Geoscience Reference
In-Depth Information
Pressure-correction projection method
Jia et al . (2002) developed a depth-averaged 2-D model based on the projection
method. The partially staggered grid shown in Fig. 6.4 is used. The pressure is
defined at the cell centers, while both velocities U x and U y are at the cell cor-
ners. The governing equations are solved using the efficient element method (Wang
and Hu, 1993). The convection terms in the momentum equations are discretized
using the upwind interpolation scheme introduced in Section 4.2.4.2, while the other
spatial derivative terms are discretized using the interpolation schemes (4.97) and
(4.98). The time-derivative terms are discretized using the Euler scheme. The fol-
lowing pressure-correction method is used to achieve the coupling of velocity and
pressure.
Figure 6.4 Partially staggered grid used by Jia et al . (2002).
The discretized momentum equations are arranged as
t
ρ (
U n + 1
U n
t G
p n
p )
=
+
+
(6.34)
where G includes all the remaining terms in Eqs. (6.2) and (6.3);
ρ
is the water density,
gz s ; and p
which is assumed to be constant; p is the pressure, defined as p
= ρ
is the
pressure correction, defined by
p n + 1
p n
p
=
+
(6.35)
The intermediate velocity is denoted as
t
ρ
U =
U n
t G
p n
+
(6.36)
 
Search WWH ::




Custom Search