The Splitting Scheme for Mathematical Modeling of the Mixed Region Dynamics in a Stratified Fluid

Study of wave motions’ fluid is one of the most important and complex problems of modern hydrodynamics. A mathematical model for dynamics of incompressible uniform viscous liquid spots in the stratified medium is considered. This model is described by Navier–Stokes equations in Boussinesq approximation. Stratification component of the medium is saltiness. Bearing in mind that in such flows there are areas with large gradients of hydrodynamic parameters, required methods should possess such properties as a high order of accuracy, minimum scheme dissipation and dispersion, as well as monotony. To solve the task, the authors are developing a method of splitting by physical factors called as Splitting on physical factors Method for Incompressible fluid Flows (SMIF) possessing by the abovementioned properties. Four stages of splitting scheme are considered. This chapter provides a brief description of SMIF method. The test calculations and comparison with some theoretical and experimental data respect to the calculations of other authors are demonstrated.