Mathematical Modeling and Analysis
Mathematical Modeling and Analysis
Variations in mesoscale ocean circulation play a significant role in the earth's climate. For example, the North Atlantic is one of the main sources of deep water, and through thermohaline circulation (global density-driven flow; temperature and salinity determine the density of water), is strongly coupled to the global climate. However, this complex flow contains a broad hierarchy of time-scales, and in particular, modes at each scale are strongly influenced by the dynamics of faster modes. Thus, to enable efficient and accurate long-time simulations, we are investigating optimal multilevel iterative solvers for fully-implicit time stepping algorithms. Fully-Implicit time evolution offers the ability to take significantly larger time steps while maintaining a nonlinearly consistent discrete solution. The implementation is based on the Jacobian-Free Newton-Krylov (JFNK) algorithm, and a critical component of its efficiency is the optimal preconditioning of the underlying Krylov iterations. Specifically, we use a semi-implicit discretization as the preconditioner and employ the adaptive hierarchical solution method implemented in the Los Alamos Algebraic Multigrid (LAMG) to solve the implicit part. We demonstrate the efficiency and scalability of this approach for wind-driven flow in the North Atlantic.
