Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective transport of individual phases. Moreover, for compressible media, the pressure equation itself is just a time-dependent convection-diffusion equation. For differen...

In the ocean, convection and plume formation occur when a fluid parcel at the ocean’s surface becomes heavier than its environment. Switching to convection in a dry atmosphere involves two main variations: a sweap over of the vertical direction, with light plumes propagating up from the ground, and a more subtle definition of what it means for an air parcel to be light. In comparing the buoyanc...

Double-diffusive steady convection in a partially porous cavity with partially permeable walls and under the combined buoyancy effects of thermal and mass diffusion was analysed numerically using finite volume method. The top wall is well insulated and impermeable while the bottom surface is partially well insulated and impermeable and partially submitted to constant temperature T1 and concentr...

We study a class of processes that are akin to the Wright-Fisher model, with transition probabilities weighted in terms of the frequency-dependent fitness of the population types. By considering an approximate weak formulation of the discrete problem, we are able to derive a corresponding continuous weak formulation for the probability density. Therefore, we obtain a family of partial different...

A singular perturbation problem from the artificial compressible system to incompressible is considered for a doubly diffusive convection when Hopf bifurcation motionless state occurs in system. It proved that also small parameter, called Mach number. The time periodic solution branch of shown converge corresponding bifurcating limit vanishing

Based on multi-dimensional multi-group radiation hydrodynamic simulations of core-collapse supernovae with the VULCAN/2D code, we study the physical conditions within and in the vicinity of the nascent protoneutron star (PNS). Conclusions of this work are threefold: First, as before, we do not see any large-scale overturn of the inner PNS material. Second, we see no evidence of doubly-diffusive...

It is largely acknowledged that inhaled particles ranging from 0.001 to 10 m are able to reach and deposit in the alveolated regions of the lungs. To date, however, the bulk of numerical studies have focused mainly on micrometer sized particles whose transport kinematics are governed by convection and sedimentation, thereby capturing only a small fraction of the wider range of aerosols leading ...

A grid of numerical simulations of double-diffusive convection is presented for the astrophysical case where viscosity (Prandtl number Pr) and solute diffusivity (Lewis number Le) are much smaller than the thermal diffusivity. As in laboratory and geophysical cases convection takes place in a layered form. The proper translation between subsonic flows in a stellar interior and an incompressible...

While the rising flux tube paradigm is an elegant theory, its basic assumptions, thin flux tubes at the bottom of the convection zone with field strengths two orders of magnitude above equipartition, remain numerically unverified at best. As such, in recent years the idea of a formation of sunspots near the top of the convection zone has generated some interest. The presence of turbulence can s...