[cig-commits] r18553 - in short/3D/PyLith/trunk/doc/userguide: . runpylith

[brad at geodynamics.org]

Author: brad
Date: 2011-06-08 14:03:39 -0700 (Wed, 08 Jun 2011)
New Revision: 18553

Modified:
   short/3D/PyLith/trunk/doc/userguide/runpylith/runpylith.lyx
   short/3D/PyLith/trunk/doc/userguide/userguide.lyx
Log:
Added section on numerical damping.

Modified: short/3D/PyLith/trunk/doc/userguide/runpylith/runpylith.lyx
===================================================================
--- short/3D/PyLith/trunk/doc/userguide/runpylith/runpylith.lyx	2011-06-08 19:53:17 UTC (rev 18552)
+++ short/3D/PyLith/trunk/doc/userguide/runpylith/runpylith.lyx	2011-06-08 21:03:39 UTC (rev 18553)
@@ -1350,6 +1350,10 @@
 
 \begin_layout Plain Layout
 Global uniform mesh refinement of 2-D and 3-D linear cells.
+ The blue lines and orange curcles identify the edges and vertices in the
+ original cells.
+ The purple lines and green circles identify the new edges and vertices
+ added to the original cells to refine the mesh by a factor of two.
 \begin_inset CommandInset label
 LatexCommand label
 name "fig:uniform:refinement:2x"
@@ -2953,6 +2957,77 @@
 \end_layout
 
 \begin_layout Subsection
+Numerical Damping in Explicit Time Stepping
+\end_layout
+
+\begin_layout Standard
+In explicit time-stepping formulations for elasticity, boundary conditions
+ and fault slip can excite short waveform elastic waves that are not accurately
+ resolved by the discretization.
+ We use numerical damping via an artificial viscosity
+\begin_inset CommandInset citation
+LatexCommand cite
+key "Knopoff:Ni:2001,Day:Ely:2002"
+
+\end_inset
+
+ to reduce these high frequency oscillations.
+ In computing the strains for the elasticity term equation 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:elasticity:integral:dynamic:t"
+
+\end_inset
+
+, we use an adjusted displacement, 
+\begin_inset Formula 
+\begin{equation}
+\vec{u}^{adj}(t)=\vec{u}(t)+\eta^{*}\Delta t\vec{\dot{u}}(t),
+\end{equation}
+
+\end_inset
+
+where 
+\begin_inset Formula $\vec{u}^{adj}(t)$
+\end_inset
+
+ is the adjusted displacement at time t, 
+\begin_inset Formula $\vec{u}(t)$
+\end_inset
+
+is the original displacement at time (t), 
+\begin_inset Formula $\eta^{*}$
+\end_inset
+
+is the normalized artificial viscosity, 
+\begin_inset Formula $\Delta t$
+\end_inset
+
+ is the time step, and 
+\begin_inset Formula $\vec{\dot{u}}(t)$
+\end_inset
+
+ is the velocity at time 
+\begin_inset Formula $t$
+\end_inset
+
+.
+ The default values for the normalized artificial viscosity is 0.1.
+ We have found values in the range 0.1-0.4 sufficiently suppress numerical
+ noise while not excessively reducing the peak velocity.
+ An example of setting the normalized artificial viscosity in a .cfg file
+ is
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.formulation]
+\end_layout
+
+\begin_layout LyX-Code
+norm_viscosity = 0.2
+\end_layout
+
+\begin_layout Subsection
 \begin_inset CommandInset label
 LatexCommand label
 name "sec:solvers"

Modified: short/3D/PyLith/trunk/doc/userguide/userguide.lyx
===================================================================
--- short/3D/PyLith/trunk/doc/userguide/userguide.lyx	2011-06-08 19:53:17 UTC (rev 18552)
+++ short/3D/PyLith/trunk/doc/userguide/userguide.lyx	2011-06-08 21:03:39 UTC (rev 18553)
@@ -266,6 +266,9 @@
 \end_inset
 
 
+\end_layout
+
+\begin_layout Standard
 \begin_inset CommandInset include
 LatexCommand input
 filename "boundaryconditions/boundaryconditions.lyx"
@@ -532,7 +535,45 @@
 \labelwidthstring Bibliography
 \begin_inset CommandInset bibitem
 LatexCommand bibitem
-label "9"
+key "Knopoff:Ni:2001"
+
+\end_inset
+
+Knopoff, L.
+ and X.X.
+ Ni (2001), Numerical instability at the edge of a dynamic fracture, 
+\emph on
+Geophysical Journal International, 
+\emph default
+147(3), 1-6, doi: 10.1046/j.1365-246x.2001.01567.x.
+\end_layout
+
+\begin_layout Bibliography
+\labelwidthstring Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+key "Day:Ely:2002"
+
+\end_inset
+
+Day, S.M.
+ and G.P.
+ Ely (2002), Effct of a shallow weak zone on fault rupture: Numerical simulation
+ of scale-model experiments, 
+\shape italic
+Bull.
+ Seismol.
+ Soc.
+ Am.
+\shape default
+, 92(8), 3022-3041, doi: 10.1785/0120010273.
+\end_layout
+
+\begin_layout Bibliography
+\labelwidthstring Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "10"
 key "Zienkiewicz:Taylor:2000"
 
 \end_inset
@@ -550,7 +591,7 @@
 \labelwidthstring Bibliography
 \begin_inset CommandInset bibitem
 LatexCommand bibitem
-label "10"
+label "11"
 key "Taylor:2003"
 
 \end_inset