD over land. Using the radiative transfer equation for plane-parallel atmosphere, two coupled differential equations for the upward and downward fluxes are derived. The boundary conditions for the upward and downward fluxes at the top and at the bottom of the atmosphere are used in these equations to provide an analytic solution for the AOD. To derive these fluxes, the aerosol single scattering albedo (SSA) and asymmetry factor are required to provide a solution. These are provided from a set of six pre-defined aerosol types with the SSA and asymmetry factor. We assume one aerosol type for a grid of 1°×1° and the surface reflectance changes little between two subsequent observations. A k-ratio approach is used in the inversion to find the best solution of atmospheric properties and surface reflectance. The k-ratio approach assumes that the surface reflectance is little influenced by aerosol scattering at 1.6 μm and therefore the ratio of surface reflectances in the solar band for two subsequent observations can be well-approximated by the ratio of the reflectances at 1.6 μm. A further assumption is that the surface reflectance varies only slightly over a period of 30 min. The algorithm makes use of numerical minimisation routines to obtain the optimal solution of atmospheric properties and surface reflectance by selection of the most suitable aerosol type from pre-defined sets. A detailed analysis of the retrieval results shows that it is suitable for AOD retrieval over land from SEVIRI data. Six AErosol RObotic NETwork (AERONET) sites with different surface types are used for detailed analysis and 42 other AERONET sites are used for validation. From 445 collocations representing stable and homogeneous aerosol type, we find that >75% of the MSG-retrieved AOD at 0.6 and 0.8 μm values compare favourably with AERONET observed AOD values, within an error envelope of ± 0.05 ± 0.15 τ and a high correlation coefficient (R>0.86). The AOD datasets derived using the TS method with SEVIRI data is also compared with collocated AOD products derived from NASA TERRA and AQUA MODIS (The Moderate-resolution Imaging Spectroradiometer) data using the Dark Dense Vegetation (DDV) method and the Deep Blue algorithms. Using the TS method, the AOD could be retrieved for more pixels than with the NASA Deep Blue algorithm. This method is potentially also useful for surface reflectance retrieval using SEVIRI observations. The current paper focuses on AOD retrieval and analysis, and the analysis and validation of reflectance will be given in a following paper.

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46

Mei, L., Y. Xue, G. de Leeuw, T. Holzer-Popp, J. Guang, Y. Li, L. Yang, et al. "Retrieval of aerosol optical depth over land based on a time series technique using MSG/SERIVI data." Atmospheric Chemistry and Physics Discussions 12, no. 2 (February 3, 2012): 4031–71. http://dx.doi.org/10.5194/acpd-12-4031-2012.

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Abstract. A novel approach for the joint retrieval of aerosol optical depth (AOD) and surface reflectance, using Meteosat Second Generation – Spinning Enhanced Visible and Infrared Imagers (MSG/SEVIRI) observations in two solar channels, is presented. The retrieval is based on a time series (TS) technique, which makes use of the two visible bands at 0.6 μm and 0.8 μm in three orderly scan times (15 min interval between two scans) to retrieve the AOD over land. Using the radiative transfer equation for plane-parallel atmospheres two coupled differential equations for the upward and downward fluxes are derived. The boundary conditions for the upward and downward fluxes at the top and at the bottom of the atmosphere are used in these equations to provide an analytic solution for the surface reflectance. To derive these fluxes, the aerosol single scattering albedo (SSA) and asymmetry factor are required to provide a solution. These are provided from a set of six pre-defined aerosol types with the SSA and asymmetry factor (g). We assume one aerosol type for a grid of 1° × 1° and the surface reflectance changes little between two consequent scans. A k approximation was used in the inversion to find the best solution of atmospheric properties and surface reflectance. The algorithm makes use of numerical minimisation routines to obtain the optimal solution of atmospheric properties and surface reflectance by selection of the most suitable aerosol type from pre-defined sets. Also, it is assumed that the surface reflectance is little influenced by aerosol scattering at 1.6 μm and therefore the ratio of surface reflectances in the solar band for two consequent scans can be well-approximated by the ratio of the reflectances at 1.6 μm. A further assumption is that the surface reflectance varies only slightly over a period of 30 min. A detailed analysis of the retrieval results show that it is suitable for AOD retrieval over land. Six Aerosol Robotic Network (AERONET) sites with different surface types were used for detailed analysis and 42 other AERONET sites were used for validation. From 445 collocations representing stable and homogeneous aerosol type, we found that >75% of MSG-retrieved AOD values compared to AERONET observed values with an error envelope of ±0.05 ± 0.15τ and a high correlation (R > 0.86). The AOD datasets derived using the TS method with SEVIRI data was also compared with collocated AOD products derived from the NASA TERRA and AQUA MODIS data using the dark dense vegetation (DDV) method and the Deep Blue algorithms. Using the TS method, AOD could be retrieved for more pixels than with the NASA Deep Blue algorithm. The AOD values derived compare favourably.

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47

Fang, Jiunn, Ijaz H. Parpia, and Stephen R. Kennon. "Sweepline algorithm for unstructured-grid generation on two-dimensional non-convex domains." International Journal for Numerical Methods in Engineering 36, no. 16 (August 30, 1993): 2761–78. http://dx.doi.org/10.1002/nme.1620361606.

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48

Baty, Roy S., and Philip J. Morris. "Conformal grid generation for high aspect ratio simply and doubly connected regions." International Journal for Numerical Methods in Engineering 38, no. 22 (November 30, 1995): 3817–30. http://dx.doi.org/10.1002/nme.1620382206.

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49

Chiu, Cheng Ping, and Ying Sheng Kuo. "STUDY OF TURBULENT HEAT TRANSFER IN RECIPROCATING ENGINE USING AN ALGEBRAIC GRID GENERATION TECHNIQUE." Numerical Heat Transfer, Part A: Applications 27, no. 3 (March 1995): 255–71. http://dx.doi.org/10.1080/10407789508913699.

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50

Liu, Xi Kang, Jian Hai Zhang, Rong Gang Yin, and Qiong Yang. "Mesh Generation for Arch Dam Abutment Slip Block Based on Virtual Grid." Applied Mechanics and Materials 170-173 (May 2012): 1954–61. http://dx.doi.org/10.4028/www.scientific.net/amm.170-173.1954.

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Abstract. In order to generate mesh for arch dam abutment slip block automatically, virtual grid method is proposed based on grid-based automatic generation algorithm. The proposed algorithm avoids generating initial grid in one time, but intersects the model with a series of plane sections firstly. Then form initial grid by using vector intersection method for adjacent sections. By modifying initial grid, a layer of mesh is formed. The algorithm proposed can better adapt to complex topography and generates hexahedral meshes for the block of arch dam abutment automatically. The method can present data for limit equilibrium analysis and numerical calculation method such as finite element method. Based on original topography and structural plane data, the automatic identification, generation and meshing of arch dam abutment block is accomplished.

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