298
5. Finite-Volume Methods
• Initialire the jluxes to zero
for each i , j do
• lncrement F and G due to jluxes through the left cell interface
for each i, j do
U = u .
n+
1
t:_1 J'
1-2 ,J
2 '
R=qJ': .-qJ': I '
I,J
1- ,J
if U > 0, then I = i-I, else I = i
!i.'! . = !i.'! . + U ( I,J
I,J
" J' - if U > 0, then I = i, else I = i-I
. n+!
n
n
!i.t
n+!
if u. . 1 > 0, then GI '+ 1 = GI ' + 1 - --RUv. ' + 1
I ,J+2
. n+!
,J 2
,J 2
n
2!i.x
!i.t
I,J 2
n+!
n
if u. . 1 <0, thenG I
· 1 =G I
· 1 ---RUv . . 1
I,J- 2
, J - 2
,J - 2
2!i.x
I,J- 2
• lncrement Fand G due to jluxes through the bottom cell interface
(as above, switching the roles of i and j, u and v, and F and G)
• Update tp
for each i, j do
TABLE 5.3. Algorithm for executing one time step of LeVeque's two-dimensional
flux-lirnited scheme in advective form on a curvilinear grid.