beq.song | R Documentation |
Song et al.'s analytic solution to Boussinesq equation in a 1D semi-infinite domain with a Dirichlet boundary condition
beq.song(t = 0.5, x = 1, s = 0.4, h1 = 1, ks = 0.01, nmax = 4, alpha = 1)
t |
time coordinate. |
x |
spatial coordinate. Default is |
s |
drainable pororosity (assumed to be constant) |
h1 |
water surface level or boundary condition coefficient at |
ks |
Hydraulic conductivity |
nmax |
order of power series considered for the analytic solution solution. Default is 4. |
alpha |
|
The water surface eletion vs time and space obtained by the analytic solution of Boussinesq Equation
For major details, see Song at al, 2007
Emanuele Cordano
Song, Zhi-yao;Li, Ling;David, Lockington. (2007), "Note on Barenblatt power series solution to Boussinesq equation",Applied Mathematics and Mechanics, https://link.springer.com/article/10.1007/s10483-007-0612-x ,\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s10483-007-0612-x")}
beq.song.dimensionless
L <- 1000
x <- seq(from=0,to=L,by=L/100)
t <- c(4,5,20) # days
h_sol1 <- beq.song(t=t[1]*3600*24,x=x,s=0.4,h1=1,ks=0.01,nmax=10,alpha=0)
h_sol2 <- beq.song(t=t[2]*3600*24,x=x,s=0.4,h1=1,ks=0.01,nmax=10,alpha=0)
h_sol3 <- beq.song(t=t[3]*3600*24,x=x,s=0.4,h1=1,ks=0.01,nmax=10,alpha=0)
plot(x,h_sol1,type="l",lty=1,
main="Water Surface Elevetion (Song at's solution) ",
xlab="x[m]",ylab="h[m]")
lines(x,h_sol2,lty=2)
lines(x,h_sol3,lty=3)
legend("topright",lty=1:3,legend=paste("t=",t,"days",sep=" "))
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