On the Eulerian–Lagrangian formulation of balance equations in porous media

Bear, Jacob; Sorek, S.; Борисов, В.В.

doi:10.1002/(sici)1098-2426(199709)13:5<505::aid-num4>3.3.co;2-k

Cited by 3 publications

(3 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Following Neuman and Sorek (1982) for transport problems (e.g. see also Neuman, 1984;Sorek, 1988a,b), for flow problems (Sorek, 1985;Sorek and Braester, 1988) and a modified Eulerian-Lagrangian method for coupled flow and transport model (Bear et al, 1997;Sorek et al, 2000), a technique consisting of the following two steps is used:…”

Section: Methods Of Characteristics / Lagrangian Methodsmentioning

confidence: 99%

Numerical Models of Groundwater Flow and Transport

Holzbecher¹,

Sorek

2005

Encyclopedia of Hydrological Sciences

Self Cite

View full text Add to dashboard Cite

The article gives an introduction to numerical modeling of flow and transport problems and to software tools that are currently in use for modeling such phenomena. Details are explained on numerical approximations leading to different numerical models. Extensions for reactive transport are mentioned. Basic guidelines and criteria are given that should be taken into account by the modeler in order to improve the accuracy of results. Inverse modeling is presented as an advanced feature. Some examples of pre‐ and postprocessing, as implemented in several codes, are given, in addition to fundamental properties of solution methods. Finally, most common codes are listed with basic features and web‐sites.

show abstract

Section: Methods Of Characteristics / Lagrangian Methodsmentioning

confidence: 99%

Numerical Models of Groundwater Flow and Transport

Holzbecher¹,

Sorek

2005

Encyclopedia of Hydrological Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…The process of groundwater flow is generally assumed to be governed by Darcy's law and the conservation of mass. The theoretical basis for the equation describing solute transport has been well documented in the literature [7][8][9][10]. Reilly et al [11] provide a conceptual framework for analyzing and modeling physical solute transport processes in groundwater.…”

Section: Modeling Of Contaminant Transport Processesmentioning

confidence: 99%

Migration of Organic Contaminants from Landfill: Minimum Thickness of Barriers

Jhamnani¹,

Singh²

2009

TOEPTJ

View full text Add to dashboard Cite

Point sources such as landfills, can release high concentrations of contaminants into the groundwater because of migration of leachate from its bottom, which is generated primarily as a result of precipitation falling on an active landfill surface, leaching out the potential organic and inorganic contaminants from landfilled waste and discharging the same to groundwater in underlying aquifer. Leachate from young landfills has high dissolved solids content as well as a high concentration of organic matter. Landfill leachate has the potential to contaminate the surrounding environment and impair groundwater use. Organic contaminants in landfill leachate originate from incoming wastes or are produced as a result of biochemical reactions taking place in landfills. To protect the groundwater from contamination by landfill leachate, it is quite essential to provide the bottom barrier of suitable thickness, and to minimize the amount of water that could enter the landfill to create leachate. The present study was undertaken to determine the rate of movement of potential contaminants from its bottom to the aquifer media, so as to evolve a rational method for the determination of thickness of bottom barrier on sound engineering practice, in place of adopting a prescriptive standard, which is very common in most of the Asian countries. The study was undertaken for non conservative contaminant Dissolved Organic Carbon (DOC). The governing equation of contaminant transport was solved using finite difference method, and finite mass boundary condition to ape the finite mass of contaminants in a landfill. The solution of the model was run in MatLab 7.0 for a range of Darcy velocities and retardation factors for a representative equivalent height of leachate. Design curves were drawn which can be used for determination of suitable barrier thickness on the basis of expected maximum concentration of DOC in landfill leachate and maximum permissible concentration of the same.

show abstract

“…Following the formulation of the MEL method (Bear et al, (1997) and its mathematical analysis (Sorek et al, 1998), the MEL formulation here is exemplified for the flow, the solute transport, and the heat-transfer equations referring to hydrodynamic processes in porous media. These PDEs are coupled when considering, e.g., the saltwater-intrusion problem.…”

Section: Introductionmentioning

confidence: 99%

Numerical modeling of coupled hydrological phenomena using the Modified Eulerian-Langrangian method

Sorek¹,

Borisov²,

Yakirevich³

2000

Theory, Modeling, and Field Investigation in Hydrogeology: A Special Volume in Honor of Shlomo P. Neumans 60th Birthday

Self Cite

View full text Add to dashboard Cite

The chapter presents the advantages of using the Modified Eulerian-Lagrangian (MEL) method for solving the transport of extensive quantities in a porous medium. In this modified formulation, the material derivatives are written in terms of modified velocities. These are the velocities at which the various phase and component variables propagate in the domain, along their respective characteristic curves. It is shown that these velocities depend on the heterogeneity of various solid matrix and fluid properties. Accordingly, an extension to the Peclet number is presented that also accounts for governing equations that may be advective dominant with no reference to the fluid velocity or even when this velocity is not introduced.A mathematical analysis proves that for coupled partial differential equations (PDEs), unlike the Eulerian implicit finite difference scheme the MEL method unconditionally guarantees the absent of spurious oscillations.The MEL formulation is demonstrated for a coupled set of PDEs concerning the problem of saltwater intrusion, with heat transfer.A numerical example suggests that the MEL scheme produces better resolution compared to the Eulerian and the Eulerian-Lagrangian ones.

show abstract

On the Eulerian–Lagrangian formulation of balance equations in porous media

Cited by 3 publications

References 0 publications

Numerical Models of Groundwater Flow and Transport

Numerical Models of Groundwater Flow and Transport

Migration of Organic Contaminants from Landfill: Minimum Thickness of Barriers

Numerical modeling of coupled hydrological phenomena using the Modified Eulerian-Langrangian method

Contact Info

Product

Resources

About