Numerical Analysis Seminar

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Date, time & place Tuesday 16:30 - 18:00 002Room #002 (Graduate School of Math. Sci. Bldg.)
Organizer(s) Norikazu Saito, Takahito Kashiwabara

2017/07/04

16:50-18:20   Room #002 (Graduate School of Math. Sci. Bldg.)
Ming-Cheng Shiue (National Chiao Tung University)
Boundary conditions for Limited-Area Models (English)
[ Abstract ]
The problem of boundary conditions in a limited domain is recognized an important problem in geophysical fluid dynamics. This is due to that boundary conditions are proposed to have high resolution over a region of interest. The challenges for proposing later boundary conditions are of two types: on the computational side, if the proposed boundary conditions are not appropriate, it is well-known that the error from the lateral boundary can propagate into the computational domain and make a major effect on the numerical solution; on the mathematical side, the negative result of Oliger and Sundstrom that these equations including the inviscid primitive equations and shallow water equations in the multilayer case are not well-posed for any set of local boundary conditions.
In this talk, three-dimensional inviscid primitive equations and (one-layer and two-layer) shallow water equations which have been used in the limited-area numerical weather prediction modelings are considered. Our goals of this work are two folds: one is to propose boundary conditions which are physically suitable. That is, they let waves move freely out of the domain without producing spurious waves; the other is to numerically implement these boundary conditions by proposing suitable numerical methods. Numerical experiments are presented to demonstrate that these proposed boundary conditions and numerical schemes are suitable.