@ref vector_valued module.
-<h2>The two phase flow problem</h2>
+<h3>The two phase flow problem</h3>
Modeling of two phase flow in porous media is important for both
environmental remediation and the management of petroleum and groundwater
will inform our discretization strategy for the two equations.
-<h2>Time discretization</h2>
+<h3>Time discretization</h3>
In the reservoir simulation community, it is common to solve the equations
derived above by going back to the first order, mixed formulation. To this
-<h2>Space discretization</h2>
+<h3>Space discretization</h3>
In each time step, we then apply the mixed finite method of @ref step_20
"step-20" to the velocity and pressure. To be well-posed, we choose
fluxes can also be found in @ref step_12 "step-12".
-<h2>Linear solvers</h2>
+<h3>Linear solvers</h3>
The linear solvers used in this program are a straightforward extension of the
ones used in @ref step_20 "step-20". Essentially, we simply have to extend
<code>old_solution</code> for use in the next time step.
-<h2>Choosing a time step</h2>
+<h3>Choosing a time step</h3>
A general rule of thumb in hyperbolic transport equations like the equation we
have to solve for the saturation equation is that if we use an explicit time
wave equation, another hyperbolic problem.
-<h2>The test case</h2>
+<h3>The test case</h3>
For simplicity, this program assumes that there is no source, $q=0$, and that
the heterogeneous porous medium is isotropic $\mathbf{K}(\mathbf{x}) =