A two-step interface capturing scheme, implemented within the framework of conservative level set method, is developed in this study to simulate the gas/water two-phase fluid flow. In addition to solving the pure advection equation, which is used to advect the level set function for tracking interface, both nonlinear and stabilized features are taken into account for the level set function so t...

Study in surface water quality is important. Rivers are one of the main sources of water supply fordrinking, agriculture and industry. Unfortunately, sometime Rivers where wastewater dischargesare considered. For this reason,the pollutant transmission in river is one of the most importantproblems in Environmental Engineering. the Advection Dispersion Equation (ADE) is governedon the pollutant t...

The present work solves two-dimensional Advection-Dispersion Equation (ADE) in a semi-infinite domain. A variable source concentration is regarded as the monotonic decreasing function at the source boundary (x=0). Depth-dependent variables are considered to incorporate real life situations in this modeling study, with zero flux condition assumed to occur at the exit boundary of the domain, i.e....

[1] The multiscaling fractional advection-dispersion equation (ADE) is a multidimensional model of solute transport that encompasses linear advection, Fickian dispersion, and super-Fickian dispersion. The super-Fickian term in these equations has a fractional derivative of matrix order that describes unique plume scaling rates in different directions. The directions need not be orthogonal, so t...

the purpose of this paper is to present a 2d depth-averaged model for simulating and examining unsteady flow patterns in open channel bends. in particular, this paper proposes a 2d depth-averaged model that takes into account the influence of the secondary flow phenomenon through calculation of the dispersion stresses. the dispersion terms which arose from the integration of the product of the ...

We develop the basic tools of fractional vector calculus including a fractional derivative version of the gradient, divergence, and curl, and a fractional divergence theorem and Stokes theorem. These basic tools are then applied to provide a physical explanation for the fractional advection–dispersion equation for flow in heterogeneous porous media. r 2005 Elsevier B.V. All rights reserved.

Danshui River estuarine system is the largest estuarine system in northern Taiwan and is formed by the confluence of Tahan Stream, Hsintien Stream and Keelung River. A comprehensive one-dimensional model was used to model hydrodynamics and cohesive sediment transport in this branched River estuarine system. The applied unsteady model uses advection/dispersion equation to model the cohesive sedi...

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...

Rainwater streaking down a vertical wall exhibited the characteristics of “fingered flow.” The wall serves as an analogy to film flow in a relatively smooth and wide aperture fracture. A digital photograph of the wall suggests that the vertical distribution of water is heavy-tailed. A fractional-order advection-dispersion equation is used as a model.

We extend the dispersion-velocity particle method that we recently introduced to advection models in which the velocity does not depend linearly on the solution or its derivatives. An example is the Korteweg de Vries (KdV) equation for which we derive a particle method and demonstrate numerically how it captures soliton–soliton interactions.