Saul’yev-type asymmetric schemes have been widely used in solving diffusion and advection equations. In this work, we show that Saul’yev-type schemes can be derived from the exponential splitting of the semidiscretized equation which fundamentally explains their unconditional stability. Furthermore, we show that optimal schemes are obtained by forcing each scheme’s amplification factor to match...

Abstract In this paper, we investigate a delay reaction–diffusion–advection model with ideal free dispersal. The stability of positive steady-state solutions and the existence associated Hopf bifurcation are obtained by analyzing principal eigenvalue an elliptic operator. By normal form theory center manifold reduction, direction bifurcating periodic obtained. Moreover, numerical simulations br...

Abstract: Solving or approximating the advection-diffusion/dispersion equation (ADE) is a challenging and important problem and has thus motivated a great deal of intense research. A specific complication arises from the nature of the governing partial differential equation: it is characterized by a hyperbolic non-dissipative advective transport term, a parabolic dissipative diffusive (dispersi...

Autocatalytic reaction fronts generate density gradients that may lead to convection. Fronts propagating in vertical tubes can be flat, axisymmetric, or nonaxisymmetric, depending on the diameter of the tube. In this paper, we study the transitions to convection as well as the stability of different types of fronts. We analyze the stability of the convective reaction fronts using three differen...

In the present study, analytical solutions are obtained for two-dimensional advection dispersion equation for conservative solute transport in a semi-infinite heterogeneous porous medium with pulse type input point source of uniform nature. The change in dispersion parameter due to heterogeneity is considered as linear multiple of spatially dependent function and seepage velocity whereas seepag...

A one-component bistable reaction-diffusion system with asymmetric nonlocal coupling is derived as a limiting case of a two-component activator-inhibitor reaction-diffusion model with differential advection. The effects of asymmetric nonlocal couplings in such a bistable reaction-diffusion system are then compared to the previously studied case of a system with symmetric nonlocal coupling. We c...

Abstract: The use of the conventional advection diffusion equation in many physical situations has been questioned by many investigators in recent years and alternative diffusion models have been proposed. Fractional space derivatives are used to model anomalous diffusion or dispersion, where a particle plume spreads at a rate inconsistent with the classical Brownian motion model. When a fracti...

in this paper, we propose a new method for solving the stochastic advection-diffusion equation of ito type. in this work, we use a compact finite difference approximation for discretizing spatial derivatives of the mentioned equation and semi-implicit milstein scheme for the resulting linear stochastic system of differential equation. the main purpose of this paper is the stability investigatio...

In this paper, we unify advection and diffusion into a single hyperbolic system by extending the firstorder system approach introduced for the diffusion equation in [J. Comput. Phys., 227 (2007) 315-352] to the advection-diffusion equation. Specifically, we construct a unified hyperbolic advection-diffusion system by expressing the diffusion term as a first-order hyperbolic system and simply ad...

Atmospheric air pollution turbulent fluxes can be assumed to be proportional to themean concentration gradient. This assumption, alongwith the equation of continuity, leads to the advection-diffusion equation. Moreover, large eddies are able to mix scalar quantities in a manner that is counter to the local gradient. We present a general solution of a two-dimension steady state advection-diffusi...