In this paper, the exponential B-spline functions are used for the numerical solution of the advection-diffusion equation. Two numerical examples related to pure advection in a finitely long channel and the distribution of an initial Gaussian pulse are employed to illustrate the accuracy and the efficiency of the method. Obtained results are compared with some early studies.

We consider a system of reaction-diffusion equations with passive advection term and Lewis number Le not equal to one. Such systems are used to describe chemical reactions in a flow in a situation where temperature and material diffusivities are not equal. It is expected that the fluid advection will distort the reaction front, increasing the area of reaction and thus speeding up the reaction p...

This paper presents a formal exact solution of the linear advection–diffusion transport equation with constant coefficients for both transient and steady-state regimes. A classical mathematical substitution transforms the original advection–diffusion equation into an exclusively diffusive equation. The new diffusive problem is solved analytically using the classic version of Generalized Integra...

This paper provides a new fully discrete domain decomposition algorithm for the advection diffusion reaction equation. It relies on the optimized Ventcell–Schwarz algorithm with a finite volume discretization of the subdomain problems. The scheme includes a wide range of advection fluxes with a special treatment on the boundary. A complete analysis of the scheme is presented, and the convergenc...

We consider convective systems in a bounded domain, in which viscous fluids described by the Stokes system are coupled using the Boussinesq approximation to a reaction-advection-diffusion equation for the temperature. We show that the resulting flows possess relaxation-enhancing properties in the sense of [12]. In particular, we show that solutions of the nonlinear problems become small when th...

The numerical solutions of the advection-diffusion equation are themselves numerous and sometimes very sophisticated, in order to avoid two undesirable features: oscillatory behavior and numerical diffusion. It is known that the common practice of “splitting-up” the solution is not always the best approach to the advection-diffusion problem. By using the ordinary differential equation analogy m...

This paper deals with the analysis of existence of traveling wave solutions (TWS) for a diffusion-degenerate (at D(0) = 0) and advection-degenerate (at h'(0) = 0) reaction-diffusion-advection (RDA) equation. Diffusion is a strictly increasing function and the reaction term generalizes the kinetic part of the Fisher-KPP equation. We consider different forms of the convection term h(u): (1)  h'(u...

the transport of dissolved contaminants in groundwater is usually described by the advectiondispersion equation with reaction. several numerical methods for solving the one-dimensional are availableincluding finite difference methods, finite volume methods, and finite element methods. stringent conditions,such as small peclet (pe) and courant (cr) numbers, must be satisfied to ensure the accura...