From 4d578a5c6c15f5ba0e68be7f2e070b03a0dc9473 Mon Sep 17 00:00:00 2001 From: Alberto Botto Poala Date: Wed, 15 Jan 2025 10:56:31 +0100 Subject: [PATCH 1/3] syntax correction in exercise 5.3 --- advection/advection-higherorder.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/advection/advection-higherorder.tex b/advection/advection-higherorder.tex index 71f5d3c..12e361a 100644 --- a/advection/advection-higherorder.tex +++ b/advection/advection-higherorder.tex @@ -355,7 +355,7 @@ \subsection{Limiting} \begin{exercise}[Limiting and reduction in order-of-accuracy] {Show analytically that if you fully limit the slopes - (i.e.\ set $\partial a/\partial x |_i = 0$, that the second-order + (i.e.\ set $\partial a/\partial x |_i = 0$),then the second-order method reduces to precisely our first-order finite-difference discretization, Eq.~\ref{eq:fo}. } \end{exercise} From 220b10d4b74d9af1f996fc8f60fb408dafbfc0bc Mon Sep 17 00:00:00 2001 From: Alberto Botto Poala Date: Wed, 15 Jan 2025 10:59:07 +0100 Subject: [PATCH 2/3] Two syntax errors in R-E-A procedure description --- advection/advection-higherorder.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/advection/advection-higherorder.tex b/advection/advection-higherorder.tex index 12e361a..2e9a3d1 100644 --- a/advection/advection-higherorder.tex +++ b/advection/advection-higherorder.tex @@ -425,9 +425,9 @@ \subsection{Reconstruct-evolve-average} &=& a_{i} - \frac{1}{2} \Delta a_{i} \cfl \end{eqnarray} -The final part of the R-E-A procedure is to average the over the +The final part of the R-E-A procedure is to average over the advected profiles in the new cell. The weighted average of the -amount brought in from the left of the interface and that that remains +amount brought in from the left of the interface and that remains in the cell is \begin{align} a_i^{n+1} &= \cfl \mathcal{I}_< + (1 - \cfl) \mathcal{I}_> \\ From db8e2566d427e3f4b18a30eb73fc29b52a2b7a46 Mon Sep 17 00:00:00 2001 From: Alberto Botto Poala Date: Wed, 15 Jan 2025 13:53:35 +0100 Subject: [PATCH 3/3] syntax error in 5.4.3 timestepper limiter multi D --- advection/advection-higherorder.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/advection/advection-higherorder.tex b/advection/advection-higherorder.tex index 2e9a3d1..1be6d9c 100644 --- a/advection/advection-higherorder.tex +++ b/advection/advection-higherorder.tex @@ -896,7 +896,7 @@ \subsection{Timestep limiter for multi-dimensions} Eq.~\ref{eq:adv:timestep:multid}. For the CTU method described above, \cite{colella:1990} argues that -the inclusion of the transverse information removes some of the some +the inclusion of the transverse information removes some of the instability inherent in simpler schemes, allowing for a larger timestep, restricted by Eq.~\ref{eq:adv:timestep:multid}.