| Full text | |
| Author(s): |
Steinstraesser, Joao Guilherme Caldas
;
Schreiber, Martin
;
Peixoto, Pedro S.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS; v. 59, n. 3, p. 34-pg., 2025-06-04. |
| Abstract | |
In this work, we study and extend a class of semi-Lagrangian exponential methods, which combine exponential time integration techniques, suitable for integrating stiff linear terms, with a semi-Lagrangian treatment of nonlinear advection terms. Partial differential equations involving both processes arise for instance in atmospheric circulation models. Through a truncation error analysis, we show that previously formulated semi-Lagrangian exponential schemes are limited to first-order accuracy due to the approximation of the integration factor acting on the discretization of the linear term; we then formulate a new discretization leading to second-order accuracy. Also, a detailed stability study is conducted to compare several Eulerian and semi-Lagrangian exponential schemes, as well as a well-established semi-Lagrangian semi-implicit method, which is used in operational atmospheric models. Numerical simulations of the shallow-water equations on the rotating sphere are performed to assess the orders of convergence, stability properties, and computational cost of each method. The proposed second-order semi-Lagrangian exponential method was shown to be more stable and accurate than the previously formulated schemes of the same class at the expense of larger wall-clock times; however, the method is more stable and has a similar cost compared to the well-established semi-Lagrangian semi-implicit method; therefore, it is a competitive candidate for potential operational applications in atmospheric circulation modeling. (AU) | |
| FAPESP's process: | 21/03777-2 - Parallel-in-time resolution of the shallow water equations on the rotating sphere using spherical harmonics and semi-Lagrangian discretization |
| Grantee: | João Guilherme Caldas Steinstraesser |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 21/06176-0 - Numerical methods for a new generation of weather and climate models |
| Grantee: | Pedro da Silva Peixoto |
| Support Opportunities: | Research Grants - Research Program on Global Climate Change - Young Investigators - Phase 2 |