In this paper, a highly accurate method is introduced to achieve the numerical solution of advection diffusion equation (ADE). This approach contains collocation technique based on nonic B-spline functions in spatial-domain discretization and Adams Moulton scheme temporal-domain discretization. Two test problems are studied validate effectiveness new presented efficiency approximate results tes...

Despite the growing popularity of Lattice Boltzmann schemes for describing multi-dimensional flow and transport governed by non-linear (anisotropic) advectiondiffusion equations, there are very few analytical results on their stability, even for the isotropic linear equation. In this paper, the optimal two-relaxation-time (OTRT) model is defined, along with necessary and sufficient (easy to use...

We give a brief overview of stabilized finite element methods and illustrate the developments applied to the advection-diffusion equation.

For the advection-diffusion equation, the characteristic-Oalerkin formulations are obtained by temporal discretization of the total derivative. These formulations, by construction, are EulerianLagrangian, and therefore can handle time-dependent domains without difficulty. The Oalerkin/leastsquares space-time formulation, on the other hand, is written over the space-time domain of a problem, and...

This paper describes a comparison of some numerical methods for solving the advection-diffusion (AD) equation which may be used to describe transport of a pollutant. The one-dimensional advection-diffusion equation is solved by using cubic splines (the natural cubic spline and a ”special” AD cubic spline) to estimate first and second derivatives, and also by solving the same problem using two s...

We model the evolution of the concentration field of macromolecules in a symmetric field-flow fractionation (FFF) channel by a onedimensional advection-diffusion equation. The coefficients are precisely determined from the fluid dynamics. This model gives quantitative predictions of the time of elution of the molecules and the width in time of the concentration pulse. The model is rigorously su...