Argonne National Laboratory

Nonlinear Compact Finite-Difference Schemes with Semi-Implicit Time Stepping

TitleNonlinear Compact Finite-Difference Schemes with Semi-Implicit Time Stepping
Publication TypeJournal Article
Year of Publication2014
AuthorsGhosh, D, Constantinescu, EM
JournalSpringer's Lecture Notes in Computational Science and Engineering (LNCSE) Series
IssueICOSAHOM 2014
Date Published2015
Other NumbersANL/MCS-P5199-0914
AbstractAtmospheric flows are characterized by a large range of length scales as well as strong gradients. The accurate simulation of such flows requires numerical algorithms with high spectral resolution, as well as the ability to yield nonoscillatory solutions across regions of high gradients. These flows exhibit a large range of time scales as well—the slowest waves propagate at the flow velocity and the fastest waves propagate at the speed of sound. Time integration with explicit methods are thus inefficient and algorithms with semi-implicit time integration have been successfully used in past studies. We propose a finite-difference method for atmospheric flows that uses a weighted compact scheme for spatial discretization and the implicit-explicit additive Runge-Kutta methods for time integration. We present results for benchmark atmospheric flows and compare our results with existing ones in the literature.