A new run-up algorithm based on local high-order analytic expansions

被引：7

作者：

Khakimzyanov, Gayaz ^{[1
]}

Shokina, Nina Yu. ^{[1
]}

Dutykh, Denys ^{[2
]}

Mitsotakis, Dimitrios ^{[3
]}

机构：

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

[2] Univ Savoie Mt Blanc, CNRS, LAMA, UMR 5127, Campus Sci, F-73376 Le Bourget Du Lac, France

[3] Victoria Univ Wellington, Sch Math Stat & Operat Res, POB 600, Wellington 6140, New Zealand

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2016年 / 298卷

基金：

俄罗斯科学基金会;

关键词：

Nonlinear shallow water equations; Finite volumes; Finite differences; Wave run-up; Asymptotic expansion; SHALLOW-WATER EQUATIONS; BOUNDARY-CONDITIONS; FINITE-VOLUME; SCHEMES; WAVES; SHORELINE; SOLVER; BEACH;

D O I：

10.1016/j.cam.2015.12.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The practically important problem of the wave run-up is studied in this article in the framework of Nonlinear Shallow Water Equations (NSWE). The main novelty consists in the usage of high order local asymptotic analytical solutions in the vicinity of the shoreline. Namely, we use the analytical techniques introduced by S. KOVALEVSKAYA and the analogy with the compressible gas dynamics (i.e. gas outflow problem into the vacuum). Our run-up algorithm covers all the possible cases of the wave slope on the shoreline and it incorporates the new analytical information in order to determine the shoreline motion to higher accuracy. The application of this algorithm is illustrated in several important practical examples. Finally, the simulation results are compared with the well-known analytical and experimental predictions. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：82 / 96

页数：15

共 46 条

[1] The boundary value problem for the nonlinear shallow water equations [J].

Antuono, Matteo ;

Brocchini, Maurizio .

STUDIES IN APPLIED MATHEMATICS, 2007, 119 (01) :73-93

[2] On the role of the Chezy frictional term near the shoreline [J].

Antuono, Matteo ;

Soldini, Luciano ;

Brocchini, Maurizio .

THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS, 2012, 26 (1-4) :105-116

[3] Behavior of finite volume schemes for hyperbolic conservation laws on adaptive redistributed spatial grids [J].

Arvanitis, Ch. ;

Delis, A. I. .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2006, 28 (05) :1927-1956

[4]

Barth T., 2004, FINITE VOLUME METHOD

[5] Use of analytic solutions in the statement of difference boundary conditions on a movable shoreline [J].

Bautin, S. P. ;

Deryabin, S. L. ;

Sommer, A. F. ;

Khakimzyanov, G. S. ;

Shokina, N. Yu. .

RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING, 2011, 26 (04) :353-377

[6]

BAUTIN SP, 2005, MATH MODELLING IDEAL

[7]

BAUTIN SP, 2009, CHARACTERISTIC CAUCH

[8] On using Boussinesq-type equations near the shoreline: a note of caution [J].

Bellotti, G ;

Brocchini, M .

OCEAN ENGINEERING, 2002, 29 (12) :1569-1575

[9] On the shoreline boundary conditions for Boussinesq-type models [J].

Bellotti, G ;

Brocchini, M .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 2001, 37 (04) :479-500

[10]

Bogacki P., 1989, Appl. Math. Lett., V2, P321, DOI [DOI 10.1016/0893-9659(89)90079-7, 10.1016/0893-9659(89)90079-7, 10.1016/0893-9 659(89)90079-7]

← 1 2 3 4 5 →