# beq.lin: Analytic exact solution for One-Dimensional Boussinesq... In boussinesq: Analytic Solutions for (ground-water) Boussinesq Equation

## Description

Analytic exact solution for One-Dimensional Boussinesq Equation in a two-bounded domain with two constant-value Dirichlet Condition

## Usage

 ```1 2 3``` ``` 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) ```

## Arguments

 `t` time coordinate. `x` spatial coordinate. Default is `seq(from=0,to=L,by=by)`. `big` maximum level of Fourier series considered. Default is 10^7. `by` see `seq` `L` length of the domain. `h1` water surface level at `x=0`. Left Dirichlet Bounday Condition. `h2` water surface level at `x=L`. Right Dirichlet Bondary Condition. `ks` Hydraulic conductivity `s` drainable pororosity (assumed to be constant) `p` empirical coefficient to estimate hydraulic diffusivity D=ks/(s *(p*h1+(1-p)*h2)). It ranges between 0 and 1.

## Value

Solutions for the indicated values of `x` and `t`.

## Author(s)

Emanuele Cordano

`beq.lin.dimensionless`
 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```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")) ```