2012
DOI: 10.1016/j.matcom.2011.09.006
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Numerical solution of the ‘classical’ Boussinesq system

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Cited by 36 publications
(60 citation statements)
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“…The systems (1) are Boussinesq approximations of the two-dimensional Euler equations and model two-way propagation of long waves of small amplitude (when the Stokes number is of O (1)) of an incompressible, inviscid fluid in a uniform horizontal channel of finite depth with a free surface. The variables in (1) are nondimensional and unscaled: x and t are proportional to position along the channel and time, respectively, while η(x, t) and u(x, t) are proportional to the deviation of the free surface above an undisturbed level, and to the horizontal velocity of the fluid at a height y = −1 + θ(1 + η(x, t)), respectively.…”
Section: Corresponding Authormentioning
confidence: 99%
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“…The systems (1) are Boussinesq approximations of the two-dimensional Euler equations and model two-way propagation of long waves of small amplitude (when the Stokes number is of O (1)) of an incompressible, inviscid fluid in a uniform horizontal channel of finite depth with a free surface. The variables in (1) are nondimensional and unscaled: x and t are proportional to position along the channel and time, respectively, while η(x, t) and u(x, t) are proportional to the deviation of the free surface above an undisturbed level, and to the horizontal velocity of the fluid at a height y = −1 + θ(1 + η(x, t)), respectively.…”
Section: Corresponding Authormentioning
confidence: 99%
“…In [4] the present authors studied the well-posedness of three types of initial-boundary-value problems (ibvp's) for the Bona-Smith systems (1) on bounded spatial intervals [−L, L], in which (1) and the initial conditions η(x, 0) = η 0 (x), u(x, 0) = u 0 (x), x ∈ [−L, L], are supplemented by three types of boundary conditions posed at x = ±L for t ≥ 0: (i) Nonhomogeneous Dirichlet boundary conditions, wherein η and u are given functions of t at x = ±L. (ii) Reflection boundary conditions, i.e.…”
Section: Corresponding Authormentioning
confidence: 99%
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