Flow and transport take place in a heterogeneous medium made up from inclusions of conductivity K submerged in a matrix of conductivity K-0. We consider two-dimensional isotropic media, with circular inclusions of uniform radii, that are placed at random and without overlap in the matrix. The system is completely characterized by the conductivity contrast kappa=K/K-0 and by the volume fraction n. The flow is uniform in the mean, of velocity U=const. The derivation of the velocity field is achieved by a numerical method of high accuracy, based on analytical elements. Approximate analytical solutions are derived by a few methods: composite elements, effective medium, dilute systems and first-order approximation in logconductivity variance. The latter was employed by Rubin (1995), while the dilute system approximation was used by Eames and Bush (1999) and Dagan and Lessoff (2001). Transport is solved in a Lagrangean framework, with trajectories determined numerically from the velocity field, by particle tracking. Results for the velocity variance and for the longitudinal macrodispersivity, for a few values of kappa and n, are presented in Part 2.
Fiori, A., Jankovic, I., Dagan, G. (2003). Flow and transport through two-dimensional isotropic media of binary conductivity distribution. Part 1: NUMERICAL methodology and semi-analytical solutions RID A-2321-2010. STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT, 17(6), 370-383 [10.1007/s00477-003-0166-0].
Flow and transport through two-dimensional isotropic media of binary conductivity distribution. Part 1: NUMERICAL methodology and semi-analytical solutions RID A-2321-2010
FIORI, ALDO;
2003-01-01
Abstract
Flow and transport take place in a heterogeneous medium made up from inclusions of conductivity K submerged in a matrix of conductivity K-0. We consider two-dimensional isotropic media, with circular inclusions of uniform radii, that are placed at random and without overlap in the matrix. The system is completely characterized by the conductivity contrast kappa=K/K-0 and by the volume fraction n. The flow is uniform in the mean, of velocity U=const. The derivation of the velocity field is achieved by a numerical method of high accuracy, based on analytical elements. Approximate analytical solutions are derived by a few methods: composite elements, effective medium, dilute systems and first-order approximation in logconductivity variance. The latter was employed by Rubin (1995), while the dilute system approximation was used by Eames and Bush (1999) and Dagan and Lessoff (2001). Transport is solved in a Lagrangean framework, with trajectories determined numerically from the velocity field, by particle tracking. Results for the velocity variance and for the longitudinal macrodispersivity, for a few values of kappa and n, are presented in Part 2.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.