This study depicts that to find the Analytical and numerical solutions of Diffusion – Convections Equations Galactic Cosmic Rays (GCRs) by Finite Element method (FEM) also Energy Equation GCRs using a part Parker’s transport equation. considers moreover centres on exactness acknowledgment FEM strategy utilizing dissemination blunder, scattering mistake add up blunder investigation. The comes ab...

We consider an unsteady convection diffusion equation which models the transport of a dissolved species in two-phase incompressible flow problems. The so-called Henry interface condition leads to a jump condition for the concentration at the interface between the two phases. In [A. Hansbo, P. Hansbo, Comput. Methods Appl. Mech. Engrg. 191 (20002)], for the purely elliptic stationary case, exten...

A magnetic flux tube is treated as a body in addition to a confined field. As a field, both the cyclonic convection (α-effect) and differential rotation (Ω-effect) play a role. As a body, the tube experiences not only a buoyant force, but also a dynamic pressure of downflows above the tube. When these two dynamic effects are incorporated into the αΩ dynamo equation by adding to it two diffusion...

In this work, the 2D Convection - Diffusion equation was used to model process of contaminant transport by convection and diffusion. particular, we assume that are modeling pollutant in shallow water with a unidirectional flow movement convective part. The diffusion coefficient is considered constant depends only on nature substance, value 0.004 has been considered. Finite difference numerical ...

Study in surface water quality is important. Rivers are one of the main sources of water supply fordrinking, agriculture and industry. Unfortunately, sometime Rivers where wastewater dischargesare considered. For this reason,the pollutant transmission in river is one of the most importantproblems in Environmental Engineering. the Advection Dispersion Equation (ADE) is governedon the pollutant t...

In the first part of this paper [1], a complete description of Q-conditional symmetries for two classes of reaction-diffusion-convection equations with power diffusivities is derived. It was shown that all the known results for reaction-diffusion equations with power diffusivities follow as particular cases from those obtained in [1] but not vise versa. In the second part the symmetries obtaine...

the aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. the method is a combination of the asymptotic expansion technique and the reproducing kernel method (rkm). first an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. then the reduced regular delayed diffe...

We present a scalable iterative solver for high-order hybridized discontinuous Galerkin (HDG) discretizations of linear partial differential equations. It is an interplay between domain decomposition methods and HDG discretizations, and hence inheriting advances from both sides. In particular, the method can be viewed as a Gauss-Seidel approach that requires only independent element-by-element ...

Here, we adapt the concept of transformational thermodynamics, whereby the flux of temperature is controlled via anisotropic heterogeneous diffusivity, for the diffusion and transport of mass concentration. The n-dimensional, time-dependent, anisotropic heterogeneous Fick's equation is considered, which is a parabolic partial differential equation also applicable to heat diffusion, when convect...