The governing equation of longitudinal dispersion phenomenon of one-dimensional concentration distribution in fluid flow through porous media has been obtained in term of one-dimensional non-linear advection-diffusion equation. This equation has been converted in term of dimensionless non-linear Burger's equation with its derivative, and it is multiplied by small parameter   0,1   . This eq...

In this paper, we consider the numerical solutions of a fractional partial differential equation with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two kinds of FPDE-RSFD are considered: the Riesz fractional diffusion equation (RFDE) and the Riesz fractional advection-dispersion equation (RFADE). RFDE is obtained from the standard diffusion equation by replacing the secondo...

Artificial phoretic particles swim using self-generated gradients in chemical species (self-diffusiophoresis) or charges and currents (self-electrophoresis). These particles can be used to study the physics of collective motion in active matter and might have promising applications in bioengineering. In the case of self-diffusiophoresis, the classical physical model relies on a steady solution ...

In this paper, we propose an algorithm estimating parameters of a source term of a linear advection-diffusion equation with an uncertain advection-velocity field. First, we apply a minimax state estimation technique order to reduce uncertainty introduced by the coefficients. Then we design a source localization algoritm which uses the state estimator as a model and estimates the parameters of t...

We prove the existence and uniqueness of a positive solution to a logistic system of differential difference equations that arises as a population model for a single species which is composed of several habitats connected by linear migration rates. Our proof is based on the proof of a similar result for a reaction-advection-diffusion equation.

We discuss L integrability estimates for the solution u of the advection-diffusion equation ∂t u + div (bu) = ∆ u, where the velocity field b ∈ Lt r Lx q . We first summarize some classical results proving such estimates for certain ranges of the exponents r and q. Afterwards we prove the optimality of such ranges by means of new original examples.

We construct four variants of space-time finite element discretizations based on linear tensor-product and simplex-type elements. The resulting are continuous in space, or discontinuous time. In a first test run, all methods applied to scalar advection-diffusion model problem. Then, the convergence properties time-discontinuous studied numerical experiments. Advection velocity diffusion coeffic...

A two-dimensional two-phase numerical model is developed to predict transport and fate of oil slicks which resulted the concentration distribution of oil on the water surface. Two dimensional governing equation of fluid flow which consists mass and momentum conservation was solved using the finite difference method on the structured staggered grid system. The resulted algebric equations were so...

Recent work on the global overturning circulation and its energetics assumes that processes caused by nonlinearities of the equation of state of seawater are negligible. Nonlinear processes such as cabbeling and thermobaricity cause diapycnal motion as a consequence of isopycnal mixing. The nonlinear equation of state also causes the helical nature of neutral trajectories; as a consequence of t...

Abstract: New numerical techniques are presented for the solution of a class of the variable order fractional advection-diffusion equation with a nonlinear source term on one-dimensional finite domain. Quasiwavelet and double quasi-wavelet are used for the spatial discretization. For the time stepping, Euler method is considered. We also tested the method proposed on several problems with very ...