[cig-commits] [commit] knepley/upgrade-petsc-interface: Added a couple of sentences about nondimsionalization, and added some more on stable time step size. (780dd63)

[cig_noreply at geodynamics.org]

Repository : ssh://geoshell/pylith

On branch  : knepley/upgrade-petsc-interface
Link       : https://github.com/geodynamics/pylith/compare/94aa2ec865fab9e6e74062842e900cc182261e16...780dd6347510363e3138470cbcacc3db5d61142b

>---------------------------------------------------------------

commit 780dd6347510363e3138470cbcacc3db5d61142b
Author: Charles Williams <C.Williams at gns.cri.nz>
Date:   Thu Jan 16 14:43:41 2014 +1300

    Added a couple of sentences about nondimsionalization, and added some more on stable time step size.


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780dd6347510363e3138470cbcacc3db5d61142b
 doc/userguide/materials/materials.lyx | 35 +++++++++++++++++++++++++++++++++--
 doc/userguide/runpylith/runpylith.lyx | 17 +++++++++++++++++
 2 files changed, 50 insertions(+), 2 deletions(-)

diff --git a/doc/userguide/materials/materials.lyx b/doc/userguide/materials/materials.lyx
index 6b7f6cb..0335db6 100644
--- a/doc/userguide/materials/materials.lyx
+++ b/doc/userguide/materials/materials.lyx
@@ -4203,15 +4203,46 @@ reference "eq:42"
 \begin_layout Standard
 Once the stresses are computed for the current time step, we can compute
  the relaxation time (used in computing the stable time step) by first computing
- an effective viscosity:
+ the effective viscous strain rate from Equation 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:79"
+
+\end_inset
+
+:
 \begin_inset Formula 
 \begin{equation}
-\eta_{eff}=\frac{1}{\phantom{}^{t+\Delta t}\gamma}=\frac{S_{0}^{n}}{\dot{e}_{0}\sqrt{\phantom{}^{t+\Delta t}J_{2}^{\prime}}}
+\dot{\bar{e}}^{C}=\frac{2\dot{e}_{0}\left(\frac{\bar{\sigma}}{\sqrt{3}}\right)^{n}}{\sqrt{3}S_{0}^{n}}\:.
 \end{equation}
 
 \end_inset
 
+Similarly, the effective elastic strain is computed as:
+\begin_inset Formula 
+\begin{equation}
+\bar{e}^{E}=\frac{\bar{\sigma}}{3\mu}\:.
+\end{equation}
 
+\end_inset
+
+The relaxation time is then the ratio between these two:
+\begin_inset Formula 
+\begin{equation}
+\tau=\frac{\bar{e}^{E}}{\bar{\dot{e}}^{C}}=\left(\frac{S_{0}}{\sqrt{J_{2}^{\prime}}}\right)^{n-1}\frac{S_{0}}{6\mu\dot{e}_{0}}\:.\label{eq:86-1}
+\end{equation}
+
+\end_inset
+
+The stable time step returned by PyLith is 1/5 of the value computed from
+ Equation 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:86-1"
+
+\end_inset
+
+.
 \end_layout
 
 \begin_layout Standard
diff --git a/doc/userguide/runpylith/runpylith.lyx b/doc/userguide/runpylith/runpylith.lyx
index cb236f7..cc36b8b 100644
--- a/doc/userguide/runpylith/runpylith.lyx
+++ b/doc/userguide/runpylith/runpylith.lyx
@@ -1668,6 +1668,23 @@ mass_density = 3.0e+3*kg/m**3
 wave_period = 1.0*s
 \end_layout
 
+\begin_layout Standard
+The default nondimensionalization is reasonable for many problems; however,
+ it may be necessary to change the default values in some cases.
+ When doing this, keep in mind that the nondimensionalization generally
+ applies to the minimum values encountered for a problem.
+ For example, in a problem with a very small mesh size, the 
+\family typewriter
+length_scale
+\family default
+ for a quasistatic problem should be on the order of the minimum cell size.
+ Similarly, for a problem involving very short relaxation times, the 
+\family typewriter
+relaxation_time
+\family default
+ should be on the order of the minimum relaxation time for the problem.
+\end_layout
+
 \begin_layout Subsection
 Finite-Element Integration Settings
 \end_layout