A Parallel and Highly Scalable Framework for Atmospheric Simulation on Parallel Computers
Predictive simulations are crucial for the success of atmospheric modeling, and it is highly desirable to obtain accurate non-negative solutions for the transport problem on the sphere in these numerical simulations. However, most existing approaches do not ensure the predicted tracer fraction to stay within the physical range, which will seriously ruin the numerical accuracy and physical significance of the simulation. In this talk, a parallel, highly scalable, Eulerian framework based on the variational inequality method is developed for the tracer transport on the sphere. More precisely, the proposed algorithmic framework involves an implicit, variational inequality discretization for naturally satisfying the basic boundedness requirement, and a nonlinearly preconditioned semismooth Newton algorithm with a domain decomposition based linear solver for the resultant nonlinear system. We numerically show that the proposed Eulerian framework is robust and highly scalable, in terms of the total computing time for solving the problem with hundreds of millions of unknowns and on a supercomputer with over 10,000 processor cores.