Mesh generation scheme

P.L. George. Automatic Mesh Generation. Wiley, New York, 1991. This is an excellent introduction to mesh generation. It contains a survey of all the major mesh generation schemes. 

Table 4.1 shows the data used in the 3D finite-element analysis. Figures 4.3 and 4.20 show the finite-element mesh generation scheme of the vessel, wall nozzles and closure heads. These are the important sections and locations in the reactor vessels from the point of view of fracture assessment. Figure 4.21a, b shows the pressure—time and temperature—time relationships. Figures 4.22. 23 indicate various stresses in different zones due to a LOCA Table 4.3. The defect size in each region is checked using the R6 method of the former CEGB (UK) which is given in Tables 4.4—4.6.

Figures 5.6 and 5.7 show 3D and 2D finite element mesh generation schemes of a prestressed concrete vessel designed for a high-temperature gas-cooled reaetor. Both internal and external loads have been computed in accordance with the method given in Chapter 3. The program CREEP, which...

Zienkiewicz,0.C. and Philips, D.V., An automatic mesh generation scheme for plane and curved surfaces by isoparametric co-ordinates, Int. J. numer. methods eng.,3, 519-528(1971)... 

The development of more robust, accurate, flexible and versatile mesh generation methods for facilitating the application of modern computational schemes is an area of active research. 

The neutron calculations and thermal-hydraulic calculations stated in Sects. 7.5.2.1 and 7.5.2.2 are all implemented into an automatic calculation scheme written in Perl and Awk script languages. The macroscopic cross section sets and HFFs are prepared for given coolant densities and bumup states by the staged homogenization of the unit cell and the assembly transport calculation. The auxiliary mesh generation module produces the Tri-Z mesh stmcture to be used in COREBN and CITATION. 

In conjunction with the discrete penalty schemes elements belonging to the Crouzeix-Raviart group arc usually used. As explained in Chapter 2, these elements generate discontinuous pressure variation across the inter-element boundaries in a mesh and, hence, the required matrix inversion in the working equations of this seheme can be carried out at the elemental level with minimum computational cost. 

The properties of techniques (2.26)-(2.29), and (2.31) are, indeed, quite instructive. Their amplitude errors are less than the phase ones, for any wavenumber. Moreover, time integration generates drastically smaller errors than the spatial discretization, and so allowing the phase discrepancies to be independent of the Courant limit. The above schemes are able to perform even when propagation direction is not aligned with the mesh axes. 

For illustration, let us estimate the dispersion error of the aforementioned narrow-band technique and compare it with the one induced by the wideband method of (2.107)—(2.115). The cell dimensions are chosen as Ay = 2Ax and T2D = 0-85 in (5.46). Figure 5.5 gives the results for two mesh resolutions with respect to Ax. In contrast with the performance of the latter scheme, the narrow-band approach achieves a remarkable reduction around the design frequency, whereas its accuracy deteriorates at finer resolutions. This is, however, not a serious shortcoming, since a given computational domain appears to have a smaller electrical size at lower frequencies and, consequently, the dispersion error is not as considerable as in the high-frequency band. Moreover, it is noteworthy to observe that the narrow-band scheme generates smaller errors for coarser lattices and thus, its application to broadband simulations should not be ruled out. 

Once again, remember that these mass balance equations are nonlinear (because of the nonlinear adsorption expression) hence, they can not be solved by direct analytical means. Generally, numerical methods must be used to solve this problem. However, when the adsorption rate is much faster than the diffusion rate (i.e., ix < 1), conventional numerical methods will run into some difficulty owing to instability. This arises because of the steepness of the profiles generated. To achieve convergence with conventional numerical schemes, a large number of discretization points must be used for the spatial domain. The fine mesh is necessary to observe such a very sharp change in the profile. 

Using this scheme to analyse the mesh elements generated in this case using Coarser size and the time step At, we found that they are both spatially and temporally converged. 

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