[cig-commits] r8096 - doc/CitcomS/manual

tan2 at geodynamics.org tan2 at geodynamics.org
Wed Oct 10 13:15:13 PDT 2007 

Author: tan2
Date: 2007-10-10 13:15:12 -0700 (Wed, 10 Oct 2007)
New Revision: 8096

Modified:
   doc/CitcomS/manual/citcoms.lyx
Log:
Added cookbook 8 and other small modification in history and equations.

Modified: doc/CitcomS/manual/citcoms.lyx
===================================================================
--- doc/CitcomS/manual/citcoms.lyx	2007-10-10 20:11:00 UTC (rev 8095)
+++ doc/CitcomS/manual/citcoms.lyx	2007-10-10 20:15:12 UTC (rev 8096)
@@ -630,7 +630,8 @@
 n dependent viscosity and heat generation by Thorsten Becker; (7) compressed
  ASCII output by Thorsten Becker; (8) an easier way for mesh refinement
  for the radial coordinate by Thorsten Becker; (9) an exchanger package
- for solver coupling; and (10) an option to disable monitoring of maximum
+ for solver coupling; (10) removing the ridig rotation component from the
+ velocity by Shijie Zhong; and (11) an option to disable monitoring of maximum
  temperature.
  Additional backward incompatible changes include: (1) the viscosity field
  at element level is not smoothed (this might slow down the convergence
@@ -802,6 +803,12 @@
 
 \begin_layout Section
 Governing Equations
+\begin_inset LatexCommand label
+name "sec:Governing-Equations"
+
+\end_inset
+
+
 \end_layout
 
 \begin_layout Standard
@@ -1006,7 +1013,7 @@
 \begin_layout Standard
 \align right
 \begin_inset Formula \begin{equation}
-\Gamma=\frac{1}{2}\left(1+\tanh\left(\frac{1-r-d_{ph}-s(T-T_{ph})}{w_{ph}}\right)\right)\label{eq:phase function}\end{equation}
+\pi=\rho g(1-r-d_{ph})-\gamma_{ph}(T-T_{ph})\label{eq:reduced pressure}\end{equation}
 
 \end_inset
 
@@ -1014,8 +1021,22 @@
 \end_layout
 
 \begin_layout Standard
+\align right
+\begin_inset Formula \begin{equation}
+\Gamma=\frac{1}{2}\left(1+\tanh\left(\frac{\pi}{\rho gw_{ph}}\right)\right)\label{eq:phase function}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
 \noindent
 where 
+\begin_inset Formula $\pi$
+\end_inset
+
+is the reduced pressure, 
 \begin_inset Formula $d_{ph}$
 \end_inset
 
@@ -1025,7 +1046,11 @@
 
  are the ambient depth and temperature of a phase change, 
 \emph on
-s
+
+\begin_inset Formula $\gamma_{ph}$
+\end_inset
+
+
 \emph default
  is the Clapeyron slope of a phase change, and 
 \begin_inset Formula $w_{ph}$
@@ -1062,7 +1087,7 @@
 \begin_layout Standard
 \align right
 \begin_inset Formula \begin{equation}
-T=\Delta TT'+T_{0}\label{eq:T dim}\end{equation}
+T_{0}=\Delta TT_{0}'\label{eq:T0 dim}\end{equation}
 
 \end_inset
 
@@ -1072,6 +1097,16 @@
 \begin_layout Standard
 \align right
 \begin_inset Formula \begin{equation}
+T=\Delta T(T'+T_{0}')\label{eq:T dim}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align right
+\begin_inset Formula \begin{equation}
 t=\frac{R_{0}^{2}}{\kappa}t^{'}\label{eq:t dim}\end{equation}
 
 \end_inset
@@ -9826,6 +9861,628 @@
  A model of higher resolution will not have this kind of artifact.
 \end_layout
 
+\begin_layout Section
+Cookbook 8: Compressible Stead-State Convection
+\end_layout
+
+\begin_layout Subsection
+Problem
+\end_layout
+
+\begin_layout Standard
+This example is a benchmark problem for compressible thermal convection.
+ The initial temperature has a single spherical harmonic perturbation.
+ The numerical solution of the velocity and stress fields can be compared
+ with semi-analytical solution.
+ The Stokes solver is benchmarked and validated.
+ However, no analytical solution exits for the benchmark on the energy euation
+ solver, which is nonlinear.
+ The steady state solution is usually used for the comparison with other
+ numerical solutions.
+ 
+\end_layout
+
+\begin_layout Subsection
+Solution
+\end_layout
+
+\begin_layout Standard
+This cookbook example will run for 10000 time step to reach steady state.
+ It will use 12 processors and take 1-2 days to finish on a modern computer.
+ At every 1000 time step interval, a checkpoint for the internal state of
+ the solver is saved.
+\end_layout
+
+\begin_layout LyX-Code
+checkpointFrequency = 1000
+\end_layout
+
+\begin_layout Standard
+If the solver is interrupted before finishing the computation, one can resume
+ the computation from the checkpointed state.
+ To shorten the computation time, a checkpoint at 9000 time step is provided.
+ (Note that the checkpoint files are produced by a x86 machine and may not
+ be usable by other types of machines, e.g.
+ PowerPC.) To resume the computation from the 9000 time step checkpoint,
+ set these parameters:
+\end_layout
+
+\begin_layout LyX-Code
+[CitcomS.solver.ic]
+\newline
+restart = on
+\newline
+solution_cycles_init = 9000
+\end_layout
+
+\begin_layout Standard
+A compressible convection model has four dimensionless numbers: the Rayleigh
+ number, the dissipation number, the Gruneisen parameter, and the non-dimensiona
+lized absolute surface temperature, which are defined in Section 
+\begin_inset LatexCommand ref
+reference "sec:Governing-Equations"
+
+\end_inset
+
+.
+ The Rayleigh number of CitcomS is scaled by the radius of Earth.
+ If scaled to the thickness of the mantle, the effective Rayleigh number
+ is 
+\begin_inset Formula $7\times10{}^{3}$
+\end_inset
+
+ (
+\begin_inset Formula $=7\times10{}^{3}\times(r_{outer}-r_{inner})^{3}$
+\end_inset
+
+).
+ Under these non-dimensional numbers, the convection is of low vigor and
+ low compressibility.
+ If 
+\family typewriter
+reference_state=0
+\family default
+, constant gravity, heat capacity, thermal expansivity, and 
+\begin_inset Formula $\rho_{r}=exp\left(\frac{D_{i}}{\gamma}(1-r)\right)$
+\end_inset
+
+ is used as the reference state.
+ If 
+\family typewriter
+reference_state=1
+\family default
+, the reference state is read from a file 
+\family typewriter
+refstate_file
+\family default
+.
+ See Appendix 
+\begin_inset LatexCommand ref
+reference "cha:Appendix-A:-Input"
+
+\end_inset
+
+ for the file format.
+\end_layout
+
+\begin_layout LyX-Code
+reference_state = 1
+\newline
+refstate_file = ref.dat
+\end_layout
+
+\begin_layout Standard
+You will need the output of dynamic topography and geoid.
+ The maxima spherical harmonics degree for the geoid is 20.
+\end_layout
+
+\begin_layout LyX-Code
+output_optional = geoid,surf,botm
+\newline
+output_ll_max = 20
+\end_layout
+
+\begin_layout Standard
+Various parameters tune the performance of the solver.
+ The maxima size of time step is determined dynamically by the Courant criterion.
+ The enhance the stability of the energy equation solver, you will only
+ use three quaters of the maxima Courant time step size.
+\end_layout
+
+\begin_layout LyX-Code
+finetunedt = 0.75
+\end_layout
+
+\begin_layout Standard
+You will use the multigrid solver to solve the matrix equation 
+\begin_inset Formula $\mathbf{A}x=b$
+\end_inset
+
+ for x.
+ Multigrid solver is more efficient than the conjugate gradient solver (
+\family typewriter
+Solver=cgrad
+\family default
+) for bigger problems.
+ Several parameters control the behavior of the multigrid solver: 
+\family typewriter
+mg_cycle=1
+\family default
+ for V cycle and 2 for W cycle; 
+\family typewriter
+down_heavy
+\family default
+ and 
+\family typewriter
+up_heavy
+\family default
+ are the number of smoothing cycles for downward/upward smoothing; and 
+\family typewriter
+vlowstep
+\family default
+ and 
+\family typewriter
+vhighstep
+\family default
+ are the number of smoothing passes at lowest/highest levels.
+ 
+\end_layout
+
+\begin_layout LyX-Code
+Solver = multigrid
+\newline
+mg_cycle = 1
+\newline
+down_heavy = 2
+\newline
+up_heavy = 2
+\newline
+vlowstep = 20
+\newline
+vhighstep
+ = 2
+\end_layout
+
+\begin_layout Standard
+The following parameters turn on the pre-conditioner and specify the desired
+ accuracy for the matrix equation solver (either multigrid or conjugate
+ gradient).
+\end_layout
+
+\begin_layout LyX-Code
+precond = on
+\newline
+accuracy = 0.001
+\end_layout
+
+\begin_layout Standard
+The stiffness matrix uses augmented Lagrangian formulation to improve the
+ convergence for large viscosity variations 
+\begin_inset LatexCommand cite
+key "Moresi/Zhong/Gurnis The accuracy"
+
+\end_inset
+
+.
+ These parameters specify whether to enable the formulation and how much
+ weight for the formulation.
+\end_layout
+
+\begin_layout LyX-Code
+aug_lagr = on
+\newline
+aug_number = 2.0e3
+\end_layout
+
+\begin_layout Standard
+The discrete Stokes' equations 
+\begin_inset LatexCommand ref
+reference "eq:discrete continuite eqn"
+
+\end_inset
+
+and 
+\begin_inset LatexCommand ref
+reference "eq:discrete momentum eqn"
+
+\end_inset
+
+are solved using a Uzawa algorithm, which iteratively updates the pressure
+ and velocity solutions.
+ Three variations of Uzawa algorithm are used in CitcomS, one for the incompress
+ible case, and the other two for the compressible case.
+ Two parameters are common to the three variations.
+ These parameters specify the maxima number of iterations and the desired
+ residual level for the continuity equation 
+\begin_inset LatexCommand ref
+reference "eq:discrete continuite eqn"
+
+\end_inset
+
+.
+ Sometimes, larger values of 
+\family typewriter
+piterations
+\family default
+ and 
+\family typewriter
+tole_compressibility
+\family default
+ are required for convergence if complicated velocity boundary conditions
+ are used.
+\end_layout
+
+\begin_layout LyX-Code
+piterations = 375
+\newline
+tole_compressibility = 1e-08
+\end_layout
+
+\begin_layout Standard
+For the compressible case, two choices of Uzawa algorithm are available.
+ If 
+\family typewriter
+uzawa=cg
+\family default
+, the algorithm described in Equation 
+\begin_inset LatexCommand ref
+reference "eq:iter-cg"
+
+\end_inset
+
+ is used.
+ In this case, two additional parameters control the maxima number and the
+ desired accuracy of outer iterations.
+ If If 
+\family typewriter
+uzawa=bicg
+\family default
+, the algorithm described in Equation 
+\begin_inset LatexCommand ref
+reference "eq:bicg"
+
+\end_inset
+
+is used.
+\end_layout
+
+\begin_layout LyX-Code
+uzawa = cg
+\newline
+compress_iter_maxstep = 100
+\newline
+relative_err_accuracy = 0.001
+\end_layout
+
+\begin_layout Standard
+Finaly, the rigid rotation component of the velocity solution is removed.
+ The mode of rigid body rotation is unconstrainted by the Stokes' equation,
+ if free-slip boundary conditions are used for the top and bottom boundaries
+ of a full spherical model.
+ However, for models with imposed plate velocity, it is advised to turn
+ off 
+\family typewriter
+remove_rigid_rotation
+\family default
+.
+\end_layout
+
+\begin_layout LyX-Code
+remove_rigid_rotation = on
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout Subsubsection
+Example: Compressible Stead-State Convection, cookbook8.cfg
+\end_layout
+
+\begin_layout LyX-Code
+# Cookbook 8: Compressible Model and Checkpointing
+\newline
+
+\newline
+[CitcomS]
+\newline
+solver = full
+\newline
+steps
+ = 10000
+\newline
+
+\newline
+
+\newline
+[CitcomS.controller]
+\newline
+monitoringFrequency = 1000
+\newline
+checkpointFrequency
+ = 1000
+\newline
+
+\newline
+
+\newline
+[CitcomS.solver]
+\newline
+datadir = output
+\newline
+datafile = cookbook8
+\newline
+datadir_old =
+ restart
+\newline
+datafile_old = cookbook8
+\newline
+
+\newline
+rayleigh = 7.68175583e4
+\newline
+dissipation_number
+ = 0.5
+\newline
+gruneisen = 1.25
+\newline
+surfaceT = 0.1
+\newline
+
+\newline
+
+\newline
+[CitcomS.solver.mesher]
+\newline
+nodex = 33
+\newline
+nodey =
+ 33
+\newline
+nodez = 33
+\newline
+levels = 5
+\newline
+
+\newline
+coor = 1
+\newline
+coor_file = coord.dat
+\newline
+
+\newline
+
+\newline
+[CitcomS.solver.param]
+\newline
+reference
+_state = 1
+\newline
+refstate_file = ref.dat
+\newline
+
+\newline
+
+\newline
+[CitcomS.solver.output]
+\newline
+output_optional = geoid,sur
+f,botm
+\newline
+output_ll_max = 20
+\newline
+
+\newline
+
+\newline
+[CitcomS.solver.ic]
+\newline
+tic_method = 3
+\newline
+num_perturbations
+ = 1
+\newline
+perturbl = 3
+\newline
+perturbm = 2
+\newline
+perturblayer = 17
+\newline
+perturbmag = 0.01
+\newline
+
+\newline
+restart = off
+\newline
+soluti
+on_cycles_init = 9000
+\newline
+
+\newline
+
+\newline
+[CitcomS.solver.visc]
+\newline
+VISC_UPDATE = on
+\newline
+visc_smooth_method
+ = 1
+\newline
+
+\newline
+TDEPV = on
+\newline
+rheol = 1
+\newline
+num_mat = 4
+\newline
+viscE = 2.99573,2.99573,2.99573,2.99573
+\newline
+viscT
+ = 0.5,0.5,0.5,0.5
+\newline
+visc0 = 1,1,1,1
+\newline
+
+\newline
+VMIN = on
+\newline
+visc_min = 0.001
+\newline
+VMAX = on
+\newline
+visc_max =
+ 1e+06
+\newline
+
+\newline
+
+\newline
+[CitcomS.solver.tsolver]
+\newline
+finetunedt = 0.75
+\newline
+
+\newline
+
+\newline
+[CitcomS.solver.vsolver]
+\newline
+uzawa
+ = cg
+\newline
+Solver = multigrid
+\newline
+mg_cycle = 1
+\newline
+down_heavy = 2
+\newline
+up_heavy = 2
+\newline
+vlowstep =
+ 20
+\newline
+vhighstep = 2
+\newline
+
+\newline
+aug_lagr = on
+\newline
+aug_number = 2.0e3
+\newline
+precond = on
+\newline
+
+\newline
+piterations =
+ 375
+\newline
+accuracy = 0.001
+\newline
+tole_compressibility = 1e-08
+\newline
+compress_iter_maxstep = 100
+\newline
+relati
+ve_err_accuracy = 0.001
+\newline
+
+\newline
+remove_rigid_rotation = on
+\end_layout
+
+\begin_layout Subsection
+Discussion
+\end_layout
+
+\begin_layout Standard
+The results for this problem are presented in Figure 
+\begin_inset LatexCommand ref
+reference "fig:Cookbook-8"
+
+\end_inset
+
+.
+ A tetrahedra symetric pattern is developed for the convection.
+ The surface heatflux 
+\begin_inset Formula $Q_{surf}$
+\end_inset
+
+ at the steady state is 3.892, and the bottom heatflux 
+\begin_inset Formula $Q_{botm}$
+\end_inset
+
+ is 12.817.
+ The heatflux inbalance (
+\begin_inset Formula $Q_{botm}r_{inner}^{2}/Q_{surf}r_{outer}^{2}-1$
+\end_inset
+
+) is -0.38%.
+ (TODO: The semi-analytical solution of surface topography at 0th step is.)
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement h
+wide false
+sideways false
+status collapsed
+
+\begin_layout Standard
+\align center
+\begin_inset Graphics
+	filename graphics/cookbook8.png
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Caption
+
+\begin_layout Standard
+\begin_inset LatexCommand label
+name "fig:Cookbook-8"
+
+\end_inset
+
+Cookbook 8: The steady state temperature field at 10000 time step.
+ A tetrahedra symetric convection pattern is developed.
+ Two temperature isosurfaces of 0.4 and 0.8 are shown.
+ 
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Cookbook 9: Solver Coupling for Ridge-Plume Interaction
+\end_layout
+
+\begin_layout Subsection
+Problem
+\end_layout
+
+\begin_layout Subsection
+Solution
+\end_layout
+
+\begin_layout Subsubsection
+Example: Solver Coupling for Ridge-Plume Interaction, cookbook9.cfg
+\end_layout
+
+\begin_layout Subsection
+Discussion
+\end_layout
+
 \begin_layout Part
 Appendices
 \end_layout
@@ -12898,7 +13555,7 @@
 up_heavy
 \family default
 \size default
- are the smoothing factors for downward/upward smoothing.
+ are the number of smoothing passes for downward/upward smoothing.
  
 \family typewriter
 \size small
@@ -21253,6 +21910,23 @@
 
 \begin_layout Bibliography
 \begin_inset LatexCommand bibitem
+key "Moresi/Zhong/Gurnis The accuracy"
+
+\end_inset
+
+Moresi, L., S.
+ Zhong, and M.Gurnis (1996), The accuracy of finite element solutions of
+ Stokes' flow with strongly varying viscosity, 
+\shape italic
+Phys.
+ Earth Planet.
+ Inter.
+\shape default
+, 97, 83-94.
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
 label "3"
 key "Moresi/Gurnis Contraints"

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