# [cig-commits] r8209 - doc/CitcomS/manual

tan2 at geodynamics.org tan2 at geodynamics.org
Tue Nov 6 12:38:07 PST 2007

Author: tan2
Date: 2007-11-06 12:38:07 -0800 (Tue, 06 Nov 2007)
New Revision: 8209

Modified:
doc/CitcomS/manual/citcoms.lyx
Log:
Fixed an error in the cg-iter algorithm. Added documentation for geoid.

Modified: doc/CitcomS/manual/citcoms.lyx
===================================================================
--- doc/CitcomS/manual/citcoms.lyx	2007-11-06 19:25:59 UTC (rev 8208)
+++ doc/CitcomS/manual/citcoms.lyx	2007-11-06 20:38:07 UTC (rev 8209)
@@ -1594,11 +1594,13 @@
.
The right-hand-side vector is updated by the velocity solution of the previous
iteration.
+ This equation can be solved using the same conjugate gradient scheme as
+ the incompressible case.
\end_layout

\begin_layout Standard
\begin_inset Formula $$-\mathbf{\mathbf{B}^{\mathit{T}}}\mathbf{A}^{\mathbf{\mathit{-1}}}\mathbf{B}\mathit{p^{(i)}=\mathbf{\mathbf{B}^{\mathit{T}}A^{\mathit{-1}}\mathit{\left(f+\mathbf{C}u^{(i-1)}\right)}}}\label{eq:iter-cg}$$
+\mathbf{\mathbf{B}^{\mathit{T}}}\mathbf{A}^{\mathbf{\mathit{-1}}}\mathbf{B}\mathit{p^{(i)}=\mathbf{\mathbf{B}^{\mathit{T}}A^{\mathit{-1}}\mathit{f-\mathbf{C}u^{(i-1)}}}}\label{eq:iter-cg}

\end_inset

@@ -1607,9 +1609,7 @@

\begin_layout Standard
\noindent
-This equation can be solved using the same conjugate gradient scheme as
- the incompressible case.
- The second strategy is to transform Equation
+The second strategy is to transform Equation
\begin_inset LatexCommand ref
reference "eq:discrete momentum eqn"

@@ -10015,7 +10015,7 @@
\end_inset

(
-\begin_inset Formula $=7\times10{}^{3}\times(r_{outer}-r_{inner})^{3}$
+\begin_inset Formula $=7.68175583\times10{}^{4}\times(r_{outer}-r_{inner})^{3}$
\end_inset

).
@@ -10055,6 +10055,24 @@
\end_layout

\begin_layout Standard
+We are interested in the geoid, dynamic topography, and heat flux.
+ The dynamic topography and heat flux are computed on the surface grids.
+ The geoid is computed in the spherical harmonics, with maximal degree of
+
+\family typewriter
+20
+\family default
+.
+
+\end_layout
+
+\begin_layout LyX-Code
+output_optional = geoid,surf,botm
+\newline
+output_ll_max = 20
+\end_layout
+
+\begin_layout Standard
The initial temperature is a conductive profile with a single spherical
harmonic perturbation.
The perturbation is located at mid-depth and is defined as:
@@ -10115,7 +10133,16 @@
\family typewriter
\family default
-) for bigger problems.
+) for bigger problems (e.g.
+ more than 17
+\begin_inset Formula $\times$
+\end_inset
+
+17
+\begin_inset Formula $\times$
+\end_inset
+
+17 nodes per processor).
Several parameters control the behavior of the multigrid solver:
\family typewriter
mg_cycle=1
@@ -10530,9 +10557,74 @@
\end_inset

) is -0.38%.
+ The total viscous heating is 7.68991, and the totoal adiabatic cooling is
+ 7.71719.
+ Under a steady state, these two terms should be exactly balanced.
\end_layout

\begin_layout Standard
+The geoid is output as spherical harmonic coefficients.
+ A post processing program is provided to project the geoid coefficients
+ to a regular (longitude, latitude) grid.
+ To use a regular grid of
+\begin_inset Formula $1^{\circ}$
+\end_inset
+
+ spacing, running this command:
+\end_layout
+
+\begin_layout LyX-Code
+$visual/project_geoid cookbook8.geoid.0.10000 geoid.xyz 361 181 +\end_layout + +\begin_layout Standard +It will generate a file +\family typewriter +geoid.xyz +\family default +. + There are 3 columns in the file, which are (longitude, latitude, geoid). + The geoid is in a unit of meters. + Several dimensional constants are required for the computation of geoid. + These constants have sensible default values (in SI units) for the Earth. + Note that the temperature drop from the core-mantle boundary to the surface + ( +\begin_inset Formula$\Delta T\$
+\end_inset
+
+ in Equation
+\begin_inset LatexCommand ref
+reference "eq:T dim"
+
+\end_inset
+
+) is derived from these constants and the Rayleigh number.
+\end_layout
+
+\begin_layout LyX-Code
+[CitcomS.solver.const]
+\newline
+\newline
+density=3340
+\newline
+thermdiff=1e-06
+\newline
+gravacc=9.81
+\newline
+thermex
+p=3e-05
+\newline
+refvisc=1e+21
+\newline
+cp=1200
+\newline
+density_above=1030
+\newline
+density_below=6600
+\end_layout
+
+\begin_layout Standard
\begin_inset Float figure
placement H
wide false