FLOOD06499

• County: Statewide
• Basin: Statewide
• Title: Development of Generalized Free Surface Flow Models Using Finite Element Techniques
• Date: 2/1/1979
• Prepared For: US
• Prepared By: COE
• Floodplain - Doc Type: Educational/Technical/Reference Information

the two different approaches with respect to stability,
convergence, accuracy and practicality; 'and finally, (3) to
compare relative run times and simulation costs tetween the
two methods for similar problems. The follo~ling paragraphs
present the fundamental equatic.ns used by the two models.

Governing Equations
-li.olh models incorporate similar fOr1'lS of the so-called phenom-
enological equations for monl2ntum, along V1ith the continuity
equation and a form of the convective-diffusion equation for
thermal or material transport in the vertical. Note, however,
that the FEM model retains the vertical n,omentum equation,
which is replaced by the hydrostatic pressure distribution in
the FDM model. Both models utilize a Cartesian coordinate
system with the longitudinal x dimension positive downstream.
The vertical z dimension is referenced positive upward from
the x-axis in the FEM model, while it is positive downward
from the x-axis in LARM. Both models allow for a variable
width in the lateral y direction.

F_EM Hydrodynamic Model
Momentum Equation:

b (ll!+ ll!+ au) +
p at uax waz

d.(PEl _ Exx.L (b-"J:!.) _ EXZ .L (b~)
ax ax ax az az

2 2
+ pgC- uJulAb - ,Va Cos ~ As = D

(4)

bp (~~ + ~ + w~~) + df!J- + bpg - EXZ ~x (b~~)

E. a (aw)
- zz - b-
az az

= 0

(5)

Continuity Equation:
fx-{bU) + ~z(bW) = 0 (6)

Convective-Diffusion Equation for Density:
.a.~ + b (ul.e. + wap) - D _L (b"E.) - D ~- (b~-)= 0 (7)
at ax az x ax ax z. az az

whe re
u, w =
b =
P =
Dx' Dz =
Ab =
As =

fluid velocity in the x and z directions respectively
breadth
pressure
eddy diffusion coefficients in the x and z directions
respectively
area over which bottom stress is effective
the area over \',hich the wind stress is effective

Other variables have previously been defined.

1;1,