Atmosphere Ocean Science Friday Seminar

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A 3rd/2nd order MOOD limited well-balanced scheme for the shallow water equations

Speaker: Sophie Hörnschemeyer, Achen University, Germany

Location: Warren Weaver Hall 1314

Date: Friday, March 3, 2023, 4 p.m.

Synopsis:

The talk presents a high-order accurate, positivity-preserving and well-balanced finite volume scheme for the shallow water equations with variable topography. An unlimited third-order scheme is combined with the recent, second-order accurate Bottom-Surface-Gradient Method (BSGM). This is monitored by an a-posteriori MOOD (Multidimensional Optimal Order Detection) limiting step, which detects possible local instabilities of a high-order candidate solution such as loss of positivity or local oscillations, and switches locally to a lower order, stable and robust “parachute” scheme if necessary. The accuracy, effectiveness and robustness of the proposed adaptive methodology is demonstrated with numerical experiments, both for near-equilibrium and non-equilibrium depth-averaged flows.