tAdd analytical solution to pressure variation - cngf-pf-exp1 - experiments for first paper with continuum granular model
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       ---
 (DIR) commit 63709c7bdabc7953803e85e4b1ac902388f619de
 (DIR) parent b944650f811707194c52ed1621b4672d3caaa472
 (HTM) Author: Anders Damsgaard <anders@adamsgaard.dk>
       Date:   Thu, 27 Jun 2019 15:04:14 +0200
       
       Add analytical solution to pressure variation
       
       Diffstat:
         A p_f_analytical.jl                   |      27 +++++++++++++++++++++++++++
       
       1 file changed, 27 insertions(+), 0 deletions(-)
       ---
 (DIR) diff --git a/p_f_analytical.jl b/p_f_analytical.jl
       t@@ -0,0 +1,27 @@
       +#!/usr/bin/env julia
       +import PyPlot
       +
       +n = 50                          # resolution
       +z = range(0, stop=2, length=n)  # spatial grid
       +k = 2e-17                       # permeability
       +ϕ = 0.25                        # porosity
       +μ_f = 1e-3                      # water viscosity
       +β_f = 4.5e-10                   # water compressibility
       +κ = k/(ϕ*μ_f*β_f)               # diffusivity
       +ω = 2*π*1/(3600*24)             # diurnal circular frequency
       +
       +# T is water pressure in kPa
       +T0 = 50                         # initial pressure
       +ΔT = 50                         # pressure perturbation amplitude
       +
       +# Turcotte and Schubert, eq. 4.89
       +T_(z,t) = T0 .+ ΔT.*exp.(-z.*sqrt(ω/(2κ))).*cos.(ω*t .- z.*sqrt(ω/(2κ)))
       +
       +# plot hourly curves for a full day
       +for t=0:3600:24*3600
       +        PyPlot.plot(reverse(T_(z,t)), z)
       +end
       +
       +PyPlot.xlabel("Water pressure [kPa]")
       +PyPlot.ylabel("Vertical position [m]")
       +PyPlot.savefig("p_f_analytical.pdf")