manus_continuum_granular1

manuscript files for first continuum-till paper
git clone git://src.adamsgaard.dk/manus_continuum_granular1
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commit e0b02423e77ecbfcac3c286471d93684ec0364fb
parent 683e1f92b790dddd6f2a82af2ef43aff81057289
Author: Anders Damsgaard <anders@adamsgaard.dk>
Date:   Tue,  3 Dec 2019 16:58:19 +0100

Remove unused abbreviation

Diffstat:
Msi.tex | 2+-
1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/si.tex b/si.tex @@ -276,7 +276,7 @@ As for the granular flow solution, we also use operator splitting and finite dif \label{eq:p_f_solution} \end{equation} \end{linenomath*} -For each time step $\Delta t$, a solution to Eq.~\ref{eq:p_f_solution} is found by the Crank-Nicholson (CN) method \cite<e.g.,>[] {Patankar1980, Ferziger2002, Press2007}. +For each time step $\Delta t$, a solution to Eq.~\ref{eq:p_f_solution} is found by the Crank-Nicholson method \cite<e.g.,>[] {Patankar1980, Ferziger2002, Press2007}. In the procedure the pressure field at $t + \Delta t$ is found by mixing explicit and implicit solutions with equal weight. The method is unconditionally stable and second-order accurate in time and space. Our implementation of grain and fluid dynamics is highly efficient, and for the presented experiments each time step completes in less than 1 ms on a single CPU core.