Title: Implicit modeling of fluid dynamics for Earth systems applications

Speaker: Kate Evans, ORNL

Date/Time: Monday, December 17, 2007, 10:00 am - 11:00 am

Location: CSRI Building, Room 90 (Sandia NM)

Brief Abstract: Major algorithmic challenges are posed for the accurate simulation of problems with coupled nonlinear physics, specifically those with relatively long time scales. A convection simulation with a melt front is presented whereby multiple roll cells develop at early times. The discrete equation set for the model is solved with the Jacobian-Free Newton-Krylov (JFNK) nonlinear inexact Newton's method. SIMPLE, a pressure-correction algorithm, is used as a physics-based preconditioner. The issue of temporal error is explored by comparing solutions using JFNK-SIMPLE converged to first and second order accuracy and SIMPLE converged to a mass balance condition.

Increasing discrepancies in the vorticity field over time illustrate the accuracy constraints of mass balance and first order nonlinear convergence methods. The sensitivity of the fluid solution to the solution method has motivated the implementation of the fully nonlinear JFNK method into a test case within an Earth system model. For our atmospheric model, the shallow water equations are solved on a cubed sphere using spectral element spatial discretization. The JFNK algorithm implementation plan will be outlined, and several options to maximize solver performance as measured by accuracy, efficiency, and scaling will be discussed.