The stability of boundary conditions for an angled-derivative difference scheme
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Tidal forcing of the shallow water equations is typical of a class of problems where an approximate equilibrium solution is sought by long time integration of a differential equation system. A combination of the angled-derivative scheme with a staggered leap-frog scheme is sometimes used to discretise this problem. It is shown here why great care then needs to be taken with the boundary conditions to ensure that spurious solution modes do not lead to numerical instabilities. Various techniques are employed to analyse two simple model problems and display instabilities met in practical computations; these are then used to deduce a set of stable boundary conditions.
Keywordsnumerical stability Godunov-Ryabenkii conditions initial boundary value problem angled-derivative difference scheme tidally-forced shallow water equations
AMS subject classification64N99 65L10
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