2017/04/03 by Jan Scheffel, Kristoffer Lindvall, Hiu Fai Yik +1 · 16 citations
Earth and Planetary Sciences · Environmental Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Artificial intelligence #Chaotic #Chebyshev filter #Climate variability and models #Computer science #Finite difference #Finite difference method #Lorenz system #Mathematical analysis #Mathematical optimization #Mathematics #Meteorological Phenomena and Simulations #Meteorology #Numerical weather prediction #Physics #Precipitation Measurement and Analysis #Series (stratigraphy) #Spectral method #Time domain #physics.comp-ph
paper · pdf · doi:10.1016/j.cpc.2018.01.010
published in Computer Physics Communications 226, 127-135 (Elsevier BV)
arxiv created 2017/04/03 · openalex publication_date 2018/02/07 · arxiv updated 2018/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Finite difference methods are traditionally used for modelling the time domain in numerical weather prediction (NWP). Time-spectral solution is an attractive alternative for reasons of accuracy and efficiency and because time step limitations associated with causal, CFL-like critera are avoided. In this work, the Lorenz 1984 chaotic equations are solved using the time-spectral algorithm GWRM. Comparisons of accuracy and efficiency are carried out for both explicit and implicit time-stepping algorithms. It is found that the efficiency of the GWRM compares well with these methods, in particular at high accuracy. For perturbative scenarios, the GWRM was found to be as much as four times faster than the finite difference methods. A primary reason is that the GWRM time intervals typically are two orders of magnitude larger than those of the finite difference methods. The GWRM has the additional advantage to produce analytical solutions in the form of Chebyshev series expansions. The results are encouraging for pursuing further studies, including spatial dependence, of the relevance of time-spectral methods for NWP modelling.