We consider a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are respectively piecewise constant and affine. We use a projection method to deal with the incompressibility constraint. The stability of the scheme has been proven in [15]. We infer from it its convergence. Mathematics Subject ...

In this paper, with the aid of Maple, the (G ′ /G) and (1/G ′ )-expansion methods are applied to determine the exact solutions of (N+1)-dimensional generalized Boussinesq equation and (N+1)-dimensional sine-cosine-Gordon equation.These equations play a very important role in mathematical physics and engineering sciences. This methods are more powerful and will be used in further works to establ...

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...

We consider systems of reactive Boussinesq equations in two dimensional strips that are not aligned with gravity’s direction. We prove that for any width of such strips and for arbitrary Rayleigh and Prandtl numbers, the systems admit smooth, non-planar traveling wave solutions with the fluid’s velocity satisfying no-slip boundary conditions.

In this paper, with the aid of Maple, the (G ′ /G) and (1/G ′ )-expansion methods are applied to determine the exact solutions of (N+1)-dimensional generalized Boussinesq equation and (N+1)-dimensional sine-cosine-Gordon equation.These equations play a very important role in mathematical physics and engineering sciences. This methods are more powerful and will be used in further works to establ...

This paper is concerned with a two-dimensional Whitham–Boussinesq system modeling surface waves of an inviscid incompressible fluid layer. We prove that the associated Cauchy problem well-posed for initial data low regularity, existence time scale [Formula: see text], where text] and are small parameters related to level dispersion nonlinearity, respectively. In particular, in KdV regime text]}...

in this paper, reduced order proper orthogonal decomposition method has been used for simulation of unsteady incompressible flow fields. after projection of the governing equations along pod modes, a low-dimensional dynamical system is achieved. normally, standard low-dimensional models, due to some reasons, do not predict time variations of flow field accurately. accuracy of dynamical system h...

Fully nonlinear extensions of Boussinesq equations are derived to simulate surface wave propagation in coastal regions. By using the velocity at a certain depth as a dependent variable (Nwogu 1993), the resulting equations have significantly improved linear dispersion properties in intermediate water depths when compared to standard Boussinesq approximations. Since no assumption of small nonlin...