Description

This postdoctoral research opportunity at the Naval Research Laboratory (NRL) in Monterey, California focuses on the development of state-of-the-art numerical methods for atmospheric modeling applications. The project emphasizes constructing element-based Galerkin methods such as spectral element and discontinuous Galerkin methods that are:

• Local in nature
• High-order accurate
• Geometrically flexible
• Efficient on large vector and distributed-memory computers

The research includes spatial discretization techniques and various time-integrators: explicit, semi-implicit, fully implicit, and Lagrangian. A key challenge addressed is overcoming the CFL (Courant-Friedrichs-Lewy) condition that limits time-step size in explicit methods. Semi-implicit methods reduce this constraint, while fully implicit and Lagrangian integrators avoid it entirely, allowing larger time-steps but requiring efficient solutions to large sparse matrix problems using iterative solvers and preconditioners.

Additional components involve developing grid generators and domain decomposition methods to distribute computational domains across many processors. The atmospheric modeling problems of interest include hydrostatic, non-hydrostatic, and unified continuous equation sets, with attention to global/local conservation and monotonicity-preserving properties.