Parallel-in-time resolution of the shallow water equations on the rotating sphere using spherical harmonics and semi-Lagrangian discretization

• Grant number: 21/03777-2
• Support type: Scholarships in Brazil - Post-Doctorate
• Effective date (Start): December 01, 2021
• Effective date (End): November 30, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal researcher: Pedro da Silva Peixoto
• Grantee: João Guilherme Caldas Steinstraesser
• Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 16/18445-7 - Numerical methods for the next generation weather and climate models, AP.JP

Abstract

This postdoctoral project aims to study the numerical resolution of atmospheric fluid dynamics models using parallel-in-time schemes. As a component of complex climate and weather prediction models, atmospheric modelling must provide accurate numerical solutions, which are computationally expensive; therefore, temporal parallelization is a promising approach for reducing the high computational times necessary for performing these accurate simulations. We focus on the resolution of the shallow water equations (SWE) on the rotating sphere, a two-dimensional model widely used in the atmospheric modelling community since it is a simplified model presenting most of the properties and challenges of more complex ones. The equations are discretized in space and time using respectively spherical harmonics and a semi-Lagrangian method, two approaches widely used in this domain. The temporal parallelization will be performed using different methods, \eg the parareal, the MGRIT and the PFASST, which have been recently applied to the resolution of the SWE on the rotating sphere, but combined with other temporal discretizations. For this application, the temporal parallelization is especially challenging because parallel-in-time methods present instabilities and/or slow convergence when applied to hyperbolic or advection-dominated problems, such as the ones arising in atmospheric modelling. Recently, the combination of the parareal method with a semi-Lagrangian discretization showed promising results for improving its stability. Therefore, we consider this approach as guideline in this work and we investigate further improvements of the parallel-in-time methods. The proposed numerical schemes will be executed, validated and compared in real parallel high performance computing (HPC) systems. (AU)