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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

SEMI-LAGRANGIAN EXPONENTIAL INTEGRATION WITH APPLICATION TO THE ROTATING SHALLOW WATER EQUATIONS

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Author(s):
Peixoto, Pedro S. [1] ; Schreiber, Martin [2]
Total Authors: 2
Affiliation:
[1] Univ Sao Paulo, Appl Math, BR-05508090 Sao Paulo, SP - Brazil
[2] Tech Univ Munich, D-85748 Garching - Germany
Total Affiliations: 2
Document type: Journal article
Source: SIAM JOURNAL ON SCIENTIFIC COMPUTING; v. 41, n. 5, p. B903-B928, 2019.
Web of Science Citations: 0
Abstract

In this paper we propose a novel way to integrate time-evolving partial differential equations that contain nonlinear advection and stiff linear operators, combining exponential integration techniques and semi-Lagrangian methods. The general formulation is built from the solution of an integration factor problem with respect to the problem written with a material derivative, so that the exponential integration scheme naturally incorporates the nonlinear advection. Semi-Lagrangian techniques are used to treat the dependence of the exponential integrator on the flow trajectories. The formulation is general, as many exponential integration techniques could be combined with different semi-Lagrangian methods. This formulation allows an accurate solution of the linear stiff operator, a property inherited by the exponential integration technique. It also provides a sufficiently accurate representation of the nonlinear advection, even with large time-step sizes, a property inherited by the semi-Lagrangian method. Aiming for application in weather and climate modeling, we discuss possible combinations of well-established exponential integration techniques and state-of-the-art semi-Lagrangian methods used operationally in the application. We show experiments for the planar rotating shallow water equations. When compared to traditional exponential integration techniques, the experiments reveal that the coupling with semi-Lagrangian allows stabler integration with larger time-step sizes. From the application perspective, which already uses semi-Lagrangian methods, the exponential treatment could improve the solution of wave dispersion when compared to semi-implicit schemes. (AU)

FAPESP's process: 16/18445-7 - Numerical methods for the next generation weather and climate models
Grantee:Pedro da Silva Peixoto
Support Opportunities: Research Grants - Young Investigators Grants