Corner point grid

More material and illustrations relating to corner point grids can be foimd in Section 7.1 on structmal modelfing. 

Geometry, Topology and Construction of Corner Point Grids The main components of a corner point grid are ... 

Input Data for Comer Point Grids In the earliest corner point grid building applications, the input data were in the form of horizons and fault traces. The fault traces were used to drive the construction of the tubes. The sides of a particular sequence of coordinate tubes then defined the fault surfaces. Horizons were used as the tube dividing surfaces. This workflow is still widely used, although it can involve a lot of work in editing fault traces so that they lie on their associated fault surface. An early case study is [74]. Often the horizon surfaces are inconsistent as they are constructed separately from one another, and the fault traces are assigned separately to each surface. If the... 

When building surfaces directly inside the corner point grid application there are no problems with reverse faults, as the coordinate lines conform to the fault surfaces, and in the local coordinate system defined by the coordinate tubes there are no reverse faults. This is very convenient and powerful. The approach has only been partially exploited so far, and one looks forward to improvements in efficiency and quality. Much more remains to be done with regard to the proper evaluation of statistical uncertainty in structural modelling. Some discussion of this can be found in [152]. 

Reservoir simulators usually handle two different t3q>es of grid geometry Block-Centred (BC) and Corner-Point (CP), as illustrated in Figure 9. These geometries have either tetragons in two dimensions or hexahedrons in three dimensions as grid cell shapes. 

Fig. 9. Comparison of Block Centred (BC) and Corner Point (CP) grid geometries. BC grids (left) are simply formed by cells with parallelepiped shapes only. Cells forming CP grids (right) can have less restricted shape thereby allowing CP grids to reproduce most kind of geological structure.

Fig. 10. [Reproduced in colour in Plate 20 on page 435.] Cell connection across fault plane. Left Block Centred (BC) grid. Right Corner Point (CP) grid. Colour scale given by oil saturation values. Fault plane is not taken into account with the BC grid. Cells are connected according to their grid indices and not their physical location in space.

The first step in applying FEA is the construction of a model that breaks a component into simple standardized shapes or (usual term) elements located in space by a common coordinate grid system. The coordinate points of the element corners, or nodes, are the locations in the model where output data are provided. In some cases, special elements can also be used that provide additional nodes along their length or sides. Nodal stiffness properties are identified, arranged into matrices, and loaded into a computer where they are processed with certain applied loads and boundary conditions to calculate displacements and strains imposed by the loads (Appendix A PLASTICS DESIGN TOOLBOX). 

The resulting equations are solved numerically to compute the film thickness distribution or the interface shapes and the radius of the meniscus at the channel s corner. The implicit conservative scheme was used to obtain the solution. We used non-uniform grid pattern near moving film-meniscus contact point. Simultaneously with calculation of the interface shape, the heat transfer problem has been solved in the symmetry element of the channel. For the case of uniform heat production in the wall we have solved conservation energy equations in channel wall area ... 

The least-squares procedure used to evaluate the coefficients involves sampling r (r ) on a grid of points, typically a radial distribution based on that of Herman and Skillman (every tenth point) coupled with an angular mesh consisting of the 12 vertices of a regular icosahedron or 14 points defined by the corners and face centers of a cube. Both of these grids are accurate through fifth-order spherical harmonics. 

Normally, the steric and electrostatic fields are kept separate for ease of interpretation of the results. Grid points without variance (e.g. inside the volume shared by all molecules) or with small variance (e.g. in the corners of the box, far away from the van der Waals spheres of the molecules) are eliminated before the PLS analysis is performed. 

Atlantic Rainforest Sensor Net Research. In 2009, Microsoft Research collaborated with researchers from The Johns Hopkins University, the Universi-dade de Sao Paolo, the Fundagao de Amparo a Pes-quisa do Estatdo de Sao Paulo (FAPESP), and the Instituto Nacional de Pesquisas Espaciais (INPE, the Brazilian National Institute for Space Research) to collect data about the microecology of the Serra do Mar rainforest located in the southeast corner of Brazil. To collect the data, a grid of hundreds of wireless sensors collected 18 million data points over... 

FIGURE 8 The role of processor 0 (in the bottom left corner). The update stencil, Eq. (4), is applied to each point at which 0 is unknown. To update the grid points on the upper and right-hand boundaries, processor 0 must communicate with the processors above and to the right of it. 

FIGURE 7-6 The points in the lower right-hand corner are a symptom oi air-grid failure. 

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