Numerical Turbulence Algorithms and Code Development

	This image shows the interaction of two colliding fronts as a solution to the multi-dimensional Burgers equation, produced using the GASpAR code. Illustrated is the x-velocity field over one-quarter of the entire grid. This solution demonstrates the ability of the adaptive refinement algorithms to capture even relatively complicated localized, non-linear flow features accurately.

The IMAGe Turbulence Numerics Team (TNT) develops both tools and models that enhance our capability to investigate geophysical turbulence, and it applies these capabilities to fundamental scientific objectives. This program complements the IMAGe Geophysical Turbulence Program and focuses on the accurate simulation and understanding of fluid turbulence, as found in the atmosphere and for charged flows in the presence of magnetic fields. TNT research emphasizes simplified physical systems that still reproduce the complexity and multi-scale properties associated with turbulent flows but that allow for the highest possible Reynolds number.

TNT code development supports NCAR's work to provide highly scalable numerical tools for geophysical flows. TNT applications support NCAR's efforts to perform multi-scale investigations using enhanced modeling capability. This work advances NCAR's strategic priorities of "Conducting research in computer science, applied mathematics, statistics, and numerical methods" and "Developing and providing advanced services and tools."

TNT members have broad experience in developing a variety of algorithms for studying turbulence. Our highly scalable codes include a 2D and 3D pseudo-spectral hydro- and magnetohydrodynamics (MHD) code that may include a Hall current. This code has also been modified to include a Lagrandian-averaged ('alpha') model that smooths the velocity locally and has proved useful for very high Reynolds number studies. We also have a new fully spectral method to solve the equations of MHD in spherical geometry, with which studies can be made of fluid turbulence at moderate Reynolds numbers with a variety of boundary conditions.

Through FY 2006, TNT has been actively developing a high-order adaptive mesh refinement code that has been tested on the two-dimensional Burgers and Navier-Stokes equations. An MHD solver is being added presently, and this represents the main direction of research for FY 2007. The code is being improved by adding optimized preconditioners for its Krylov pressure solver and by accelerating inter-processor communications. We plan to add the 'alpha' model for high Reynolds number calculations in two space dimensions, and we plan on beginning to add code to accommodate the compressible MHD equations later, as per the physical requirements of the objects we want to model (such as in the solar wind and the Sun).

Finally, we are developing a proof-of-concept one-dimensional moving grid algorithm that has spectral accuracy.

TNT research is sponsored by NSF Core funds and partially by NSF grant CMG-0327888.