TY - JOUR

T1 - Finite difference methods for 2D shallow water equations with dispersion

AU - Khakimzyanov, Gayaz S.

AU - Fedotova, Zinaida I.

AU - Gusev, Oleg I.

AU - Shokina, Nina Yu

PY - 2019/4/1

Y1 - 2019/4/1

N2 - Basic properties of some finite difference schemes for two-dimensional nonlinear dispersive equations for hydrodynamics of surface waves are considered. It is shown that stability conditions for difference schemes of shallow water equations are qualitatively different in the cases the dispersion is taken into account, or not. The difference in the behavior of phase errors in one- and two-dimensional cases is pointed out. Special attention is paid to the numerical algorithm based on the splitting of the original system of equations into a nonlinear hyperbolic system and a scalar linear equation of elliptic type.

AB - Basic properties of some finite difference schemes for two-dimensional nonlinear dispersive equations for hydrodynamics of surface waves are considered. It is shown that stability conditions for difference schemes of shallow water equations are qualitatively different in the cases the dispersion is taken into account, or not. The difference in the behavior of phase errors in one- and two-dimensional cases is pointed out. Special attention is paid to the numerical algorithm based on the splitting of the original system of equations into a nonlinear hyperbolic system and a scalar linear equation of elliptic type.

KW - dispersion

KW - finite difference methods

KW - Nonlinear dispersive equations

KW - phase error

KW - stability

UR - http://www.scopus.com/inward/record.url?scp=85064844106&partnerID=8YFLogxK

U2 - 10.1515/rnam-2019-0009

DO - 10.1515/rnam-2019-0009

M3 - Article

AN - SCOPUS:85064844106

VL - 34

SP - 105

EP - 117

JO - Russian Journal of Numerical Analysis and Mathematical Modelling

JF - Russian Journal of Numerical Analysis and Mathematical Modelling

SN - 0927-6467

IS - 2

ER -