Applying local discretization methods in the NASA finite-volume general circulation model

You can simulate the atmosphere’s activities, climate modeling, by programming approximate solutions to the physical laws that govern it. An atmospheric model usually has two parts: a dynamical core that solves a set of partial differential equations for an idealized atmosphere and a set of physical parameterizations that provides realistic forcing (such as precipitation, surface friction, and solar radiation) to this atmosphere. These two parts are usually treated separately. Recently, designing computing algorithms for climate modeling, which requires massive computation for longterm simulations, has come to rely on efficiently implementing parallel computation with distributed memory. Although numerical methods based on local memory have parallel efficiency with distributed memory, fundamental issues arise when applying these local methods to global climate modeling. (See the related sidebar.) To address these issues, we developed a general circulation model (GCM) at the NASA Goddard Space Flight Center using monotonic finite-volume transport schemes. The physical quantity choices are conservative following the motion in the idealized smooth atmosphere. To establish transport in one dimension, we adopted a set of finite-volume schemes, including Sergei Godunov’s piecewise constant scheme,1 Bram van Leer’s piecewise linear scheme,2 and Phil Colella and Paul Woodward’s piecewise-parabolic method (PPM).3 We based our model’s dynamical core on Shian-Jiann Lin and Richard Rood’s work in the 1990s4–7 and based the physical parameterizations on those of the community climate model developed by the National Center for Atmospheric Research. In this article, we present the NASA finite-volume dynamical core’s basic ideas, concentrating on how to use Lagrangian conservation to improve the approximate solutions’ accuracy for the idealized atmosphere.