Abstract
Advection of trace species (tracers), also called tracer transport, in models of the atmosphere and other physical domains is an important and potentially computationally expensive part of a model's dynamical core (dycore). Semi-Lagrangian (SL) advection methods are efficient because they permit a time step much larger than the advective stability limit for explicit Eulerian methods. Thus, to reduce the computational expense of tracer transport, dycores often use SL methods to advect passive tracers. The class of interpolation semi-Lagrangian (ISL) methods contains potentially extremely efficient SL methods. We describe a set of ISL bases for element-based transport, such as for use with atmosphere models discretized using the spectral element (SE) method. An ISL method that uses the natural polynomial interpolant on Gauss-Legendre-Lobatto (GLL) SE nodes of degree at least three is unstable on the test problem of periodic translational flow on a uniform element grid. We derive new alternative bases of up to order of accuracy nine that are stable on this test problem; we call these the Islet bases. Then we describe an atmosphere tracer transport method, the Islet method, that uses three grids that share an element grid: a dynamics grid supporting, for example, the GLL basis of degree three; a physics grid with a configurable number of finite-volume subcells per element; and a tracer grid supporting use of our Islet bases, with particular basis again configurable. This method provides extremely accurate tracer transport and excellent diagnostic values in a number of validation problems. We conclude with performance results that use up to 27,600 NVIDIA V100 GPUs on the Summit supercomputer.
Highlights
Trace atmosphere species, or tracers, are an important part of atmosphere models for the study of climate
We describe a set of interpolation semi-Lagrangian (ISL) bases for element-based transport, such as for use with atmosphere models discretized using the spectral element (SE) method
Order of accuracy (OOA) nspubmin − 1, the support sizes nspub for each region ordered left to middle, and the supports
Summary
Tracers, are an important part of atmosphere models for the study of climate. Because of the large number of tracers in climate models, tracer transport can be computationally very expensive To address this cost, often semi-Lagrangian (SL) methods are used to carry out passive tracer transport. Interpolation is in contrast to cell-integrated methods; these latter integrate the basis of a target (e.g. Lagrangian) element 30 against those of the source This integration entails substantially greater cost for two reasons: first, larger computational cost due to sphere-to-reference point calculation and interpolant evaluations at many quadrature points; second, larger communication volume because all data from the target element must be made available to a source element. In trade for these additional costs, flux-form and exact cell-integrated remap-form methods have the benefits of, first, local mass conservation and, second, stability obtained from the L2 projection. We seek ISL methods that satisfy a necessary condition for stability
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