2006 Purdue Workshop for Compressible Mantle Convection

West Lafayette, Indiana

Summary Report for the 2006 Purdue Workshop for Compressible Mantle Convection


Format and Agenda


Planned Activites and Recommendations to CIG

  1. 2D benchmark
  2. Science
  3. 3D compressible code development
  4. An abstract to 2006 Fall AGU
  5. ConMan


Background. One of the primary projects that were identified at the 2005 Boulder mantle workshop for the CIG to help our mantle convection community was the development of modeling software for compressible mantle convection. To move this project forward, in the fall of 2005, the CIG requested Scott King and Shijie Zhong to help organize a small scale workshop to discuss issues relevant to the compressible mantle convection. Before the 2005 Fall AGU, Scott King (main organizer) and Shijie Zhong sent emails to a large number of people with potential interest in compressible mantle convection to call for participation to the workshop. Although the workshop was open to anyone with interest in the topic, the actual participants were largely those who responded the email calls positively.

Format and Agenda. The workshop was held from March 27 and 28 at Purdue University and was attended by 12 geophysicists (4 of them are graduate students) including geodynamicists and mineral physicists and 2 CIG staff members. At the workshop, twelve presentations were given with extensive discussions covering a number of important topics. The discussions were rather effective and productive, partly because many of participants had had extensive email discussions about formulations and benchmarks before coming to the workshop. The presentations are listed as following (and are available here): Louis Moresi talked the Uzawa algorithm, Shijie Zhong talked about CitcomS structure, Gary Jarvis reviewed his 1980 paper with McKenzie, Eh Tan and David May each discussed their experience in implementing different solution methods for compressible mantle convection, Dave Yuen talked about the effects of variable thermodynamic parameters (diffusivity and expansivity), Scott King reviewed his early work on compressible convection with Joel Ita. John Baumgardner discussed the implementation of compressible convection in Terra. Marc Parmentier emphasized on the importance of compressible convection in melt migration problems. Peter van Keken presented his recent 2D benchmark results for compressible convection (Eh Tan and Shijie Zhong also presented some results on 2D benchmarks). The workshop also invited two mineral physicists. Jay Bass talked about the equation of state for the mantle from mineral physics point of view, and Bob Liebermann discussed the COMPRESS project. Paul Tackley and Masanori Kameyama were unable to come to the workshop, but they made slides for the workshop that were presented by Shijie Zhong and Dave Yuen, respectively. Masanori Kameyama’s presentation was on their convection code with Ying-Yang grids. Paul Tackley’s slides summarized his implementation of compressible convection in STAG3D.


  1. Clarified the set of governing equations to be solved (Anelastic liquid approximation or ALA and truncated anelastic liquid approximation or TALA)
  2. Identified the areas for more studies including the effects of different reference states and different formulation
  3. Identified a number of algorithms (e.g., GMRES, BiCGstab) that can be potentially used in the CIG’s 3D compressible convection code
  4. Defined benchmark problems for compressible mantle convection

Planned Activities and Recommendations to CIG.

  1. 2D benchmark: There will be two types of benchmarks. First, we will benchmark for instantaneous Stokes flow for ALA and TALA formulations and for isoviscous and layered and columnar viscosity structure for which analytic solutions are available. Second, we will re-do some cases from Blankenbach et al. [1989] with ALA and TALA formulations. Louise Moresi, David May, Peter van Keken, Eh Tan, Paul Tackley (unconfirmed yet), Scott King, and Shijie Zhong may participate in this activity. These different groups use different numerical methods and algorithms (finite elements, finite volume, GMRES, BiCG, penalty function formulation,…). The hope is to examine which methods/formulations are more suitable for the planned CIG software for 3D compressible mantle convection.

    Analytic solutions for the Stokes’ flow problems in Cartesian geometry for ALA and TALA are already available. However, the corresponding solutions in spherical geometry still need to be developed. One of Shijie Zhong’s graduate students is working on it and they hope to deliver the solutions in a few weeks.

    Given that Eh Tan will join the CIG this summer and that he has worked extensively on compressible mantle convection, Geoframework and Pyre, we felt that Eh is the most suitable person to coordinate and take charge of this activity. Luis Armendariz can also help us document and design the benchmarks.

  2. Science: At the workshop, questions were raised whether we understood well about the physics of compressible mantle convection. For example, is TALA sufficiently accurate or do we have to stick to ALA? How is the total energy balanced out? How should we deal with reference states, phase changes, and compositional changes? We felt that some additional studies are needed to better understand these problems.

    Since none of us at the workshop is currently funded to work on the compressible convection problems, we suggest that Eh and possibly David May if Louis Moresi and David May are interested spend some effort to work on these problems. This activity is closely associated with the benchmarks, but has more science components that may benefit Eh and David. It seems that all of those participating in the benchmark activity can also participate in this activity by directly working with Eh and David, if they want to.

  3. 3D compressible code development: Two directions were discussed. First, we may implement some existing algorithms including BiCG or iterative schemes into CitcomS to have a working version of the code. This should be relatively straightforward, given that the modifications will be mostly done to the outer loop of the Uzawa algorithm as done by Eh Tan and David May. Second, we may explore what the PETSc can offer to help develop the 3D compressible convection code. This may present a significant departure from the existing software at the CIG, but may become very useful later on if we decide to develop codes for flexible (high order elements/adaptive refinement) mesh and more advanced solvers.

    Again, Eh shall play a major role in pursuing these two directions. The priority is the first direction (i.e., to get a working version of CitcomS with compressibility), for which Eh can work closely with Shijie Zhong and Louis Moresi. Having such a code will enable us to start 3D benchmark for spherical compressible mantle convection problems and to test validity of various 3D algorithms. For the second direction using PETSc, we felt that this is also very important for future development of our convection software. Now that Eh joins the CIG, we can start into this possibility more seriously. It looks like David May and Louis Moresi have already gained some experience at this front. At a certain point (preferably after we get CitcomS to work with the compressible convection), Eh may start to experiment with PETSc, for which Matt Knepley can provide some great help.

  4. An abstract to 2006 Fall AGU: We will submit an abstract to 2006 Fall AGU meeting. This provides an opportunity for us to get together at the AGU to discuss our progress, and also helps us focus our effort to get relevant work done. Either Eh Tan, Scott King, Peter van Keken, Louis Moresi or Shijie Zhong can be the contact person for this abstract. We shall discuss more about the abstract idea this summer.
  5. ConMan. Scott King will contribute a cleaned up version of ConMan that has vectorization and some of the never-used features and switches removed. This will provide a cleaner starting point for testing 2D compressible convection ideas with a direct solver (as well as many other potential uses.)
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