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Discrete transparent boundary conditions for the linearized Green-Naghdi system of equations. (arXiv:1710.04016v1 [math.AP])
来源于:arXiv
In this paper, we introduce artificial boundary conditions for the linearized
Green-Naghdi system of equations. The derivation of such continuous
(respectively discrete) boundary conditions include the inversion of Laplace
transform (respectively Z-transform) and these boundary conditions are in turn
non local in time. In the case of continuous boundary conditions, the inversion
is done explicitly. We consider two spatial discretisations of the initial
system either on a staggered grid or on a collocated grids, both of interest
from the practical point of view. We use a Crank Nicolson time discretization.
The proposed numerical scheme with the staggered grid permits explicit
Z-transform inversion whereas the collocated grid discretization do not. A
stable numerical procedure is proposed for this latter inversion. We test
numerically the accuracy of the described method with standard Gaussian initial
data and wave packet initial data which are more convenient to explore the
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