This problem is governed by the Richards’ equation. A 1 meter high sand column is initially satured. The liquid pressure is initialized as: p_l = p_{atm} - g(x - 1). At t=0 we drained the column from the bottom by imposing the pressure to p_l=p_{atm}. The input data file is given below.
| inputs | comments |
# Drainage of | You can write some comments |
# a sand column | by beginning any line with #. |
GEOM | Geometry of the problem |
1 Plan | 1D pb, plane symmetry |
MESH | Mesh |
col.msh | The mesh is read in this file (format Gmsh). This mesh consists in a 20 elements mesh between 0 and 1. There are 2 regions. The region 1 is the point at 0. The region 2 is the line between 0 and 1. There is 1 material. |
MATE | Material 1 |
Model = m1 | code name of the model |
gravite = -9.81 | gravity |
phi = 0.3 | porosity |
rho_l = 1000 | fluid mass density |
k_int = 4.4e-13 | intrinsic permeability |
mu_l = 0.001 | fluid viscosity |
p_g = 100000 | gas pressure |
Curves = tab | in the file tab, there 3 columns: p_c S_l k_{rl} |
FLDS | Fields |
2 | 2 fields |
Type = affine Value = 1.e5 Gradient = -9.81 Point = 1. | affine field defined by 10^5 - 9.81*(x - 1) |
Type = affine Value = 1.e5 Gradient = 0. Point = 0. | constant field equal to 10^5 |
INIT | Initial conditions |
1 | 1 initial condition |
Region = 2 Unknown = p_l Field = 1 | in the region 2, p_l=10^5-9.81*(x-1.). |
FUNC | Time functions f(t) |
0 | here there is no function |
COND | Boundary conditions |
1 | 1 boundary condition |
Region = 1 Unknown = p_l Field = 2 Function = 0 | in the region 1, p_l=f(t)*10^5 (by default f(t)=1) |
LOAD | Loads |
0 | there is no load |
POIN | Points where we want outputs |
0 | no points |
DATE | Dates where we want outputs |
2 | 2 dates |
0. 1800000 | t_0=0 and t_1=1800000 |
OBJE | Objective variations of unknowns |
p_l = 1000 | objective variation \Delta p_l=1000 |
ITER | Parameters for the iterative process |
Iterations = 20 | 20 iterations |
Tolerance = 1e-10 | the tolerance is 10^{-10} |
Repetitions = 0 | no repetition |
TIME | Parameters for time steps calculation |
Dtini = 1 | initial time step equal to 1. |
Dtmax = 3600 | maximum time step equal to 3600. |