In the present study, analytical solutions are developed for three-dimensional advection-dispersion equation (ADE) in semi-infinite adsorbing saturated homogeneous porous medium with time dependent dispersion coefficient. It means porosity of the medium is filled with single fluid(water). Dispersion coefficient is considered proportional to seepage velocity while adsorption coefficient inversel...

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...

In the present study, analytical solutions are developed for three-dimensional advection-dispersion equation (ADE) in semi-infinite adsorbing saturated homogeneous porous medium with time dependent dispersion coefficient. It means porosity of the medium is filled with single fluid(water). Dispersion coefficient is considered proportional to seepage velocity while adsorption coefficient inversel...

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...

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 develop a numerical resolution of the space-time fractional advection-dispersion equation. We utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. By using Bernstein polynomial basis, the problem is transformed in...

The numerical solutions of the advection-diffusion equation are themselves numerous and sometimes very sophisticated, in order to avoid two undesirable features: oscillatory behavior and numerical diffusion. It is known that the common practice of “splitting-up” the solution is not always the best approach to the advection-diffusion problem. By using the ordinary differential equation analogy m...

We propose a technique that could significantly improve the accuracy of the levelset method and has the potential for fully conservative treatment. Level set method uses the levelset function, usually an approximate signed distance function Φ to indirectly represent the interface by the zero set of Φ. When Φ is advanced to the next time level by an advection equation, it is no longer a signed d...