Deterministic Advection-Diffusion Model Based on Markov Processes

Ferreira, João S.; Costa, Manuel

doi:10.1061/(asce)0733-9429(2002)128:4(399)

Cited by 14 publications

(3 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Analytical solutions from Reference [3] have been used against the solutions provided by numerical methods in, e.g. Ferreira and Costa [19], and Manson and Wallis [20], who all reported a good agreement. They were also used by Leij et al [21] in an application to solute transport in porous media.…”

Section: Analytical Solutionmentioning

confidence: 99%

Limitations of an analytical solution for advection–diffusion with spatially variable coefficients

Néelz¹

2005

Commun. Numer. Meth. Engng.

View full text Add to dashboard Cite

SUMMARYThe aim of the article is to show that a published analytical solution for advection-di usion in streams is of limited relevance. The analytical solution is based on the assumptions that the velocity increases linearly with distance and that the di usion coe cient increases quadratically with distance. This implies that a solute concentration proÿle travelling down the channel is submitted to a stretching e ect, due to continuity, that completely counteracts the e ect of the increase in the di usion coe cient. Therefore, these particular assumptions are equivalent to the simpler case of uniform velocity and di usion coe cient, as far as the e ect of di usion is concerned. Two examples are proposed where results of a solute transport simulation using a semi-Lagrangian numerical model were compared to results using this analytical solution.

show abstract

Section: Analytical Solutionmentioning

confidence: 99%

Limitations of an analytical solution for advection–diffusion with spatially variable coefficients

Néelz¹

2005

Commun. Numer. Meth. Engng.

View full text Add to dashboard Cite

show abstract

“…Dispar is a mathematical formulation to solve advection-diffusion problems in aquatic systems. The Dispar transport model is a 2D model able to simulate several pollutant scenarios (Ferreira and Costa, 2002). In our application, Dispar is applied to the Tejo estuary (Lisbon).…”

Section: Servermentioning

confidence: 99%

Mobile Environmental Visualization

Danado

Dias

Romão

et al. 2005

The Cartographic Journal

View full text Add to dashboard Cite

Environmental processes are a major point of concern for researchers, environmental engineers and the general public. This paper presents a multi-user mobile system to visualize environmental processes. This system enables multiple users to visualize and simulate environmental processes, and also retrieve additional information in real time, while moving through the environmental area under analysis. Each user is able to contribute to the simulation and assess the impact of adding or removing agents to or from the model, respectively.This system uses a modular approach, allowing its deployment through different platforms. Two main modules compose the system under development: a geo-referenced model and an Augmented Reality (AR) composition module. The georeferenced model describes the environmental processes being modelled and tracks all users. The AR composition module allows users to visualize the geo-referenced model evolution and to interact with the model through two different views, namely animated map view and AR view.

show abstract

“…It simulates mass or energy transportation by the fluid in a movement. This type of equation occurs in the problems of physics, chemistry and biology involving diffusion or dispersion (Van Beinum et al , 2000; Ferreira and Costa, 2002; Dehghan, 2004; Bocksell and Loth, 2006; Bakunin, 2008; Mohebbi and Dehghan, 2010). One can form fractional advection-diffusion equation (FADE) by making its some or all derivatives of arbitrary order, but then it becomes more complicated or sometimes impossible to solve such problems analytically.…”

Section: Introductionmentioning

confidence: 99%

High-order approximation for generalized fractional derivative and its application

Yadav

Pandey

Shukla

et al. 2019

HFF

View full text Add to dashboard Cite

Purpose This paper aims to present a high-order scheme to approximate generalized derivative of Caputo type for μ ∈ (0,1). The scheme is used to find the numerical solution of generalized fractional advection-diffusion equation define in terms of the generalized derivative. Design/methodology/approach The Taylor expansion and the finite difference method are used for achieving the high order of convergence which is numerically demonstrated. The stability of the scheme is proved with the help of Von Neumann analysis. Findings Generalization of fractional derivatives using scale function and weight function is useful in modeling of many complex phenomena occurring in particle transportation. The numerical scheme provided in this paper enlarges the possibility of solving such problems. Originality/value The Taylor expansion has not been used before for the approximation of generalized derivative. The order of convergence obtained in solving generalized fractional advection-diffusion equation using the proposed scheme is higher than that of the schemes introduced earlier.

show abstract

Deterministic Advection-Diffusion Model Based on Markov Processes

Cited by 14 publications

References 11 publications

Limitations of an analytical solution for advection–diffusion with spatially variable coefficients

Limitations of an analytical solution for advection–diffusion with spatially variable coefficients

Mobile Environmental Visualization

High-order approximation for generalized fractional derivative and its application

Contact Info

Product

Resources

About