From 39f5825bfc511c40f8dfb6f27a304af240e59f0b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Dennis=20Gl=C3=A4ser?= <dennis.glaeser@iws.uni-stuttgart.de> Date: Thu, 1 Jun 2023 10:58:06 +0000 Subject: [PATCH] [handbook][mpfa] Use term sub-control volume face --- doc/handbook/6_spatialdiscretizations.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/doc/handbook/6_spatialdiscretizations.tex b/doc/handbook/6_spatialdiscretizations.tex index 680e2ec0c3..a77316dac9 100644 --- a/doc/handbook/6_spatialdiscretizations.tex +++ b/doc/handbook/6_spatialdiscretizations.tex @@ -124,7 +124,7 @@ with $t_{K,\sigma},t_{L,\sigma}$ as defined in equation \eqref{eq:conormalDecTpf In the following, a multi-point flux approximation method (Mpfa-O method), which was introduced in \citet{A3:aavatsmark:2002}, is presented. The main difference to the Tpfa scheme is the fact that a consistent discrete gradient is constructed, i.e. the term $\nabla u \cdot \mathbf{d}^{\bot}_{K,\sigma}$ is not neglected. For this scheme, a dual grid is created by connecting the barycenters of the cells with the barycenters of the faces ($d=2$) or the barycenters of the faces and edges ($d=3$). -This divides each primary grid face into $n$ sub-faces $\sigma^v$, where $n$ is the number of corners of the primary grid face and the superscript $v$ refers to the vertex the +This divides each primary grid face into $n$ sub-control volume faces $\sigma^v$, where $n$ is the number of corners of the primary grid face and the superscript $v$ refers to the vertex the sub-face can be associated with (see Figure \ref{pc:interactionRegion_mpfa}). Also, it sub-divides the control volume $K$ into regions $K_v$ that can be associated with the vertex $v$. We allow for piecewise constant $\mathbf{\Lambda}$ (denoted as $\mathbf{\Lambda}_K$ for each cell $K$) and construct discrete gradients $\nabla_\mathcal{D}^{K_v} u$. -- GitLab