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.
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.
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.
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.