boussinesq (version 1.0.3)

beq.song: Song et al.'s analytic solution to Boussinesq equation in a 1D semi-infinite domain with a Dirichlet boundary condition

Description

Song et al.'s analytic solution to Boussinesq equation in a 1D semi-infinite domain with a Dirichlet boundary condition

Usage

beq.song(t = 0.5, x = 1, s = 0.4, h1 = 1, ks = 0.01, nmax = 4, alpha = 1)

Arguments

t

time coordinate.

x

spatial coordinate. Default is seq(from=0,to=L,by=by).

h1

water surface level or boundary condition coefficient at x=0. Left Dirichlet Bounday Condition.

ks

Hydraulic conductivity

s

drainable pororosity (assumed to be constant)

nmax

order of power series considered for the analytic solution solution. Default is 4.

alpha

$\alpha$ exponent see Song at al, 2007

Value

The water surface eletion vs time and space obtained by the analytic solution of Boussinesq Equation

References

Song, Zhi-yao;Li, Ling;David, Lockington. (2007), "Note on Barenblatt power series solution to Boussinesq equation",Applied Mathematics and Mechanics, http://www.springerlink.com/content/w0u8667772712801/ ,http://dx.doi.org/10.1007/s10483-007-0612-x

See Also

beq.song.dimensionless

Examples

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=" "))