advection-diffusion equation and its related analytical solutions have gained wide applications in different areas. compared with numerical solutions, the analytical solutions benefit from some advantages. as such, many analytical solutions have been presented for the advection-diffusion equation. the difference between these solutions is mainly in the type of boundary conditions, e.g. time pat...

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...

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...

We consider a discontinuous Galerkin finite element method for the advection–reaction equation in two space–dimensions. For polynomial approximation spaces of degree greater than or equal to two on triangles we propose a method where stability is obtained by a penalization of only the upper portion of the polynomial spectrum of the jump of the solution over element edges. We prove stability in ...

[1] We thank Lim [2005] for providing this opportunity to clarify the restrictions and confirm the applicability of the results of LaBolle et al. [2000]. LaBolle et al. [2000] develop generalized stochastic differential equations (SDE) that converge to advection dispersion equations with discontinuous dispersion tensor D. The problem of interest here relates to equation (15a) of LaBolle et al. ...

This paper is concerned with the existence, uniqueness and globally asymptotic stability of traveling wave fronts in the quasi-monotone reaction advection diffusion equations with nonlocal delay. Under bistable assumption, we construct various pairs of superand subsolutions and employ the comparison principle and the squeezing technique to prove that the equation has a unique nondecreasing trav...

Numerical solutions presented in a companion paper show that two-dimensional mesoscale terrain becomes a much stronger barrier to a continuously stratified flow when the flow contains warm advection. Here it is shown that this baroclinic enhancement is a strictly nonlinear phenomenon. The linear analysis indicates a weakening of the upstream response in warm advection. However, a weakly nonline...