in this work we solve the set of hydrodynamical equations for accretion disks in the spherical coordinates (r,θ,ϕ) to obtain the explicit structure along θ direction. we study a two-dimensional advective accretion disc in the presence of thermal conduction. we find self-similar solutions for an axisymmetric, rotating, steady, viscous-resistive disk. we show that the global structure of an advec...

We derive sufficient conditions for advection-driven backward motion of the free boundary in a chemotaxis model with degenerate mobility. In this model, a porous-medium-type diffusive term and an advection term are in competition. The former induces forward motion, the latter may induce backward motion of the free boundary depending on the direction of advection. We deduce conditions on the gro...

The advection equation is the basis for mathematical models of continuum mechanics. In the approximate solution of nonstationary problems it is necessary to inherit main properties of the conservatism and monotonicity of the solution. In this paper, the advection equation is written in the symmetric form, where the advection operator is the half-sum of advection operators in conservative (diver...

A new algorithm for volume tracking which is based on the concept of flux-corrected transport (FCT) is introduced. It is applicable to incompressible 2D flow simulations on finite volume and difference meshes. The method requires no explicit interface reconstruction, is direction-split and can be extended to 3D and orthogonal curvilinear meshes in a straightforward manner. A comparison of the n...

The effects of radial advection and thermal diffusion were considered in investigating the linear stability of an optically thin, two-temperature accretion disc. If the disc has only very little advection, we proved that the thermal instability exists when the disc is geometrically thin. But it dispears in a geometrically slim disc if the thermal diffusion was considered. Moreover, if the disc ...

The usefulness of high order numerical schemes for treating the advection of momentum in the primitive equations is examined. It is shown that the use of high order advection schemes for themomentum advection can improve the dynamics of potential vorticity for length scales similar to the deformation radius. This is illustrated using numerical experiments in academic and realistic configuration...

Dye advection is an intuitive and versatile technique to visualize both steady and unsteady flow. Dye can be easily combined with noise-based vector field representations and is an important element in user-centric visual exploration processes. However, texture-based dye advection usually does not consider the convergence and divergence of flow to adapt the intensity of the dye color. In this p...

We prove the stability and a priori global and local error analysis for the residual-free bubbles finite element method applied to advection dominated advection-diffusion problems.

Evaporation from small reservoirs, wetlands, and lakes continues to be a theoretical and practical problem in surface hydrology and micrometeorology because atmospheric flows above such systems can rarely be approximated as stationary and planar-homogeneous with no mean subsidence (hereafter referred to as idealized flow state). Here, the turbulence statistics of temperature (T) and water vapor...

In this work we show some results about the reduced basis approximation of advection dominated parametrized problems, i.e. advection-diffusion problems with high Péclet number. These problems are of great importance in several engineering applications and it is well known that their numerical approximation can be affected by instability phenomena. In this work we compare two possible stabilizat...