On the properties of difference schemes for solving nonlinear dispersion equations of increased accuracy. II. The case of two spatial variables
Z.I. Fedotova, G.S. Khakimzyanov, O.I. Gusev
Federal Research Center for Information and Computational Technologies, Novosibirsk, Russia
Keywords: long surface waves, nonlinear dispersion equations, finite difference scheme, dispersion, stability, phase error
Abstract
For the case of two spatial variables, a finite-difference scheme of the predictor--corrector type is constructed for solving nonlinear dispersion equations of wave hydrodynamics with a higher order of approximation of the dispersion relation. The numerical algorithm is based on splitting the original system of equations into a hyperbolic system and a scalar equation of the elliptic type. Two methods of approximating the elliptic part are considered. For each of the variants of the difference scheme, dissipation and dispersion analysis is performed, stability conditions are obtained, formulas for the phase error are analyzed, and the behavior of the harmonic attenuation coefficient is studied. A comparative analysis is carried out to identify the advantages of each of the schemes.
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