Geometry discretisation

Computational fluid dynamics (CFD) is essentially a computer-based numerical analysis approach for fluid flow, heat transfer and related phenomena. CFD techniques typically consist of the following five subprocesses geometrical modelling, geometry discretisation, boundary condition definition, CFD-based problem solving, and post-processing for solution visualisation. 

Figure 7.1 Geometry discretisation (a) original domain (b) coarse mesh (c) refined mesh.

With an accurate flow space or domain defined in terms of its geometry and a strategy for discretisation determined, it is necessary to select a suitable specific discretisation method before a problem can be solved. Having studied the field of... 

From the mathematical point of view the complexity is reduced because the system of equations which has to be solved is a function defined on the two-dimensional manifold of the control volumes boundary and leads to a dimension reduction. Practically the discretisation of the boundary usually is more simple than the meshing of complex three dimensional volumes. Especially this pertains to the transient flow channel geometry in co-rotating twin screw extruders. The surface meshes for the screws can independently be rotated inside the screw and barrel mesh analogous to the batchwise working internal mixer (Banbury Mixer) shown in the bottom part of Fig. 5.26. 

In order to solve the equation systems described in section 4.5, they are first cast into a finite volume form. The channels, interconnects and electrolyte are treated as one dimensional. In the axial direction the reactor geometry is discretised into 200 cells. The anode is discretised into 25 cells along the thickness and the cathode into 10 cells. Eqs. 4.37, 4.38, 4.41, 4.42, 4.46, 4.47, 4.48, 4.53, 4.54 and 2.9, form a system of coupled non-linear equations, which... 

Within the approaches based on the discretised finite-element solution of Laplace s equation (Sect. 17.4), the shape of the cavity is not constrained and can be in principle of any morphology. For this reason, the cavity is usually modelled on the basis of the molecular geometry. In particular, given a specific nuclear... 

The Mesh features enable the discretisation of the geometry model into small units of simple shapes, referred to as elements. In the Mesh page, from Sequence type list, there are two mesh techniques, which are Physics-controlled mesh and User-controlled mesh, respectively. In this FEM case, we choose Physics-controlled mesh for simplicity. From Element size list. Coarser size is selected. Click Build All (1.) button in the left upper comer of Mesh page. Now we have a discretised (meshed) model shown in Figure 7.13. In the Messages window, readers can find all kinds of information regarding the current command. It displays the number of elements in the current mesh, which is 2463 in this case, see Figure 7.14. 

The element mesh of the male teeth can be seen in the detail (5b). Each contacting tooth surface was discretised as 2x10 elements, leading to 5x21 = 105 surface nodes. This was found to be sufficient to allow a comparison between different geometries and loading conditions whilst minimising the time taken for analysis. 

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