Use of analytic solutions in the statement of difference boundary conditions on a movable shoreline

被引：6

作者：

Bautin, S. P. ^{[1
]}

Deryabin, S. L. ^{[1
]}

Sommer, A. F. ^{[2
]}

Khakimzyanov, G. S. ^{[3
]}

Shokina, N. Yu. ^{[3
]}

机构：

[1] Ural State Univ Railway Engn, Ekaterinburg 620034, Russia

[2] Novosibirsk State Univ, Novosibirsk 630090, Russia

[3] Russian Acad Sci, Inst Computat Technol, Siberian Branch, Novosibirsk 630090, Russia

来源：

RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING | 2011年 / 26卷 / 04期

基金：

俄罗斯基础研究基金会;

关键词：

RUN-UP; SOLITARY WAVES; SLOPING BEACH; LONG WAVES; BORE;

D O I：

10.1515/RJNAMM.2011.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 using an explicit predictor-corrector scheme of the second order of approximation on adaptive grids retracing the position of the water-land boundary. The results of these calculations are presented.

引用

页码：353 / 377

页数：25

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