Abstract
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.
Funding: The work was supported by the Program of the Presidium of RAS No. 27 ‘Fundamental problems of solving sophisticated practical problems using supercomputers’.
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Articles in the same Issue
- Frontmatter
- Influence of electron temperature on breaking of plasma oscillations
- Sharp error estimate for implicit finite element scheme for American put option
- Numerical study of properties of air heat content indicators based on stochastic models of the joint meteorological series
- Finite difference methods for 2D shallow water equations with dispersion
- Numerical study of plane Couette flow: turbulence statistics and the structure of pressure–strain correlations
Articles in the same Issue
- Frontmatter
- Influence of electron temperature on breaking of plasma oscillations
- Sharp error estimate for implicit finite element scheme for American put option
- Numerical study of properties of air heat content indicators based on stochastic models of the joint meteorological series
- Finite difference methods for 2D shallow water equations with dispersion
- Numerical study of plane Couette flow: turbulence statistics and the structure of pressure–strain correlations