Abstract: We prove the existence and uniqueness of weak solutions to the variational formulation of the Maxwell-Boussinesq approximation problem. Some further regularity in W , δ > 0, is obtained for the weak solutions. The shape sensitivity analysis by the boundary variations technique is performed for the weak solutions. As a result, the existence of the strong material derivatives for the we...

We use the Cahn-Hilliard approach to model the slow dissolution dynamics of binary mixtures. An important peculiarity of the Cahn-Hilliard-Navier-Stokes equations is the necessity to use the full continuity equation even for a binary mixture of two incompressible liquids due to dependence of mixture density on concentration. The quasicompressibility of the governing equations brings a short tim...

Considered herein are a number of variants of the classical Boussinesq system and their higher-order generalizations. Such equations were first derived by Boussinesq to describe the two-way propagation of small-amplitude, long wavelength, gravity waves on the surface of water in a canal. These systems arise also when modeling the propagation of long-crested waves on large lakes or the ocean and...

High resolution computer simulations of two-dimensional convection using the anelastic approximation are presented. These calculations span Rayleigh numbers from 10(8)-10(12) for Prandtl number equal to unity, with the fluid density decreasing by a factor of 12 from the bottom to the top of the convection region. This range covers several decades in the "hard" turbulent regime. While many studi...

High resolution computer simulations of two-dimensional convection using the anelastic approximation are presented. These calculations span Rayleigh numbers from 10 10 for Prandtl number equal to unity, with the uid density decreasing by a factor of 12 from the bottom to the top of the convection region. This range covers several decades in the \hard" turbulent regime. While many studies of thi...

Lattice Boltzmann (LB) method for atmospheric dynamics is developed by considering the characteristics of anelastic approximation. After introducing reference base state values in flows, an LB model, with external force term, has been constructed framework. In proposed mass and momentum conservation equations are solved a regularization procedure, temperature field or scalar transport simulated...

The primitive equations of large-scale oceanic dynamics form a fundamental model in geophysical flows. It is well-known that the can be formally derived by hydrostatic approximation. In this paper, we rigorously derive full from mathematical point view. More precisely, prove scaled Boussinesq with rotation converge to strong sense, globally time, convergence rate $$O(\varepsilon )$$ , as aspect...