Report to the CIG from the Boulder Mantle Convection Workshop

Five different 3D convection codes were discussed in the workshop: Citcom/CitcomS, Gable’s code, STAG3D, Terra, and Muenster group’s code. All these codes are parallelized with MPI and are capable of solving convection with variable viscosity (e.g., temperature-dependent viscosity, perhaps with the exception of Gable’s code). Citcom codes and Terra are finite element codes, while STAG3D and Muenster group’s code are finite volume codes. Citcom codes use elements each of which has 8 velocity nodes and 1 pressure node at the center of each element, while Terra uses tetrahedral elements. STAG3D and Terra have the capability for compressible media, while Citcom codes and Muenster group’s code are either for purely incompressible or for non-Boussinesq approximation. Citcom/CitcomS, STAG3D, and Terra all implemented multigrid solvers, while Gable’s and Muenster group’s code use either spectral or conjugate gradient solver.

B) Short-term goals and recommendations (next 6-12 months):

1. To initiate the communications with authors of 3D parallelized full multigrid Cartesian Citcom, and Terra and STAG3D to seek their contributions of these codes to the CIG software repository. This will make available to the community finite element and finite volume thermochemical/thermal convection codes in both spherical and 2D-3D Cartesian and 2D axially symmetric geometries that use several different advection methods including streamline upwind and MPDATA for advecting field variables and tracer particle advection.
2. Provide source codes, makefiles, examples, graphics package, user manuals and documentation for the codes in the CIG repository. Provide user-friendly interfaces and architectures (including Pyre and traditional methods) for the codes in CIG repository. Standardize input and output for the codes in the repository.
3. Set up effective user support service in the CIG. This includes short workshop or training programs to help students and researchers learn to understand and use the codes in the repository. The service should also include having staff from the CIG answering users’ questions about the codes via email/telephone. For each code, set up a website that includes the relevant user manuals and documentation.
4. To start benchmarks of spherical and Cartesian (3D) convection codes. At the moment, three spherical convection codes (CitcomS, Terra, and Muenster’s group) are available for benchmarks, and we hope that other codes will be included in the future. For Cartesian codes, Citcom and perhaps STAG3D may be used for benchmarks. A number of benchmark cases were defined with more to come. Set up a web page to help researchers communicate their benchmark results.
5. Identify workshops that address new methodologies that may advance the research in our field and that address common interests in different CIG areas (e.g., mantle dynamics and long-term lithosphere deformation).
6. Incorporate the PETSc into existing codes in the CIG repository and compare it with traditional parallel codes. This may require first decoupling solvers from the existing codes in the repository. Ultimately, the goal is to make us more efficient in developing new modular components.
7. Reactivate or develop certain computational functions in the existing codes, for example, the computation of the geoid anomalies.
8. Develop education and outreach component to the CIG. Possibly appoint an education and outreach steering committee (several participants have already volunteered their service to this committee). Goals could be broadly defined, from K-12 to graduate education. We need to be particularly concerned about encouraging a group of developing mantle geodynamicists who are well educated in applied math and numerical methods. Make examples available to help geophysics faculty more easily incorporate numerical methods into courses and examples that applied math faculty might use to interest geophysics students.

C) Long-term goals (2-5 years):

1. Develop compressible spherical convection code(s). Test and benchmark the code. We may start with CitcomS or/and Terra. Extend beyond simple extended-Boussinesq to include more general EOS.
2. Develop methods to couple small-scale physics, especially lithospheric deformation (elasto-plastic deformation), and melting/melt migration, into large scale mantle flow models. Also support the development of codes that allow history dependent and anisotropic rheologies.
3. Develop modular tools for variable grid methods, element types, and solvers. This will allow users to mix and match different modular to explore possible schemes that would fit users’ specific problems. This will also allow users to easily couple their own application modular.
4. Continue to introduce PYRE to mantle dynamics community.
5. Continue to hold CIG-funded workshops with more focus on new methodologies, e.g., level set method for interfaces, and multiscale methods.
6. Continue benchmark efforts with focus on thermochemical convection and non-linear rheology.