Journal of Scientific Computing

, Volume 41, Issue 1, pp 139–164 | Cite as

Semi-Lagrangian Runge-Kutta Exponential Integrators for Convection Dominated Problems



In this paper we consider the case of nonlinear convection-diffusion problems with a dominating convection term and we propose exponential integrators based on the composition of exact pure convection flows. These methods can be applied to the numerical integration of the considered PDEs in a semi-Lagrangian fashion. Semi-Lagrangian methods perform well on convection dominated problems (Pironneau in Numer. Math. 38:309–332, 1982; Hockney and Eastwood in Computer simulations using particles. McGraw-Hill, New York, 1981; Rees and Morton in SIAM J. Sci. Stat. Comput. 12(3):547–572, 1991; Baines in Moving finite elements. Monographs on numerical analysis. Clarendon Press, Oxford, 1994).

In these methods linear convective terms can be integrated exactly by first computing the characteristics corresponding to the gridpoints of the adopted discretization, and then producing the numerical approximation via an interpolation procedure.


Additive Runge-Kutta methods Commutator-free methods Convection-diffusion equations Semi-Lagrangian methods 


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Institutt for Matematiske FagNTNUTrondheimNorway

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