Analysis and improvement of a semi-Lagrangian exponential scheme for the shallow-water equations on the rotating sphere

Autor(es)

Steinstraesser, Joao Guilherme Caldas ; Schreiber, Martin ; Peixoto, Pedro S.

• Tipo de documento: Artigo Científico
• Fonte: ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS; v. 59, n. 3, p. 34-pg., 2025-06-04.

Resumo

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)

• Processo FAPESP: 21/03777-2 - Paralelização temporal das equações de águas rasas na esfera usando harmônicos esféricos e discretização semi-lagrangeana
• Beneficiário: João Guilherme Caldas Steinstraesser
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 21/06176-0 - Métodos numéricos para uma nova geração de modelos de previsão de tempo e clima
• Beneficiário: Pedro da Silva Peixoto
• Modalidade de apoio: Auxílio à Pesquisa - Programa de Pesquisa sobre Mudanças Climáticas Globais - Jovens Pesquisadores - Fase 2