2011
DOI: 10.1515/rjnamm.2011.020
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Use of analytic solutions in the statement of difference boundary conditions on a movable shoreline

Abstract: Solutions to initial boundary value problems are constructed for the shallow water equations in the form of series locally convergent in the neighbourhood of a movable water-land boundary for an arbitrary bottom relief. The motion law and the velocity of this boundary are determined for various wave-shore interaction modes. The obtained results of analytic study of the solutions are used for the development of approximations of boundary conditions on the movable shoreline. Test problems are numerically solved … Show more

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Cited by 11 publications
(18 citation statements)
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“…These values, obtained using the TVD+SPH method, are significantly larger than the results from the work [4] for practically all considered amplitudes. Yet, they are close to the results obtained using the methodology from the work [6], which, however, happen to be somewhat smaller for the largest amplitudes. Let us note, that if for the absolute values of the run-up values R the monotonic increase takes place, then the corresponding relative values R/A increase first (up to the ampli- (1, 4), the methods from [6] (2, 5) and [4] (3, 6); the domain of applicability of the analytical solution [13] is marked by grey color.…”
Section: Numerical Resultssupporting
confidence: 85%
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“…These values, obtained using the TVD+SPH method, are significantly larger than the results from the work [4] for practically all considered amplitudes. Yet, they are close to the results obtained using the methodology from the work [6], which, however, happen to be somewhat smaller for the largest amplitudes. Let us note, that if for the absolute values of the run-up values R the monotonic increase takes place, then the corresponding relative values R/A increase first (up to the ampli- (1, 4), the methods from [6] (2, 5) and [4] (3, 6); the domain of applicability of the analytical solution [13] is marked by grey color.…”
Section: Numerical Resultssupporting
confidence: 85%
“…For small amplitudes (nearly up to A = 1 m) the values, obtained by the TVD+SPH method, increase monotonically and practically coincides with the results from [4], which starts to decrease sharply and tend to zero for the largest amplitude. On the contrary, the results, obtained by the TVD+SPH algorithm, continue the stable monotonic increase and stay smaller than the results from [6] for the whole range of amplitude variation. The analysis of the graphs with the maximal values |R|/A in the run-down phase points in the first place to the preserving anomalous tendency of the results from [4] to zero for A > 1 m and their closeness to the results, obtained by the TVD+SPH algorithm, up to the amplitude A = 1 m. The behavior of the TVD+SPH results are qualitatively close to the distribution computed by the methodology from [6], which however is positioned significantly higher.…”
Section: Numerical Resultscontrasting
confidence: 54%
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