Computational transport processes for micromixers* - Micromixers Fundamentals Design and Fabrication - page 84

check-board distribution of the pressure field. The discrete form of Eqn (3.41) can then be
written as:
r P F P r P F

P D

o

V

þðru FÞ e A e ðru FÞ w A w þðru FÞ n A n ðru FÞ s A s

D t

(3.43)

v vx v vx v vy v vy

¼ G A e G A w þ G A n G A s þð S C þ S P F P ÞD V :

e w n s

The source term S in Eqn (3.41) is linearized as
S

¼ S C þ S P F P (3.44)

where S C and S P are the related coefficients.
The convective terms are modeled using the first-order upwind scheme as

F e F e ¼ F e F P þðF P F E Þk F e ; 0 k (3.45a)

F w F w ¼ F w F P ðF P F W Þk F w ; 0 k (3.45b)

F n F n ¼ F n F P þðF P F N Þk F n ; 0 k (3.45c)

F s F s ¼ F s F P ðF P F S Þk F s ; 0 k (3.45d)

where is defined as the greater of A and B , and the diffusive terms are modeled with a central

difference scheme as

kA; Bk

v vx

G A e ¼ D e ðF E F P Þ (3.46a)

e

v vx

G A w ¼ D w ðF P F W Þ (3.46b)

w

v vx

G A n ¼ D n ðF N F P Þ (3.46c)

n

v vx

G A s ¼ D s ðF P F S Þ

(3.46d)

s

where

D e ¼ G e A e
dx e

F e ¼ðruÞ e A e ; (3.47a)

D w ¼ G w A w
dx w

F w ¼ðru Þ w A w ; (3.47b)

D n ¼ G n A n
dy n

F n ¼ðrv Þ n A n ; (3.47c)

D s ¼ G s A s
dy s

F s ¼ðrv Þ s A s ; (3.47d)