Exact Solutions to Shallow Water Equations for a Water Oscillation Problem in an Idealized Basin and Their Use in Verifying Some Numerical Algorithms

Standard

Exact Solutions to Shallow Water Equations for a Water Oscillation Problem in an Idealized Basin and Their Use in Verifying Some Numerical Algorithms. / Matskevich, N. A.; Chubarov, L. B.

In: Numerical Analysis and Applications, Vol. 12, No. 3, 01.07.2019, p. 234-250.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{72a727b115004257b216776fd055b74d,

title = "Exact Solutions to Shallow Water Equations for a Water Oscillation Problem in an Idealized Basin and Their Use in Verifying Some Numerical Algorithms",

abstract = "We present some approaches to solving a problem of shallow water oscillations in a parabolic basin (including an extra case of a horizontal plane). Some requirements on the form of the solutions and effects of Earth{\textquoteright}s rotation and bottom friction are made. The resulting solutions are obtained by solving ODE systems. The corresponding free surfaces are first- or second-order ones. Some conditions of finiteness and localization of the flow are analyzed. The solutions are used to verify the numerical algorithm of the large-particle method. The efficiency of the method is discussed in tests on wave run-up on shore structures.",

keywords = "bottom friction, Coriolis force, exact solutions, free surface, large-particle method, mathematical modeling, numerical algorithms, ordinary differential equations, shallow water equations, verification, wave run-up",

author = "Matskevich, {N. A.} and Chubarov, {L. B.}",

year = "2019",

month = jul,

day = "1",

doi = "10.1134/S1995423919030030",

language = "English",

volume = "12",

pages = "234--250",

journal = "Numerical Analysis and Applications",

issn = "1995-4239",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "3",

}

RIS

TY - JOUR

T1 - Exact Solutions to Shallow Water Equations for a Water Oscillation Problem in an Idealized Basin and Their Use in Verifying Some Numerical Algorithms

AU - Matskevich, N. A.

AU - Chubarov, L. B.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - We present some approaches to solving a problem of shallow water oscillations in a parabolic basin (including an extra case of a horizontal plane). Some requirements on the form of the solutions and effects of Earth’s rotation and bottom friction are made. The resulting solutions are obtained by solving ODE systems. The corresponding free surfaces are first- or second-order ones. Some conditions of finiteness and localization of the flow are analyzed. The solutions are used to verify the numerical algorithm of the large-particle method. The efficiency of the method is discussed in tests on wave run-up on shore structures.

AB - We present some approaches to solving a problem of shallow water oscillations in a parabolic basin (including an extra case of a horizontal plane). Some requirements on the form of the solutions and effects of Earth’s rotation and bottom friction are made. The resulting solutions are obtained by solving ODE systems. The corresponding free surfaces are first- or second-order ones. Some conditions of finiteness and localization of the flow are analyzed. The solutions are used to verify the numerical algorithm of the large-particle method. The efficiency of the method is discussed in tests on wave run-up on shore structures.

KW - bottom friction

KW - Coriolis force

KW - exact solutions

KW - free surface

KW - large-particle method

KW - mathematical modeling

KW - numerical algorithms

KW - ordinary differential equations

KW - shallow water equations

KW - verification

KW - wave run-up

UR - http://www.scopus.com/inward/record.url?scp=85071735364&partnerID=8YFLogxK

U2 - 10.1134/S1995423919030030

DO - 10.1134/S1995423919030030

M3 - Article

AN - SCOPUS:85071735364

VL - 12

SP - 234

EP - 250

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 3

ER -

ID: 21472672