In this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. A numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. Truncation errors are derived for both continuous and discontinuous problems. Parameter uni...

We describe a novel Eulerian interface-sharpening approach for the efficient numerical resolution of interfaces arising from inviscid compressible flow in more than one space dimension. The algorithm uses the single-phase compressible Euler equations as the model system, and introduces auxiliary differential terms to the model so as to neutralize numerical diffusion that is inevitable when the ...

Numerical approaches in atmospheric and oceanic modeling inevitably introduce diffusion (or dissipation) and dispersion into the approximate solution. From a physical point of view, advection of a passive tracer is the simple transition of a quantity. Therefore, dispersion, the propagation of different spatial scales at different phase speed, and diffusion are processes that are aliens to the p...

We present formulation and numerical solution of two-phase multicomponent diffusion and natural convection in porous media. Thermal diffusion, pressure diffusion, and molecular diffusion are included in the diffusion expression from thermodynamics of irreversible processes. The formulation and the numerical solution are used to perform initialization in a 2D cross section. We use both homogeneo...

Fractional diffusion equations are useful for applications where a cloud of particles spreads faster than the classical equation predicts. In a fractional diffusion equation, the second derivative in the spatial variable is replaced by a fractional derivative of order less than two. The resulting solutions spread faster than the classical solutions and may exhibit asymmetry, depending on the fr...

Article history: Received 9 April 2012 Received in revised form 30 July 2012 Accepted 17 August 2012 Available online 1 September 2012

In this paper we revisit the problem of Brownian motion in a tilted periodic potential. We use homogenization theory to derive general formulas for the effective velocity and the effective diffusion tensor that are valid for arbitrary tilts. Furthermore, we obtain power series expansions for the velocity and the diffusion coefficient as functions of the external forcing. Thus, we provide system...

The aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. The method is a combination of the asymptotic expansion technique and the reproducing kernel method (RKM). First an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. Then the reduced regular delayed diffe...

In this work we deal with the numerical solution of some problems of air pollution. Since the problems are posed on unbounded domains we have to introduce artificial boundaries to confine the computational region. We construct and analyse (discrete) transparent boundary conditions for an implicit difference scheme. We discuss the concepts of positivity and monotonicity of difference schemes and...