Exponential versus IMEX high-order time integrators for thermal convection in rotating spherical shells

Authors:
Ferran Garcia;Luca Bonaventura;Marta Net;Juan Sánchez
Affiliations:
Departament de Física Aplicada, Universitat Politècnica de Catalunya, Jordi Girona 1-3, 08034 Barcelona, Spain;MOX - Modelling and Scientific Computing, Dipartimento di Matematica "F. Brioschi", Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy;Departament de Física Aplicada, Universitat Politècnica de Catalunya, Jordi Girona 1-3, 08034 Barcelona, Spain;Departament de Física Aplicada, Universitat Politècnica de Catalunya, Jordi Girona 1-3, 08034 Barcelona, Spain
Venue:
Journal of Computational Physics
Year:
2014

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Abstract

We assess the accuracy and efficiency of several exponential time integration methods coupled to a spectral discretization of the three-dimensional Boussinesq thermal convection equations in rotating spherical shells. Exponential methods are compared to implicit-explicit (IMEX) multi-step methods already studied previously in [1]. The results of a wide range of numerical simulations highlight the superior accuracy of exponential methods for a given time step, especially when employed with large time steps and at low Ekman number. However, presently available implementations of exponential methods appear to be in general computationally more expensive than those of IMEX methods and further research is needed to reduce their computational cost per time step. A physically justified extrapolation argument suggests that some exponential methods could be the most efficient option for integrating flows near Earth's outer core conditions.