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Numerical schemes for Shallow Water equations

Matthieu Brachet (laboratoire de Mathématiques et Applications (Poitiers, France))
Onsdag, 16 december, 2020, at 15:00-16:00, The talk will be given on Zoom. Please, contact the organizers for more information.

Shallow Water equations model a fluid of low thickness and is used in climate and oceanography simulations. There are no analytic solution known and a numerical method is required to solve equations. In numerical analysis, we investigate on various points. Among other :

  • Accuracy is obviously an important point. It represent the error done using the scheme.

  • Stability is the property to retain a bounded error.

  • Computational cost is related to the ability to have results in a reasonable time.

In this talk, I will consider Exponential Integrators and hermitian finite difference scheme. The scheme is analyzed on linearized Shallow Water equations. Results are compared with those obtained with traditional methods. The computational costs are compared and the influence of the time step will be discussed. If I have enough time, I will talk about the results obtained for solving spherical equations

Organiseret af: Seminar of the Young Mathematicians of Aarhus
Kontaktperson: Benjamin Alvarez and Polyxeni Spilioti