manus_continuum_granular1

manuscript files for first continuum-till paper
git clone git://src.adamsgaard.dk/manus_continuum_granular1
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commit 33b45ecbfa70b2cba4b9a06306414cb625a45154
parent 574096d99e66aa06c735706ec9fc6504c57c2014
Author: Anders Damsgaard <anders@adamsgaard.dk>
Date:   Mon, 24 Jun 2019 13:40:50 +0200

Clean up methods text

Diffstat:
Mcontinuum-granular-manuscript1.tex | 5++---
1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/continuum-granular-manuscript1.tex b/continuum-granular-manuscript1.tex @@ -87,17 +87,16 @@ where \label{eq:cooperativity} \end{equation} -Unlike \citet{Pailha2009} we do not implicitly prescribe the viscous drag during dilation and equation, and instead solve for the fluid pressure. - \subsection{Fluid-pressure evolution}% \label{sub:fluid_pressure_evolution} -The transient evolution of pore-fluid pressure ($p_\text{f}$) is governed by Darcian pressure diffusion \citep[e.g.]{Goren2010, Goren2011, Damsgaard2017}: +We prescribe the transient evolution of pore-fluid pressure ($p_\text{f}$) by Darcian pressure diffusion \citep[e.g.][]{Goren2010, Goren2011, Damsgaard2017}: \begin{equation} \frac{\partial p_\text{f}}{\partial t} = \frac{1}{\phi\mu_\text{f}\beta_\text{f}} \nabla \cdot (k \nabla p_\text{f}) \label{eq:p_f} \end{equation} where $\mu_\text{f}$ denotes dynamic fluid viscosity [Pa s], $\beta_\text{f}$ is adiabatic fluid compressibility [Pa$^{-1}$], and $k$ is intrinsic permeability [m$^2$]. The sediment is assumed to be in the critical state throughout the domain, as in the original formulation by \citet{Henann2013}. +The fluid pressure is used to determine the effective normal stress used in the granular flow calculations (Eq.~\ref{eq:shear-strain-rate} and~\ref{eq:g_local}). \subsection{Numerical solution procedure}% \label{sub:numerical_solution_procedure}