We prove the existence of solutions to an integral equation modeling the infiltration of a fluid in an isotropic homogeneous porous medium. Let us consider the mathematical theory of the infiltration of a fluid from a cylindrical reservoir into an isotropic homogeneous porous medium. Describing this phenomena in the Boussinesq model (see [1]), we are led to the nonlinear integral equation (see ...

in recent years, the number of research works devoted to applying the highly accurate numerical schemes, in particular compact finite difference schemes, to numerical simulation of complex flow fields with multi-scale structures, is increasing. the use of compact finite-difference schemes are the simple and powerful ways to reach the objectives of high accuracy and low computational cost. compa...

This paper investigates the natural convection heat transfer performance in a complex-wavy-wall cavity filled with power-law fluid. In performing the simulations, the continuity, Cauchy momentum and energy equations are solved subject to the Boussinesq approximation using a finite volume method. The simulations focus specifically on the effects of the flow behavior index in the power-law model ...

We consider the problem of a Boussinesq fluid forced by applying both non-uniform temperature and stress at the top surface. On the other boundaries the conditions are thermally insulating and either no-slip or stress-free. The interesting case is when the direction of the steady applied surface stress opposes the sense of the buoyancy driven flow. We obtain two-dimensional numerical solutions ...

Based on the homotopy perturbation method (HPM) and Padé approximants (PA), approximate and exact solutions are obtained for cubic Boussinesq and modified Boussinesq equations. The obtained solutions contain solitary waves, rational solutions. HPM is used for analytic treatment to those equations and PA for increasing the convergence region of the HPM analytical solution. The results reveal tha...

The incompressible Boussinesq equations not only have many applications in modeling fluids and geophysical fluids but also are mathematically important. The well-posedness and related problem on the Boussinesq equations have recently attracted considerable interest. This paper examines the global regularity issue on the 2D Boussinesq equations with fractional Laplacian dissipation and thermal d...

This paper focuses on the 2D incompressible Boussinesq equations with fractional dissipation, given by Λαu in the velocity equation and by Λβθ in the temperature equation, where Λ= √−Δ denotes the Zygmund operator. Due to the vortex stretching and the lack of sufficient dissipation, the global regularity problem for the supercritical regime α+β<1 remains an outstanding problem. This paper prese...

In this paper, we rigorously derive the governing equations describing motion of a stable stratified fluid, from mathematical point view. particular, prove that scaled Boussinesq strongly converge to viscous primitive with density stratification as aspect ratio goes zero, and rate convergence is same order ratio. Moreover, in obtain result, also establish global well-posedness strong solutions ...

Abstract We study a temperature and velocity output tracking problem for two-dimensional room model with the fluid dynamics governed by linearized translated Boussinesq equations. Additionally, includes finite-dimensional models actuation sensing dynamics; thus, complete are an ODE–PDE–ODE cascade. As main contribution, we design low-dimensional internal model-based controller robust of model. ...

This paper is concerned with the global well-posedness and inviscid limits of several systems of Boussinesq equations with fractional dissipation. Three main results are proven. The first result assesses the global regularity of two systems of equations close to the critical 2D Boussinesq equations. This is achieved by examining their inviscid limits. The second result relates the global regula...