This project involves the construction of state-of-the-art numerical methods for atmospheric modeling applications. The numerical methods of interest include spatial discretization methods as well as explicit, semi-implicit, fully implicit, and Lagrangian time-integrators. Specifically, the project looks at developing element-based Galerkin methods (e.g., spectral element and discontinuous Galerkin methods) that are local in nature, high-order accurate, geometrically flexible, and efficient to use on large vector and/or distributed-memory computers. We are also interested in issues concerning global and local conservation as well as monotonicity preserving properties. The element-based nature of these methods means that any type of grid can be used to represent the solution domain; therefore, the project also involves the construction of grid generators and domain decomposition methods to divide the domain across the vast number of processes of the target computer. Explicit time-integrators work efficiently on this class of computers but the CFL condition imposes a very small time-step constraint that needs to be circumvented. Semi-implicit methods ameliorate this stringent time-step restriction but fully implicit and Lagrangian time-integrators completely avoid the CFL condition, which then allows much larger time-steps to be used. However, non-explicit methods require the solution of a large global sparse matrix problem which must be solved accurately and efficiently. For this part of the project, knowledge in iterative solvers and preconditioners is of significant interest. The types of atmospheric modeling problems that we are interested in exploring include hydrostatic, non-hydrostatic, and unified continuous equation sets.

 

key words

Adaptive; Atmospheric; Discontinuous; Element; Galerkin; Grid; Hydrostatic; Modeling; Numerical; Spectral;

Citizenship:  Open to U.S. citizens and permanent residents

Level:  Open to Postdoctoral applicants