[docu] Add docu for one test example of PVCDBC.

web/content/docs/benchmarks/liquid-flow/primary-variable-constrain-dirichlet-boundary-condition.pandoc

++++
+date = "2020-06-18T11:33:45+01:00"
+title = "Primary variable constraint Dirichlet-type boundary condition"
+weight = 171
+project = "Parabolic/LiquidFlow/SimpleSynthetics/PrimaryVariableConstraintDirichletBC/cuboid_1x1x1_hex_1000_Dirichlet_Dirichlet_1.prj"
+author = "Thomas Fischer"
+
+[menu]
+  [menu.benchmarks]
+    parent = "liquid-flow"
+
++++
+
+{{< data-link >}}
+
+## Problem description
+
+We start with the following parabolic PDE:
+$$
+\left( c \rho_R + \phi \frac{\partial \rho_R}{\partial p}\right) \frac{\partial
+p}{\partial t} - \nabla \cdot
+\left[ \rho_R \frac{\kappa}{\mu} \left( \nabla p + \rho_R g \right) \right]
+- Q_p = 0.
+$$
+where
+
+- $c$ ... a constant that characterizes the storage as a consequence that the
+  solid phase is changing
+- $\rho_R$ ... the density
+- $p$ ... pressure
+- $t$ ... time
+- $\kappa$ ... the intrinsic permeability tensor of the porous medium
+- $\mu$ ... is the pressure dependent dynamic viscosity
+- $Q_p$ ... source/sink terms
+
+In order to obtain a unique solution it is necessary to specify conditions on
+the boundary $\Gamma$ of the domain $\Omega$.
+
+The benchmark at hand should demonstrate the primary variable constraint
+Dirichlet-type boundary condition. Here, the size of the sub-domain, the
+Dirichlet-type boundary condition is defined on, is variable and changes
+according to a condition depending on the value of the primary variable.
+
+$$
+\Gamma^\ast_D = \{ x \in \mathbb{R}^d, x \in \Gamma_D, \text{Condition}(p(x))  \}
+$$
+
+## Examples:
+
+On the left (x=0) and right side (x=1) of the domain $\Omega = [0,1]^3$ the
+usual Dirichlet-type boundary conditions are set, i.e.,
+$$
+p = 1, \quad x=0 \qquad \text{and} \qquad p = 1\quad x=1
+$$
+The initial condition $p_0$ is set to zero. Additionally, a primary variable
+constraint Dirichlet-type boundary condition (PVCDBC) is specified:
+$$
+p = -0.1, \quad \text{for}\quad z = 1 \quad \text{and}\quad p(x,y,1) > 0.
+$$
+At the beginning of the simulation the PVCDBC is inactive. Because of the
+'normal' Dirichlet-type boundary conditions the pressure is greater than zero
+after the first time step and the PVCDBC is activated in the second time step.
+The effect is depicted in the figure:
+
+{{< img src="../PVCDBC_1_ts_2.png" >}}
+