Borehole Acoustics –New Approaches to Old Problems - Wave Propagation in Drilling, Well Logging and Reservoir Applications - page 387

F E

(x outer , y outer )
(x inner , y inner )

Specify (x outer , y outer ) values

I dentical (x,y) values

DE

BC G D

Specify G H (x, y ) values

Specify CD ( x, y ) v alues

A H G F

H

C

I d entical (x,y) values

x

y

Specify (x inner , y inner ) values

A B

Figure 10.8c. Multiply-connected “two-body” grid.
Applications from several areas of petroleum engineering, drawn from the
foregoing topic references, are given without further discussion. In all cases, the
geometric problem domain is first transformed into a rectangular space using a
highly efficient and fast algorithm; then, the governing partial differential
equations are recast in the new coordinates and solved with relaxation methods
for steady problems and time-marching approaches for transient ones.

Figure 10.8d. Steady non-Newtonian annular flow in
eccentric annuli for drilling and cementing applications.

Figure 10.8e. Transient non-Newtonian flow in wax clogging pipe
where a “dynamic grid” self-adjusts to reduced area with time.