We offer a synthetic exposition on the state of art for Computational Fluid Dynamics (CFD) relevant to Navier–Stokes equations with Boussinesq approximation, smoothly blending history field an accessible underlying mathematical rationale, supporting theorems and survey landmark results subject. Attention is paid those efforts which have opened up new paradigms in modern CFD, techniques that eme...

This paper modeled heating air of a room through examining free convection in a 3D chamber. The chamber had cold and hot sources with Tc and Th temperatures, respectively. Its other walls were adiabatic. This study aimed at predicting effect of temperature difference, displacement of hot and cold sources and their aspect ratio on flow field, temperature and heat transfer rate. To conduct the st...

We present an analysis of the primary bifurcations that occur in a mathematical model that uses the (three-dimensional) Navier-Stokes equations in the Boussinesq approximation to describe the flow of a near unity Prandtl number fluid (i.e. air) in the differentially heated rotating annulus. In particular, we investigate the double Hopf (Hopf-Hopf) bifurcations that occur along the axisymmetric ...

In this paper, the bioconvective flow in a porous square cavity containing oxytactic microorganism in the presence of chemical reaction is investigated. The bioconvection flow and heat transfer in porous media are formulated based on the Darcy model of Boussinesq approximation. The governing partial differential equations are solved using the Galerkin finite element method. The computational nu...

This work presents a numerical analysis of entropy generation in Γ-Shaped enclosure that was submitted to the natural convection process using a simple thermal lattice Boltzmann method (TLBM) with the Boussinesq approximation.  A 2D thermal lattice Boltzmann method with 9 velocities, D2Q9, is used to solve the thermal flow problem. The simulations are performed at a constant Prandtl number (Pr ...

A new approach to the description of stationary plane waves in ideal density stratified incompressible fluid is considered without the application of Boussinesq approximation. The approach is based on the equation derived by Dubreil-Jacotin [4, 5, 6] and Long [7] with the additional assumption that the mean vorticity of the flow is zero. It is shown that in the linear approximation the spectrum...

We investigate the response of a laboratory aquifer submitted to artificial rainfall, with an emphasis on the early stage of a rain event. In this almost two-dimensional experiment, the infiltrating rainwater forms a groundwater reservoir which exits the aquifer through one side. The resulting outflow resembles a typical stream hydrograph: the water discharge increases rapidly during rainfall a...

Abstract. A fully discrete a priori analysis of the finite element heterogenenous multiscale method (FE-HMM) introduced in [A. Abdulle, M. Grote, C. Stohrer, Multiscale Model. Simul. 2014] for the wave equation with highly oscillatory coefficients over long time is presented. A sharp a priori convergence rate for the numerical method is derived for long time intervals. The effective model over ...