Publication

Numerical experiments on dispersion in heterogeneous porous media

1990
Book Chapters

Abstract

The paper discusses numerical simulations of dispersion processes of inert solutes in two-dimensional random log-permeability fields Y(x). A suitable number of realizations is generated preserving a given spatial correlation structure. For each realization a finite element model solves the flow equation and a particle-tracking method solves the transport equation. Ensemble averaging yields then the statistics. The range of ÏƒY2 investigated is 0.2Ã·2.0. The results show that Dagan's linear theory yields acceptable results in an unexpectedly broad range of ÏƒY2. Interestingly, a linearization of the flow equation yields larger deviations from the linear theory than the corresponding fully nonlinear model, thereby suggesting that previous conclusions drawn on the limitations of the linear theory might be restrictive.

Official source

https://infoscience.epfl.ch/entities/publication/135f613a-30e9-4c81-8dc1-80602e3ac753

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1990
Book Chapters

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/135f613a-30e9-4c81-8dc1-80602e3ac753

About this result

Related concepts (32)

Euler equations (fluid dynamics)

In fluid dynamics, the Euler equations are a set of quasilinear partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular, they correspond to the Navier–Stokes equations with zero viscosity and zero thermal conductivity. The Euler equations can be applied to incompressible or compressible flow. The incompressible Euler equations consist of Cauchy equations for conservation of mass and balance of momentum, together with the incompressibility condition that the flow velocity is a solenoidal field.

Navier–Stokes equations

The Navier–Stokes equations (nævˈjeː_stəʊks ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842-1850 (Stokes). The Navier–Stokes equations mathematically express momentum balance and conservation of mass for Newtonian fluids.

Potential flow

In fluid dynamics, potential flow (or ideal flow) describes the velocity field as the gradient of a scalar function: the velocity potential. As a result, a potential flow is characterized by an irrotational velocity field, which is a valid approximation for several applications. The irrotationality of a potential flow is due to the curl of the gradient of a scalar always being equal to zero. In the case of an incompressible flow the velocity potential satisfies Laplace's equation, and potential theory is applicable.

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Numerical experiments on dispersion in heterogeneous porous media

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