Introduction

Unless the boundary element method (see Brebbia and Wrobel 1980), mesh less methods such as lattice-Boltzman (see Derksen and Van den Akker 1999), smooth particle hydrodynamics (Marongiu et al. 2007, 2010) or vortex methods (see Chapter 4) are used, then a volume mesh is needed. Indeed, ‘meshless’ methods can need a background mesh, but more for data structure purposes. There are wide ranges of meshing techniques and some of these are discussed here. Securing a mesh for numerical simulation can be an extremely time consuming task. Notably, it is hard to assess, ahead of making a simulation, if a mesh is adequate and hence mesh development can be an iterative process. Currently, the process of subsequent mesh refinement tends to be highly manual. Although adaptive refinement has been developed for some years, this approach is seldom used. A critical element of the mesh refinement process is finding an adequate heuristic that detects the mesh zones that need improvement. Such aspects are briefly discussed in Chapter 7. As with most other areas of CFD, there are a wide range of methods and concepts. Figure 3.1 attempts to summarize these. In this chapter, an overview of the concepts in this figure will be given. First, different mesh types will be described along with their applicability. The care that is needed to consider how a particular mesh will work with a particular solver is outlined. The mesh generation techniques are given along with methods for grid control. Parameters for quantifying grid quality are described. Optimal mesh forms for turbulent flow computations are discussed. Both the fields of RANS and eddy-resolving simulations are addressed along with hybrids of these. Finally, adaptive and moving meshes are considered.

Mesh Types, Applicability and Solver Compatibility

Basic Mesh Types

The mesh or grid types used in CFD can crudely be broadly classified as: structured Cartesian (or related variants such as cylindrical polar coordinates); modified structured Cartesian (trimmed cell, immersed boundary); structured curvilinear and unstructured.

Figure 3.2, gives examples of these grids for a divergent duct. The grids in frames (I–III), although amenable to solution in structured flow solvers, can of course be used in unstructured. Notably, with unstructured grids (see Frame (IV)), the element labelling does not need to follow a clear order (see Figure 3.3b).