From 49435d428c69764bfd1e5e8c3f6afb561e826752 Mon Sep 17 00:00:00 2001 From: Alberto Botto Poala Date: Fri, 31 Jan 2025 11:16:15 +0100 Subject: [PATCH 1/2] removes hypen between right and eigenvector, now consistent with the rest of the book --- Euler/Euler-theory.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Euler/Euler-theory.tex b/Euler/Euler-theory.tex index 88bad40..1fcb506 100644 --- a/Euler/Euler-theory.tex +++ b/Euler/Euler-theory.tex @@ -325,7 +325,7 @@ \section{Euler equation properties} characteristic form of the equations says that each of the waves will carry its respective jump, $\Delta \wb$. Since $d\qb = \Lb^{-1}d\wb = \Rb d\wb$, the jump in the primitive variable across each wave is proportional to -the right-eigenvector associated with that wave. So, for example, +the right eigenvector associated with that wave. So, for example, since $\rb^\evz$ is only non-zero for the density element (see Eq.~\ref{eq:euler:primRevs}), this then means that only density jumps across the $\lambda^\evz = u$ wave---pressure and velocity are From d3e6fad8c562a95cbe1d8404ed6a1892f497dfbb Mon Sep 17 00:00:00 2001 From: Alberto Botto Poala Date: Fri, 31 Jan 2025 11:22:18 +0100 Subject: [PATCH 2/2] rephrase in a different way, might be more clear --- Euler/Euler-theory.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Euler/Euler-theory.tex b/Euler/Euler-theory.tex index 1fcb506..b069abe 100644 --- a/Euler/Euler-theory.tex +++ b/Euler/Euler-theory.tex @@ -328,7 +328,7 @@ \section{Euler equation properties} the right eigenvector associated with that wave. So, for example, since $\rb^\evz$ is only non-zero for the density element (see Eq.~\ref{eq:euler:primRevs}), this then means that only density jumps -across the $\lambda^\evz = u$ wave---pressure and velocity are +across the $\lambda^\evz = u$ wave, while pressure and velocity are constant across this wave (see for example, Toro~\cite{toro:1997}, Ch.\ 2, 3 or LeVeque~\cite{leveque:2002} for a thorough discussion).