Generation of Computational Mesh for CFPD Simulations - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 75

4.2.2 Body-fitted Mesh

For non-orthogonal geometries, such as a 90 ◦ pipe bend, applying an orthogonal mesh
to the geometry produces simplifications to the computational domain particularly
on the curved boundaries where staircase-like steps are found (Fig. 4.3 ). This further
causes difficulties in developing an approximate boundary description, and the steps
at the boundary introduce errors in computations of the wall stresses, heat fluxes,
boundary layer effects, etc. The treatment of the boundary conditions at stepwise
walls generally requires a fine Cartesian mesh to resolve the curved geometry, but
this requires additional computational storage and resources due to unnecessary
refinement in interior regions which are of minimal interest. This example shows
that grid generation methods that are based on Cartesian coordinate systems have
limitations in irregular geometries. It is therefore more advantageous to work with
meshes that can handle curvature and geometric complexity more naturally.

y

x

Staircase-like steps

Fig. 4.3 An example of a mesh using staircase-like steps for the 90 ◦ bend geometry

A similar type of structured mesh called a body-fitted mesh can be applied. Es-
sentially, the basic concept of this approach centres on the mapping of a distorted
region in physical space onto a rectangular region in the curvilinear coordinate space
through the use of some transform coordinate function. In applying the body-fitted
mesh to the 90 ◦ bend geometry, it would be appropriate to make the walls coincide
with lines of constant η (see Fig. 4.4 ). The location along the geometry, say from A
to B or D to C , subsequently corresponds to specific values of ξ in the computational
domain. Corresponding points on AB and CD connected by a particular η line will
have the same value of ξ i but different η values. At a particular point ( i , j ) along this
η line, ξ = ξ i and η = η j . A corresponding point x = x ( ξ i , η j ) and y = y ( ξ i , η j )inthe
computational domain exists in the physical domain.