This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...

This paper is devoted to comparing numerical schemes for a differential equation with convection and fourth-order diffusion. Our model equation is ut þ ðu uÞx 1⁄4 ðuuxxxÞx, which arises in the context of thin film flow. First we employ implicit schemes and treat both convection and diffusion terms implicitly. Then the convection terms are treated with wellknown explicit schemes, namely Godunov,...

Based on the concept of alternating group and domain decomposition, we present a class of alternating group explicit-implicit method and an alternating group Crank-Nicolson method for solving convection-diffusion equation. Both of the two methods are effective in convection dominant cases. The concept of the construction of the methods is also be applied to 2D convection-diffusion equations. Nu...

in this article, an analytical approximate solution of nonlinear fractional convection-diffusion with modifiedriemann-liouville derivative was obtained with the help of fractional variational iteration method (fvim). a newapplication of fractional variational iteration method (fvim) was extended to derive analytical solutions in theform of a series for this equation. it is indicated that the so...

Spreading of bacteria in a highly advective, disordered environment is examined. Predictions of super-diffusive spreading for a simplified reaction-diffusion equation are tested. Concentration profiles display anomalous growth and super-diffusive spreading. A perturbation analysis yields a crossover time between diffusive and super-diffusive behavior. The time’s dependence on the convection vel...

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 this study, we presented the high-order fundamental solutions and general solutions of convection-diffusion equation. To demonstrate their efficacy, we applied the highorder general solutions to the boundary particle method (BPM) for the solution of some inhomogeneous convection-diffusion problems, where the BPM is a new truly boundaryonly meshfree collocation method based on multiple recipr...

Recently many mathematical models for image processing have been widely applied in computer visualization. The nonlinear diffusion PDE has been broadly applied in image processing. In this paper we propose a convection-diffusion filter by adding a convection term in the modified diffusion equation as a physical interpretation for removing the noise. We study the dynamics of such equations by th...

In this paper we study a nonlocal equation that takes into account convective and diffusive effects, ut = J ∗u−u+G ∗ (f(u))− f(u) in R, with J radially symmetric and G not necessarily symmetric. First, we prove existence, uniqueness and continuous dependence with respect to the initial condition of solutions. This problem is the nonlocal analogous to the usual local convection-diffusion equatio...