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An adaptive Finite Point Method (FPM) for solving shallow water problems is presented. The numerical
methodology we propose, which is based on weighted-least squares approximations on clouds of points,
adopts an upwind-biased discretization for dealing with the convective terms in the governing equations.
The viscous and source terms are discretized in a pointwise manner and the semi-discrete equations are
integrated explicitly in time by means of a multi-stage scheme. Moreover, with the aim of exploiting
meshless capabilities, an adaptive h-refinement technique is coupled to the described flow solver. The
success of this approach in solving typical shallow water flows is illustrated by means of several numerical
examples and special emphasis is placed on the adaptive technique performance. This has been assessed
by carrying out a numerical simulation of the 26th December 2004 Indian Ocean tsunami with highly
encouraging results. Overall, the adaptive FPM is presented as an accurate enough, cost-effective tool for
solving practical shallow water problems.
CitationOrtega, E. [et al.]. Finite point method to solve shallow water equations. "International journal for numerical methods in engineering", Octubre 2011, vol. 88, núm. 2, p. 180-204.
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