2.6.1 Observations at grid points

2005 ◽  
pp. 208-217
Author(s):  
G. Krause
Keyword(s):  
Grid Points

On the construction of orthogonal curvilinear grids for regional oceanic modeling: algorithm and user guide

2020 ◽  
Vol 48 (4) ◽  
pp. 45-111
Author(s):  
A. F. Shepetkin
Keyword(s):  
Inverse Problem ◽  
Numerical Solution ◽  
Elliptic Problem ◽  
Software Package ◽  
Conformal Transformation ◽  
Iterative Procedure ◽  
Geometric Shape ◽  
Curvilinear Grids ◽  
Grid Points ◽  
Grid Nodes

A new algorithm for constructing orthogonal curvilinear grids on a sphere for a fairly general geometric shape of the modeling region is implemented as a “compile-once - use forever” software package. It is based on the numerical solution of the inverse problem by an iterative procedure -- finding such distribution of grid points along its perimeter, so that the conformal transformation of the perimeter into a rectangle turns this distribution into uniform one. The iterative procedure itself turns out to be multilevel - i.e. an iterative loop built around another, internal iterative procedure. Thereafter, knowing this distribution, the grid nodes inside the region are obtained solving an elliptic problem. It is shown that it was possible to obtain the exact orthogonality of the perimeter at the corners of the grid, to achieve very small, previously unattainable level of orthogonality errors, as well as make it isotropic -- local distances between grid nodes about both directions are equal to each other.

ADAPTAÇÃO E APLICAÇÃO DE MÉTODOS DE INTELIGÊNCIA COMPUTACIONAL PARA A ESTIMAÇÃO DE UMA FONTE DE POLUENTES EM ESTUÁRIOS

Engevista ◽  
2014 ◽  
Vol 17 (2) ◽  
pp. 152
Author(s):  
Radael De Souza Parolin ◽  
Pedro Paulo Gomes Watts Rodrigues ◽  
Antônio J. Silva Neto
Keyword(s):  
Computational Intelligence ◽  
Computational Models ◽  
Source Position ◽  
Iterative Search ◽  
Contaminant Source ◽  
Resources Management ◽  
Search Spaces ◽  
Grid Points ◽  
Computational Intelligence Methods

The quality of a given water body can be assessed through the analysis of a number of indicators. Mathematical and computational models can be built to simulate the behavior of these indicators (observable variables), in such a way that different scenarios can be generated, supporting decisions regarding water resources management. In this study, the transport of a conservative contaminant in an estuarine environment is simulated in order to identify the position and intensity of the contaminant source. For this, it was formulated an inverse problem, which was solved through computational intelligence methods. This approach required adaptations to these methods, which had to be modified to relate the source position to the discrete mesh points of the domain. In this context, two adaptive techniques were developed. In one, the estimated points are projected to the grid points, and in the other, points are randomly selected in the iterative search spaces of the methods. The results showed that the methodology here developed has a strong potential in water bodies’ management and simulation.

scholarly journals Image-based textile decoding

2020 ◽  
pp. 1-14
Author(s):  
Siqiang Chen ◽  
Masahiro Toyoura ◽  
Takamasa Terada ◽  
Xiaoyang Mao ◽  
Gang Xu
Keyword(s):  
Deep Learning ◽  
Grid Point ◽  
Intermediate Representation ◽  
Training Set ◽  
Binary Matrix ◽  
The Matrix ◽  
Correct Pattern ◽  
Grid Points ◽  
Textile Fabric ◽  
Direct Correspondence

A textile fabric consists of countless parallel vertical yarns (warps) and horizontal yarns (wefts). While common looms can weave repetitive patterns, Jacquard looms can weave the patterns without repetition restrictions. A pattern in which the warps and wefts cross on a grid is defined in a binary matrix. The binary matrix can define which warp and weft is on top at each grid point of the Jacquard fabric. The process can be regarded as encoding from pattern to textile. In this work, we propose a decoding method that generates a binary pattern from a textile fabric that has been already woven. We could not use a deep neural network to learn the process based solely on the training set of patterns and observed fabric images. The crossing points in the observed image were not completely located on the grid points, so it was difficult to take a direct correspondence between the fabric images and the pattern represented by the matrix in the framework of deep learning. Therefore, we propose a method that can apply the framework of deep learning viau the intermediate representation of patterns and images. We show how to convert a pattern into an intermediate representation and how to reconvert the output into a pattern and confirm its effectiveness. In this experiment, we confirmed that 93% of correct pattern was obtained by decoding the pattern from the actual fabric images and weaving them again.

A multivariate spectral quasi-linearization method for the solution of (2+1) dimensional Burgers’ equations

2020 ◽  
Vol 21 (7-8) ◽  
pp. 683-691
Author(s):  
Phumlani G. Dlamini ◽  
Vusi M. Magagula
Keyword(s):  
Collocation Method ◽  
Three Dimensional ◽  
Linearization Method ◽  
High Accuracy ◽  
Time Variable ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Burgers Equations ◽  
Grid Points ◽  
Linearization Techniques

AbstractIn this paper, we introduce the multi-variate spectral quasi-linearization method which is an extension of the previously reported bivariate spectral quasi-linearization method. The method is a combination of quasi-linearization techniques and the spectral collocation method to solve three-dimensional partial differential equations. We test its applicability on the (2 + 1) dimensional Burgers’ equations. We apply the spectral collocation method to discretize both space variables as well as the time variable. This results in high accuracy in both space and time. Numerical results are compared with known exact solutions as well as results from other papers to confirm the accuracy and efficiency of the method. The results show that the method produces highly accurate solutions and is very efficient for (2 + 1) dimensional PDEs. The efficiency is due to the fact that only few grid points are required to archive high accuracy. The results are portrayed in tables and graphs.

Evaluation of pairwise distances among orthogonal grid points in hypercube

2017 ◽  
Author(s):  
Václav Sadílek ◽  
Miroslav Vořechovský ◽  
Magdalena Šmídová
Keyword(s):  
Orthogonal Grid ◽  
Grid Points

The Use of Subgrid Transport Equations in a Three-Dimensional Model of Atmospheric Turbulence

1973 ◽  
Vol 95 (3) ◽  
pp. 429-438 ◽  
Author(s):  
J. W. Deardorff
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Transport Equations ◽  
Subgrid Scale ◽  
Reynolds Stresses ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Truncation Errors ◽  
Subgrid Scales ◽  
Grid Points

A three-dimensional numerical model of turbulence in an atmospheric boundary layer has been revised to utilize subgrid transport equations for the subgrid Reynolds stresses and fluxes rather than subgrid eddy coefficients. It was applied to a daytime boundary layer over heated ground in a region of horizontal area 8km square and 2km deep, utilizing 40×40×40 grid points. The constraints involved in selecting four important subgrid closure constants are discussed in some detail, along with maintenance of realizability on the subgrid scale. The results indicate that the subgrid transport equations produce subgrid Reynolds stresses and fluxes which realistically simulate the transfer of larger scale variance to subgrid scales, provided truncation errors due to advective terms are not too large. They also show the superiority of this method over the use of (nonstability dependent) nonlinear eddy coefficients in maintaining the sharpness of the inversion base which lies above the mixed layer.

Effects of Particle-Particle Collisions on Particle Concentration in a Turbulent Channel Flow

2006 ◽  
Author(s):  
H. Nasr ◽  
G. Ahmadi ◽  
J. B. McLaughlin
Keyword(s):  
Particle Concentration ◽  
Random Distribution ◽  
Pseudospectral Method ◽  
Time History ◽  
Turbulent Channel Flow ◽  
Navier Stokes ◽  
Particle Collisions ◽  
Navier Stokes Equation ◽  
History Of ◽  
Grid Points

This study is concerned with the effect of inter particle collisions on the particle concentration in turbulent duct flows. The time history of the instantaneous turbulent velocity vector was generated by the two-way coupled direct numerical simulation (DNS) of the Navier-Stokes equation via a pseudospectral method. The particle equation of motion included the Stokes drag, the Saffman lift, and the gravitational forces. The effect of particles on the flow is included in the analysis via a feedback force on the grid points. Several simulations for three classes of particles (28 μm Lycopodia, 50μm glass and 70μm copper) and different mass loadings were performed, and the effect of inter particle collisions on the particle concentration was evaluated and discussed. It was found that the particle-particle collisions reduce the tendency of particles to accumulate near the wall. This might be because collisions decorrelate particles with coherent eddies which are responsible for accumulation of particles near the wall. The spatial distribution of particles at the channel centerplane was compared with the experimental results of Fessler et al. (1994). The simulation results showed that the copper and glass particles had a random distribution while Lycopodium particles showed a non-random distribution with bands of particles that were preferentially concentrated.

Accuracy Analysis of DEM Based on Coons Surface

2011 ◽  
Vol 65 ◽  
pp. 214-217
Author(s):  
Yao Ge Wang ◽  
Peng Yuan Wang
Keyword(s):  
Spatial Pattern ◽  
Spatial Autocorrelation ◽  
Boundary Curve ◽  
Digital Elevation ◽  
Grid Points ◽  
Elevation Model ◽  
Global Spatial Autocorrelation ◽  
Core Problem ◽  
Dem Model ◽  
Better Than

Interpolation is the core problem of Digital Elevation Model (DEM). The Coons DEM model is better than bilinear interpolation and moving surface fitting. It is constructed by grid boundary curve, the curve interpolates by some adjoining grid points. Its spatial pattern of error is random in global area, there is no significant global spatial autocorrelation, but it is an increasing trend along with the terrain average gradient increases.There is significant local spatial autocorrelation, the spatial pattern of error converges strongly in local areas.

Grid adaptation for unsteady flow computations

1997 ◽  
Vol 211 (4) ◽  
pp. 237-250 ◽  
Author(s):  
C B Allen
Keyword(s):  
Unsteady Flow ◽  
Unsteady Flows ◽  
Processing Unit ◽  
Flow Solver ◽  
Transfinite Interpolation ◽  
Central Processing ◽  
Grid Adaptation ◽  
Euler Flows ◽  
Adaptation Procedure ◽  
Grid Points

A grid adaptation procedure suitable for use during unsteady flow computations is described. Transfinite interpolation is used to generate structured grids for the computation of steady and unsteady Euler flows past aerofoils. This technique is well suited to unsteady flows, since instantaneous grid positions and speeds required by the flow solver are available directly from the algebraic mapping. A different approach to grid adaptation is described, wherein adaptation is performed by redistributing the interpolation parameters, instead of the physical grid positions. This results in the adapted grid positions, and hence speeds, still being available algebraically. Grid adaptation during an unsteady computation is performed continuously by imposing an ‘adaptation velocity’ on grid points, thereby applying the adaptation over several time steps and avoiding the interpolation of the solution from one grid to another, which is associated with instantaneous adaptation. For both steady and unsteady flows the adapted grid technique is shown to produce sharper shock resolution for a very small increase in CPU (central processing unit) requirements.

scholarly journals A dynamic continental runoff routing model applied to the last Northern Hemisphere deglaciation

2011 ◽  
Vol 4 (4) ◽  
pp. 2723-2750
Author(s):  
H. Goelzer ◽  
I. Janssens ◽  
J. Nemec ◽  
P. Huybrechts
Keyword(s):  
Northern Hemisphere ◽  
Ice Sheet ◽  
Ocean Model ◽  
Isostatic Adjustment ◽  
Freshwater Fluxes ◽  
Continental Runoff ◽  
Grid Points ◽  
Lake Drainage ◽  
Spatially Varying ◽  
Runoff Routing

Abstract. We describe and evaluate a dynamical continental runoff routing model for the Northern Hemisphere that calculates the runoff pathways in response to topographic modifications due to changes in ice thickness and isostatic adjustment. The algorithm is based on the steepest gradient method and takes as simplifying assumption that depressions are filled at all times and water drains through the lowest outlet points. It also considers changes in water storage and lake drainage that become important in the presence of large ice dammed proglacial lakes. Although applicable to other scenarios as well, the model was conceived to study the routing of freshwater fluxes during the last Northern Hemisphere deglaciation. For that specific application we simulated the Northern Hemisphere ice sheets with an existing 3-D thermomechanical ice sheet model, which calculates changes in topography due to changes in ice cover and isostatic adjustment, as well as the evolution of freshwater fluxes resulting from surface ablation, iceberg calving and basal melt. The continental runoff model takes this input, calculates the drainage pathways and routes the freshwater fluxes to the surface grid points of an existing ocean model. This results in a chronology of temporally and spatially varying freshwater fluxes from the Last Glacial Maximum to the present day. We analyse the dependence of the runoff routing to grid resolution and parameters of the isostatic adjustment module of the ice sheet model.

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