Block-structured grids

To resolve the problems associated with structured and unstructured grids, these fundamentally different approaches may be combined to generate mesh types which partially posses the properties of both categories. This gives rise to block-structured , overset and hybrid mesh types which under certain conditions may lead to more efficient simulations than the either class of purely structured or unstructured grids. Detailed discussions related to the properties of these classes of computational grid.s can be found in specialized textbooks (e.g, see Liseikin, 1999) and only brief definitions are given here. 

CONSIDERATIONS RELATED TO FINITE ELEMENT MESH GENERATION 193 Block-Structured grids... 

Figure 6.1 Types of interface between blocks in block-structured grids...

Grid types single/multi-block structured/unstructured/mixed... 

Figure 9.23 Examples of (a) slit block, (b) grid block, and (c) honeycomb block packing structures (Kolev, 2006).

Different positions of the probe in the xy plane were examined, while the probe was fuUy inserted into the channel. Furthermore, for the case in which the probe is in the center of a channel, nine axial positions of the probe tip were explored. For each configuration, a block-structured grid with a typical size of 700,000 prism cells was generated. 

Hence, we can maintain the block tridiagonal structure of the Jacobian in (4.5) if we introduce the parameter a as a dependent variable at m of the m -h 1 grid points and if we specify a normalization condition at the remaining grid point that does not introduce nonzero Jacobian entries outside of the three block diagonals. The success of this procedure depends upon the choice of the normalization condition. 

In flame extinction studies the maximum temperature is used often as the ordinate in bifurcation curves. In the counterflowing premixed flames we consider here, the maximum temperature is attained at the symmetry plane y = 0. Hence, it is natural to introduce the temperature at the first grid point along with the reciprocal of the strain rate or the equivalence ratio as the dependent variables in the normalization condition. In this way the block tridiagonal structure of the Jacobian can be maintained. The flnal form of the governing equations we solve is given by (2.8)-(2.18), (4.6) and the normalization condition... 

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