From 0fb88680dab6aae772f2d15bfe0e06472957c5b0 Mon Sep 17 00:00:00 2001 From: bangerth Date: Wed, 7 May 2008 14:24:53 +0000 Subject: [PATCH] Use h3 tags for headings, since higher tags are reserved for top-level headers. git-svn-id: https://svn.dealii.org/trunk@16042 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-21/doc/intro.dox | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/deal.II/examples/step-21/doc/intro.dox b/deal.II/examples/step-21/doc/intro.dox index a5a7f9ec7f..782a568a2b 100644 --- a/deal.II/examples/step-21/doc/intro.dox +++ b/deal.II/examples/step-21/doc/intro.dox @@ -16,7 +16,7 @@ vector-valued problems. A toplevel overview of this topic can be found in the @ref vector_valued module. -

The two phase flow problem

+

The two phase flow problem

Modeling of two phase flow in porous media is important for both environmental remediation and the management of petroleum and groundwater @@ -138,7 +138,7 @@ category. We will see that the different character of the two equations will inform our discretization strategy for the two equations. -

Time discretization

+

Time discretization

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 @@ -220,7 +220,7 @@ cell term to get an equation as follows: -

Space discretization

+

Space discretization

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 @@ -251,7 +251,7 @@ cell. Some more context on discontinuous element techniques and evaluation of fluxes can also be found in @ref step_12 "step-12". -

Linear solvers

+

Linear solvers

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 @@ -341,7 +341,7 @@ its content, i.e. all three of its block components, into the variable old_solution for use in the next time step. -

Choosing a time step

+

Choosing a time step

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 @@ -380,7 +380,7 @@ step_23 "step-23" and @ref step_24 "step-24" where we solve the time dependent wave equation, another hyperbolic problem. -

The test case

+

The test case

For simplicity, this program assumes that there is no source, $q=0$, and that the heterogeneous porous medium is isotropic $\mathbf{K}(\mathbf{x}) = -- 2.39.5