NAVAL POSTGRADUATE SCHOOL Monterey, California High-Order Higdon Non-Reflecting Boundary Conditions for the Shallow Water Equations
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چکیده
In this report we document the implementation of high order Higdon nonreflecting boundary conditions. We suggest a way to choose the parameters and demonstrate numerically the efficiency of our choice. The model we used is the shallow water equations and as a special case the Klein-Gordon equation. These equations are solved by the finite difference method. We comment on the use of finite elements and demonstrate a new, more efficient method. The case of curved boundary is discussed. We close with a list of topics for research. 1. Statement of the Problem Consider the shallow water equations (SWEs) in a semi-infinite channel. For simplicity we assume that the channel has a flat bottom and that there is no advection, although these assumptions may be removed in future studies. We do take into account rotation (Coriolis) effects. A Cartesian coordinate system (x, y) is introduced such that the channel is parallel to the x direction, as shown in the figure. The width of the channel is denoted b.
منابع مشابه
High-order nonre(ecting boundary conditions for the dispersive shallow water equations
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