The development of parallel Computational Fluid Dynamics (CFD) codes is a challenging task that entails efficient parallelization concepts and strategies in order to achieve good scalability values when running those codes on modern supercomputers with several thousands to millions of cores. In this paper, we present a hierarchical data structure for massive parallel computations that supports ...

Numerical investigation of mixed convection flow in a concentration-stratified fluid-saturated vertical square porous enclosure is investigated by Galerkin finite element method. The forced flow conditions are imposed by providing an inlet at the bottom wall and an outlet with a suction on the top wall. The free convection is induced by introducing a hot but isothermal temperature on the left v...

Using numerical integrations of the Boussinesq equations in rotating cylindrical domains with realistic boundary conditions, we have computed the value of the largest Lyapunov exponent lambda1 for a variety of aspect ratios and driving strengths. We study in particular the domain chaos state, which bifurcates supercritically from the conducting fluid state and involves extended propagating fron...

This paper focuses on the transient analysis of nonlinear dispersion of a pollutant ejected by an external source into a laminar flow of an incompressible fluid in a channel. The influence of density variation with pollutant concentration is approximated according to the Boussinesq approximation, and the nonlinear governing equations of momentum and pollutant concentration are obtained. The pro...

This is the third in a series of our study of Rayleigh-Bénard convection at large Prandtl number. Here we investigate whether stationary statistical properties of the Boussinesq system for Rayleigh-Bénard convection at large Prandtl number are related to those of the infinite Prandtl number model for convection that is formally derived from the Boussinesq system via setting the Prandtl number t...

A new seawater Boussinesq system is introduced, and it is shown that this approximation to the equations of motion of a compressible binary solution has an energy conservation law that is a consistent approximation to the Bernoulli equation of the full system. The seawater Boussinesq approximation simplifies the mass conservation equation to $ u 5 0, employs the nonlinear equation of state of s...

Gravitationally driven motion arising from a sustained constant source of dense fluid in a horizontal channel is investigated theoretically using shallow-layer models and direct numerical simulations of the Navier–Stokes equations, coupled to an advection–diffusion model of the density field. The influxed dense fluid forms a flowing layer underneath the less dense fluid, which initially filled ...

We consider the Maxey-Riley equation for small neutrally buoyant inertial particles in Boussinesq approximation. The main motivation is study of phytoplankton and oceanic turbulent flows. show that behave as forced damped oscillators, with different regimes depending on Stokes number fluid Brunt-V\"ais\"al\"a frequency. Using direct numerical simulations we their dynamics these flows tend to cl...

In this paper, we are concerned with the generalized Boussinesq equation including the singularly sixth-order Boussinesq equation, which describes the bi-directional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for bond number less than but very close to 1/3. By the means of two proper ansatzs, we obtain explicit traveling solitary wave solutio...

We establish the eventual regularity of suitably defined weak solutions to the Boussinesq system for Rayleigh-Bénard convection at large Prandtl number. The existence of a global attractor of the Boussinesq system at large Prandtl number is also presented.