beq.lin | R Documentation |
Analytic exact solution for One-Dimensional Boussinesq Equation in a two-bounded domain with two constant-value Dirichlet Condition
beq.lin(
t = 0,
x = seq(from = 0, to = L, by = by),
h1 = 1,
h2 = 1,
L = 100,
ks = 0.01,
s = 0.4,
big = 10^7,
by = L/100,
p = 0.5
)
t |
time coordinate. |
x |
spatial coordinate. Default is |
h1 |
water surface level at |
h2 |
water surface level at |
L |
length of the domain. |
ks |
Hydraulic conductivity |
s |
drainable pororosity (assumed to be constant) |
big |
maximum level of Fourier series considered. Default is 10^7. |
by |
see |
p |
empirical coefficient to estimate hydraulic diffusivity |
Solutions for the indicated values of x
and t
.
Emanuele Cordano
beq.lin.dimensionless
L <- 1000
x <- seq(from=0,to=L,by=L/100)
t <- 4 # 4 days
h_sol0 <- beq.lin(x=x,t=t*24*3600,h1=2,h2=1,ks=0.01,L=L,s=0.4,big=100,p=0.0)
h_solp <- beq.lin(x=x,t=t*24*3600,h1=2,h2=1,ks=0.01,L=L,s=0.4,big=100,p=0.5)
h_sol1 <- beq.lin(x=x,t=t*24*3600,h1=2,h2=1,ks=0.01,L=L,s=0.4,big=100,p=1.0)
plot(x,h_sol0,type="l",lty=1,main=paste("Water Surface Elevetion after",
t,"days",sep=" "),xlab="x[m]",ylab="h[m]")
lines(x,h_solp,lty=2)
lines(x,h_sol1,lty=3)
legend("topright",lty=1:3,legend=c("p=0","p=0.5","p=1"))
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