Mathematical Modeling of Wave Motions of Fluids

The study of wave movements of liquids is of interest both theoretically and practically. This can include flows with a free surface and flows with internal waves. For correct mathematical modeling of such flows, the finite-difference schemes of methods must have such properties as follows: high order of approximation, minimal scheme dissipation and dispersion, performance in a wide range of the Reynolds and the Froude numbers, and that is especially important the property of monotonicity. This chapter presents two approaches: splitting method for incompressible fluid flow (SMIF) method and compact accurately boundary adjusting high-resolution technique (CABARET) method, of course, whose finite-difference schemes have the properties listed above. A number of test tasks are considered and compared with theoretical, experimental data and calculations of other authors.