1. Reference problem

The objective of this test case is to test the calculation of the integral of flows on a surface.

1.1. Geometry

We consider a bar that is \(\mathrm{5m}\) long and \(\mathrm{1m}\) high.

Illustration 1: Geometry

1.2. Material properties

Only the properties on which the solution depends are given here, knowing that the command file contains other material data that plays no role in solving the problem at hand.

Liquid	Relative permeability Viscosity \(\mu (\mathit{pa}\mathrm{.}s)\) Compressibility module Liquid density \(\rho (\mathit{kg}\mathrm{/}{m}^{3})\)	\(1\) \(1\) \(0\) \(1\)
Homogenized parameters	Intrinsic permeability \(\text{K\_int}({m}^{2})\) Porosity Storage Liquid saturation	\({10}^{\text{-13}}\) \(\mathrm{0,5}\) \({10}^{\text{-10}}\) \(1\)
	Henry \(({\mathrm{Pa.mol}}^{\text{-1}}\mathrm{.}{m}^{3})\)	\({10}^{\text{10}}\)

Table 1.2-1 : Material Properties

1.3. Boundary and initial conditions

The boundary conditions are Dirichlet conditions:

On the left side of the estate, \({P}_{l}(t,x=\mathrm{0,}y)=0P\)

On the right side of the estate, \({P}_{l}(t,x=L,y)={10}^{4}P\)

The initial liquid pressure is \({P}_{l}(t=\mathrm{0,}x,y)={10}^{4}P\).

1.4. Simulation time and time step

The simulation duration is \(50000s\) and the number of time steps is 5.