Unstructured grid

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. 

Hybrid grids are used for very complex geometries where combination of structured mesh segments joined by zones of unstructured mesh can provide the best approach for discretization of the problem domain. The flexibility gained by combining structured and unstructured mesh segments also provides a facility to improve accuracy of the numerical solutions for field problems of a complicated nature. Figure 6.3 shows an example of this type of computational mesh. 

The most common approaches for the generation of unstructured grids are as follows ... 

In most types of unstructured grid generation a secondary smoothing is required to improve the mesh properties. 

In 2003, Wu and Bogy [45] introduced a multi-grid scheme to solve the slider air bearing problem. In their approach, two types of meshes, with unstructured triangles, were used. They obtained the solutions with the minimum flying height down to 8 nm. 

There are, however, additional issues when one wants to perform the LES of an industrial device, and these are to be solved if the LES methodology is ever to be a useful tool. First, the geometric intricacy of most industrial combustion chambers cannot be represented with a Cartesian mesh high-order methods on unstructured grids must be developed. Moreover, many issues about the boundary conditions are raised, such as boundary movement for blades or pistons, turbulence injection, and acoustic properties. Such challenges are not to be underestimated, as their impact on the structure of the flow might sometimes be greater than that of the turbulence model. 

Figure 2.7 Example of a structured grid (left) and of an unstructured grid constructed from triangular elements (right).

Figure2.15 Fluidic connector with an unstructured tetrahedral grid.

Fig. 6. Examples of types of meshes developed to resolve laminar flow around particles (a) Chimera grid. Reprinted, with permission, from the Annual Review of Fluid Mechanics, Volume 31 1999 by Annual Reviews www.annualreviews.org (b) Unstructured grid with layers of prismatic cells on particle surfaces. Reprinted from Chemical Engineering Science, Vol. 56, Calis et al., CFD Modeling and Experimental Validation of Pressure Drop and Flow Profile in a Novel Structured Catalytic Reactor Packing, pp. 1713-1720, Copyright (2001), with permission from Elsevier.

The grid shown in Fig. 6b was developed by Calis et al. (2001) and consisted of five layers of prismatic cells on the walls of the spheres and tube, and unstructured tetrahedral cells in between. To obtain grid-independent pressure drops under laminar flow they had to restrict the first layer of prismatic cells to be 0.052 mm thick. The thickness then increased for the following four layers. The tetrahedral cells were 0.4mm in size. In their later work (Romkes et al., 2003), which included heat transfer, they had to reduce the size of the first layer of prismatic cells by a factor of three under laminar flow. 

In order to perform space discretization, the domain over which the governing equations apply is filled with a predetermined mesh or grid. The mesh is made up of nodes (i.e. grid points) and/or elements at which the physical quantities (i.e. unknowns) are evaluated. Neighbouring points are used to calculate derivatives. Mesh generation is a very complex task for applied problems and many different approaches to it have been developed and are currently under study [74-77], First of all, computational grids are classified as structured or unstructured meshes, even if each of these classes comprises a broad fist of meshing techniques. 

In an unstructured mesh each node can have a different number of neighbours and elements have different shapes and sizes. Therefore connectivity information must be explicitly defined and stored. The unstructured grid approach, that has gained popularity with the enormous advancements of computer technology, allows handling complex geometries with a lower number of elements and a much easier realization of local and adaptive grid refinement. [77]... 

In this example, one periodic element (a cross-over) of the laboratory scale version of Katapak -S was selected for the detailed CFD simulation with CFX-5. This solver uses the finite volume discretization method in combination with hybrid unstructured grids. Around 1,100 spherical particles of 1 mm diameter were included in the computational domain. As the liquid flows through the catalyst-filled channels at operating conditions below the load point (cf. Moritz and Hasse, 1999), permeability of the channel walls made of the wire mesh is not taken into account by this particular model. The catalyst-filled channels are considered fully wetted by the liquid creeping down, whereas the empty channels are completely occupied by the counter-current gas. It means that the bypass flow... 

In fixed-grid methods, there is a predefined grid that does not move with the interface. The interface has to somehow cut across this structured or unstructured fixed grid. The popular Volume of Fluid (VOF), Level Set (Sethian, 1996) or cellular automata methods are examples of a fixed-grid approach. 

The solver used for this study is the same as in Chapter 9 a parallel fully compressible code for turbulent reacting two-phase flows, on both structured and unstructured grids. The fully explicit finite volume solver uses a cell-vertex discretization with a Lax-Wendroff centered numerical scheme [296] or a third order in space and time scheme named TTGC [268]. Characteristic boundary conditions NSCBC [339 329] are used for the gas phase. Boundary conditions are easier for the dispersed phase, except for solid walls where particles may bounce off. In the present study it is simply supposed that the particles stick to the wall, with either a slip or zero velocity. 

Having selected the numerical method, it is necessary to generate an appropriate grid, i.e. discrete representation of the solution domain and discrete locations at which variables are to be calculated. Two types of grids, namely structured and unstructured grids, are briefly discussed here. In a structured grid, there are families of grid lines... 

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