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Publication Date
22 December 2020

New Time-Stepping Algorithm Analysis Framework

With applications to atmospheric modeling​
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The article presents an improved framework for evaluating, comparing, and selecting algorithms for solving the time-evolution of the dynamics equations for atmospheric modeling.  


The new method is more selective than previous techniques, which may show that a particular algorithm and time step size is numerically stable when in fact it is not.  Previously, such instabilities could not be known until a simulation was completed, or crashed.   The new framework is capable of identifying such instabilities ahead of time.  It also provides hints for designing new algorithms with optimal stability properties for use in atmospheric modeling.  We apply it in this context to the non-hydrostatic atmosphere component of the Energy Exascale Earth System Model (E3SM).


The computational performance requirements of climate models motivate algorithms that are capable of taking large time steps, to minimize the number of time increments that must be computed in a given climate simulation.  Many algorithms are capable of taking large time steps, but some have better properties than others; for example, some may be too dissipative, and some may not capture propagating waves with sufficient accuracy. We demonstrate an improved analysis framework to compare specific algorithms from the implicit-explicit (IMEX) family of time-stepping methods.  We show that it is more sensitive than previously used algorithms, and we demonstrate its evaluation of several well-known IMEX schemes.  The new framework is used to select numerical algorithms for time-stepping the atmosphere component of the Energy Exascale Earth System Model.  

Point of Contact
Oksana Guba
Sandia National Laboratories (SNL)
Funding Program Area(s)