A comparison of high-order time integrators for thermal convection in rotating spherical shells

Authors:
F. Garcia;M. Net;B. García-Archilla;J. Sánchez
Affiliations:
Departamento de Física Aplicada, Universitat Politècnica de Catalunya, Jordi Girona Salgado s/n, Campus Nord. Mòdul B4, 08034 Barcelona, Spain;Departamento de Física Aplicada, Universitat Politècnica de Catalunya, Jordi Girona Salgado s/n, Campus Nord. Mòdul B4, 08034 Barcelona, Spain;Departamento de Matemática Aplicada II, Universidad de Sevilla, Escuela Superior de Ingenieros, Camino de los Descubrimientos, s/n, 41092 Sevilla, Spain;Departamento de Física Aplicada, Universitat Politècnica de Catalunya, Jordi Girona Salgado s/n, Campus Nord. Mòdul B4, 08034 Barcelona, Spain
Venue:
Journal of Computational Physics
Year:
2010

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Abstract

A numerical study of several time integration methods for solving the three-dimensional Boussinesq thermal convection equations in rotating spherical shells is presented. Implicit and semi-implicit time integration techniques based on backward differentiation and extrapolation formulae are considered. The use of Krylov techniques allows the implicit treatment of the Coriolis term with low storage requirements. The codes are validated with a known benchmark, and their efficiency is studied. The results show that the use of high-order methods, especially those with time step and order control, increase the efficiency of the time integration, and allows to obtain more accurate solutions.