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Internal ConstitutionEarth

by: Emmitt Bergstrom

Internal ConstitutionEarth SIO 224

Emmitt Bergstrom

GPA 3.66


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Class Notes
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This 3 page Class Notes was uploaded by Emmitt Bergstrom on Thursday October 22, 2015. The Class Notes belongs to SIO 224 at University of California - San Diego taught by Staff in Fall. Since its upload, it has received 25 views. For similar materials see /class/226809/sio-224-university-of-california-san-diego in Scripps Inst Of Oceanography at University of California - San Diego.

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Date Created: 10/22/15
SIG 224 Convection modeling with citcom 1 Introduction This tutorial is adapted from a ClDER tutorial given by Peter van Keken Carolina LithgowBertelloni and Louise Kellogg This tutorial will allow you to investigate some aspects of mantle convection modeling using the nite element code Citcom We will rst explore the installation and basic use of the code and associated applications before investigating the relationships between the Nusselt and Rayleigh numbers for isoviscous and for the brave hearted temperaturedependent Viscosity 2 Preliminaries Citcam Citcom is the name associated with a number of related nite element codes that found their origin at Caltech in the mid90s Louis Moresi is the principle author of the version we will be using You are welcome to keep a version of this code but as Louis requests in the source code please be respectful of the time that went into creating this code The code solves the incompressible Boussinesq equations for mantle convection which from the notes are Vv0 1 VP VTLRaTg 2 VVTkV2TQ 3 where Q is a nondimensional number representing internal heating Campilmg and running the cade To run Citcom and analyze the models you ll need to use the Unix shell Locate the CITCOM directory and change into it You should have a list of directories such as Citcombuild le Perlscripts tutorial Change directories to tutorial Here you should see a few example directories including 00test a doc directory which contains this document and a number of executables citcom extractN u extractVI39ms Your Mac should be able to run the citcom executable as is Check this by changing the directory to 00test and running citcom inputtest If you get messages like quot2 divergencequot you should be in business This program should terminate in less than a minute with a message about a ppm le being written and some statements about cpu timing If there are error messages you may need to recompile citcom To recompile change to the Shell scripts directory in the CITCOM folder and type quotbuildcitcomquot When the build is complete type quotcp cll tutorialcitcomquot then retry the test 3 Basic model setup In all cases we will assume a 2D Cartesian geometry The initial model has aspect ratio 1 and a uid of uniform Viscosity The box is heated from below xed temperature 1 and cooled from above xed temperature 0 The side boundaries have re ecting symmetry boundary conditions The boundaries of the bottom are stressfree ie not rigid The equations are solved by a multigrid method which requires the discretization into a fairly regular grid In these examples we ll limit ourselves to a uniform discretization with the initial model at 33x33 nodal points The initial condition for temperature is a conductive solution with a small 10 harmonic perturba tion that will initiate convection when the Rayleigh number is large enough You can also specify the name of a le that contains the initial condition which we will use to restart convection runs In the rst few examples we will try to get a steadystate which in this code is obtained by letting time integration continue long enough This works ne at moderate Ra but becomes increasingly harder when the convection wants to be timedependent 4 First full convection run Find the example director 0Ra1d4 Check out the input le input2dRa1e4 You can do this with any editor through MacOS or with vi or emacs from the shell The top 10 lines set some variables which are de ned as rayleigh Thermal Rayleigh number maxstep Maximum number of time steps netuned The multiplication factor for the selfselecting timestep data le Common root of all output lenames storagespacing Store output les every writejpacing Store output les every TDEPV Indication whether temperature dependent viscosity is used rheologyTtype Choice of viscosity function visch viscNO Parameters in viscosity function dimenx Nondimensional grid size of the mesh in xdirection levels Number of multigrid levels perturbk Wave number of the initial perturbation previoustemperature le Name of le with initial condition The last variable is commented out with a hash mark at the start of the line Remove this hash mark when you want to do a restart from an existing le The rest of the le is better left unchanged Run the citcom code with this input le citcom input2dRa1e4 If you don t like the output rolling on the screen or would like to check things in this shell while the code runs you can redirect the output and run it in the background with nohup citcom input2dRa1e4 amp Use jobs to check whether it is still running fg to bring it to the foreground ctrlC to kill it The code will produce les ending in horizave nodedata and ppm The rst contains well horizontal averages the second contains the temperature in the nodes and last one is a graphics le that can be converted to gif by a program called GraphicConvertor if you don t have this on your Mac 2 you can download a demo version off the web Some information about the run is printed in the logs ending in log which contains basic info about the convergence of the multi grid cycle computational time used and timelogs which prints model time Nu Vrms etc We will extract time series Nut and Vrmst from the latter one using the utilities extractN u and extractVrms the time series can be plotted with plotxy or any other graph plotting routine Graphics autput temperature Citcom produces plots of the temperature eld and surface velocity in PPM format Open Graphic Converter to view these les If all goes well you can navigate to the run directory and nd images of the ppms You can view the PPM les as a slide show In the images for the rst run you should see a spinup with diffusion slowly becoming more important in the middle of the box Graphics autput time series If you have t done so already run extractNu extractVrms which generates the les Nudat and Vrmsdat You can inspect the nal values by tail Nudat Vrmsdat the last values should be around 48 and 42 To plot these les you can import them in your favorite graph generator 7 I used plotxy and there is a run le c lnu to make the plot You should see the spinup and stabilization of the convection re ected in the timeseries Inspect the last 20 or so entries in Nudat you may notice that the model hasn t gotten to steadystate yet Fix this 5 Exploring mantle convection 1 Check out the input le in ljso1d4jtspect2 to see how you set up the isoviscous problem in a box of aspect ratio 2 How do Nu and Vrms change What is a good estimate for the effective aspect ratio of convection in the Earth 2 Explore the variation of Nu and Vrms with Ra for a reasonable range of values up to 106 say Can you estimate the critical Rayleigh number What is the NuRa relationship Verify the accuracy of your results with the best answers in the thermal benchmark Blankenbach et al GH 1989 Ra 104 Nu48844 Vrms42865 Ra 105Nu105412Vrms193215 Ra106 Nu21972 Vrms833990 What happens at the higher Rayleigh numbers in terms of accuracy of the solution Are there other diagnostics you could use to see there s numerical trouble It may be quite hard to get steady state results Re ne the grids for those cases that you don t feel comfortable with by increasing the input parameter levels note increase by 1 causes doubling of number of grid points in each direction and an increase in computational time of at least 4 times 3 Explore temperaturedependence of viscosity as provided in 2etaT1d4 Note that there are two input les one to set up an initial condition inputisojnitial and one to use the nal result as input for the temperaturedependent case To run this case citcom inputisoinitial


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