From 879ff6baef5e34cbc46ea747a4b1209da45146f9 Mon Sep 17 00:00:00 2001 From: bangerth Date: Wed, 8 Feb 2012 21:27:03 +0000 Subject: [PATCH] Add a remark. git-svn-id: https://svn.dealii.org/trunk@25017 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-43/doc/intro.dox | 25 ++++++++++++++++--------- 1 file changed, 16 insertions(+), 9 deletions(-) diff --git a/deal.II/examples/step-43/doc/intro.dox b/deal.II/examples/step-43/doc/intro.dox index 1ccacc8195..998e3f35a4 100644 --- a/deal.II/examples/step-43/doc/intro.dox +++ b/deal.II/examples/step-43/doc/intro.dox @@ -483,20 +483,27 @@ step-31 from which most of the implementation is derived. We will not discuss aspects of the implementation that have already been discussed in step-31. -We show numerical results for some two-phase flow equations -augmented by -appropriate initial and boundary conditions in conjunction with two different choices of the -permeability model. In the problems considered, there is no internal -source term ($q=0$). As mentioned above, quantitative numerical -results are presented in [Chueh, Djilali -and Bangerth 2011]. +We show numerical results for some two-phase flow equations augmented by +appropriate initial and boundary conditions in conjunction with two different +choices of the permeability model. In the problems considered, there is no +internal source term ($q=0$). As mentioned above, quantitative numerical +results are presented in [Chueh, Djilali and Bangerth 2011]. For simplicity, we choose $\Omega=[0,1]^d,d=2,3$, though all methods (as well as our implementation) should work equally well on general unstructured meshes. Initial conditions are only required for the saturation variable, and we -choose $S(\mathbf{x},0)=0$, i.e. the porous medium is initially filled by the -non-wetting phase. We prescribe a linear pressure on the boundaries: +choose $S(\mathbf{x},0)=0.2$, i.e. the porous medium is initially filled by a +mixture of the non-wetting (80%) and wetting (20%) phases. This differs from +the initial condition in step-21 where we had taken $S(\mathbf{x},0)=0$, but +for complicated mathematical reasons that are mentioned there in a longish +remark, the current method using an entropy-based artificial diffusion term +does not converge to the viscosity solution with this initial condition +without additional modifications to the method. We therefore choose this +modified version for the current program. + +Furthermore, we prescribe a linear pressure on +the boundaries: @f[ p(\mathbf{x},t) = 1 - x \qquad \textrm{on} \quad \partial \Omega \times [0,T]. -- 2.39.5