Grid lines

Subdivision or discretization of the flow domain into cells or elements. There are methods, called boundary element methods, in which the surface of the flow domain, rather than the volume, is discretized, but the vast majority of CFD work uses volume discretization. Discretization produces a set of grid lines or cuives which define a mesh and a set of nodes at which the flow variables are to be calculated. The equations of motion are solved approximately on a domain defined by the grid. Curvilinear or body-fitted coordinate system grids may be used to ensure that the discretized domain accurately represents the true problem domain. 

Traversing The process of moving across a grid line in a duct or on a hood with a Pitot tube in order to determine the velocity or pressure distribution. 

Example 4. A grid in a two-dimensional domain. Our final example is connected with a complex domain G in the plane x = (a , x ) of rather complicated configuration with the boundary F. One way of proceeding is to subdivide into sets of rectangles by equally spaced grid lines parallel to Ox ... 

Highly skewed cells should be avoided. The angles between the grid lines of a hexahedral mesh should be 90°. Angles < 40° or > 140° often imply a reduced accuracy or numerical instabilities. 

Fig. 3.3.10 Tagging of water flow in a bed packed with 7 mm diameter beads. The width of the grid line is 2 mm.

The plot with default settings is quite useless unless we use ngrid to superimpose the closed-loop gain and phase grid lines. Instead of zooming in, we can reset the axes with ... 

Figure 3.2 STM images obtained with a CO-terminated tip, Vt = 70 mV and /t= 1 nA. (a) Isolated CO molecule, (b) two O atoms (adsorbed on the nearest fourfold hollow sites along the [1 1 0] direction), (c) CO and two O atoms separated by 6.1 A along the [0 0 1] direction, and (e) O-CO-O complex. Grid lines are drawn through the silver surface atoms. Scan area of (a-c) and (e) is 25 A x 25 A.

Figure 3.3 Reaction of a CO molecule released from a CO-terminated tip with an O atom adsorbed on the surface, (a) STM image, taken with a CO-terminated tip, of two O atoms separated by two lattice spacings (2 x 2.89 A) along the [11 0] direction. Grid lines are drawn through the silver surface atoms, (b) Tunneling current during a 1470 mV sample bias pulse with the CO-terminated tip over one of the two O atoms (denoted by Two current rises...

Figure 8.5 Sequential images ofTiC>2(l 1 0) showingthe splitting of an OHb pair mediated by a water molecule at 187 K. OHb groups are labeled with white circles and water on Tisc sites is labeled with black squares. Solid grid lines intersect the Ob sites whereas dashed gridlines are along Ti5c rows. (Modified with permission from Ref. [19].)...

For purposes of illustration only, to circumvent the problem of a zero determinant but still show the distributions of uncertainty and information in this design, a seventh experiment was added at a factor combination just slightly removed from one of the hexagonal points (at jc, = 2.000, X2 = 0.001). The hexagonal points were also adjusted somewhat to coincide with the grid lines in the pseudo-three-dimensional plots (this is equivalent to a minor adjustment of scale in the X2 dimension). Neither of these modifications significantly affects the overall conclusions to be drawn from this example. The actual design is... 

Fig. 1. Kriged and contoured cross-section of sericite / (sericite + chlorite)) 100 Index (plotted in percent) along A - A on McIntyre grid line 3500E through the HMC deposit. White diamonds indicate sample locations. Specific rock units such as C15 are labeled with abbreviations. The Cu-Au zone is indicated cross-hatching.

Fig. 4. Kriged cross-section of 5 Occ along McIntyre grid line 3500E through the HMC deposit. White dots indicate sample locations.

Person 1 Lightly sketch in grid lines on the diagram and use them to determine the composition at the indicated point. 

The diametral compression test is performed by compressing a thick disc along a diameter of the specimen. A diameter-to-thickness ratio of approximately 3 is preferred. Figure 17 shows this test, including grid lines and gages for measuring the strains developed as the sample is compressed between the tester platens. 

Fig. 4.25 Map of the locations of an adatom on a W (110) surface after about 300 heating periods. Each dot represents an observed location of the adatom. Only a fraction of the about 300 locations are shown. These dots are clustered, and the clustery are found to register with slightly curved grid lines parallel to the [111] and [111] surface channel directions. Using this map, the length calibration can then be done accurately from the known size of the surface channels.

Figure 7.16 Gibbs-Roozeboom grid-lines (at 0.1 increments) for mole fractions of (a) component A, (b) component B, and (c) component C. In each case, the heavy line runs from x = 0 ( 0 ) to x = 1 (at the labeled vertex).

In systems involving three components, composition is plotted on a triangular section (Figure 6.2). Pure components are represented at the comers and the grid lines show the amount of each component. All of the lines parallel to AB are lines on which the %C is constant. Those nearest C have the greatest amount of C. To represent temperature, a third dimension is needed. Figure 6.3 is a sketch of a three-dimensional ternary diagram in which temperature is the vertical coordinate. 

Logarithmic scales are often labeled only at intervals differing by factors of ten with no intermediate grid lines. If x is plotted on a logarithmic scale, the distance between two values x and X2 depends on the ratio of X2/X1. The distance on the paper between 1 and 2 is the same as the distance between 2 and 4 and between 5 and 10. In reading values between 1 and 10 it is well to remember that 2 is at a point about 0.3 times the distance between 1 and 10, so 5 is represented by a point about 0.7 times of the distance between 1 and 10 (Figure 21.9). 

---