Related papers: Diffusion in stellar interiors: critical tests of …
The present work provides a critical assessment of numerical solutions of the space-fractional diffusion-advection equation, which is of high significance for applications in various natural sciences. In view of the fact that, in contrast…
This paper describes the first steps of development of a new multidimensional time implicit code devoted to the study of hydrodynamical processes in stellar interiors. The code solves the hydrodynamical equations in spherical geometry and…
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…
The purpose of this work was to obtain diffusion coefficient for the magnetic angular momentum transport and material transport in a rotating solar model. We assumed that the transport of both angular momentum and chemical elements caused…
In this paper, I explore various transport processes that have a large impact of the distribution of elements inside stars and thus, on stellar evolution. A heuristic description of the physics behind equations is provided, and key…
Anisotropic diffusion is imperative in understanding cosmic ray diffusion across the Galaxy, the heliosphere, and the interplay of cosmic rays with the Galactic magnetic field. This diffusion term contributes to the highly stiff nature of…
Convection-diffusion problems arise in the modelling of many physical processes. Their typical solutions exhibit boundary and/or interior layers. Despite the linear nature of the differential operator, these problems pose still-unanswered…
We present a review of the application of numerical methods to solve the problem of the stellar/solar wind with the local interstellar medium. Most of approaches described are developed by the authors. They include both purely gas dynamic…
The convective overshoot mixing plays an important role in stellar structure and evolution. However, the overshoot mixing is a long standing problem. The uncertainty of the overshoot mixing is one of the most uncertain factors in stellar…
Convection is ubiquitous in stellar and planetary interiors where it likely plays an integral role in the generation of magnetic fields. As the interiors of these objects remain hidden from direct observation, numerical models of convection…
Convective overshoot mixing is a critical ingredient of stellar structure models, but is treated in most cases by ad hoc extensions of the mixing-length theory for convection. Advanced theories which are both more physical and numerically…
We study the diffusion of helium and other heavy elements in the solar interior by solving exactly the set of flow equations developed by Burgers for a multi-component fluid, including the residual heat-flow terms. No approximation is made…
We present three schemes for the numerical approximation of fractional diffusion, which build on different definitions of such a non-local process. The first method is a PDE approach that applies to the spectral definition and exploits the…
Turbulent motions in the interior of a star play an important role in its evolution, since they transport chemical species, thermal energy and angular momentum. Our overall goal is to construct a practical turbulent closure model for…
We consider numerical methods for linear parabolic equations in one spatial dimension having piecewise constant diffusion coefficients defined by a one parameter family of interface conditions at the discontinuity. We construct immersed…
Thermohaline convection is a standard chemical mixing process in stellar interiors, yet its mixing efficiency is not fully settled. Competing theories predict turbulent diffusion coefficients, $D_\mu$, that can differ by orders of…
In this paper, we present a model based on a local thermodynamic equilibrium, weakly ionized plasma-mixture model used for medical and technical applications in etching processes. We consider a simplified model based on the Maxwell-Stefan…
The problem of diffusion in a porous medium with a spatially varying porosity is considered. The particular microstructure analyzed comprises a collection of impenetrable spheres, though the methods developed are general. Two different…
Stellar evolution computations provide the foundation of several methods applied to study the evolutionary properties of stars and stellar populations, both Galactic and extragalactic. The accuracy of the results obtained with these…
Context. Mixing by convective overshooting has long been suggested to play an important role for the amount of hydrogen available to nuclear burning in convective cores of stars. The best way to model this effect is still debated. Aims. We…