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A novel approach to modelling of flow in fractured porous medium

Jan Šembera, Jiří Maryška, Jiřina Královcová, Otto Severýn (2007)

Kybernetika

There are many problems of groundwater flow in a disrupted rock massifs that should be modelled using numerical models. It can be done via “standard approaches” such as increase of the permeability of the porous medium to account the fracture system (or double-porosity models), or discrete stochastic fracture network models. Both of these approaches appear to have their constraints and limitations, which make them unsuitable for the large- scale long-time hydrogeological calculations. In the article,...

A novel interval arithmetic approach for solving differential-algebraic equations with VALENCIA-IVP

Andreas Rauh, Michael Brill, Clemens Günther (2009)

International Journal of Applied Mathematics and Computer Science

The theoretical background and the implementation of a new interval arithmetic approach for solving sets of differentialalgebraic equations (DAEs) are presented. The proposed approach computes guaranteed enclosures of all reachable states of dynamical systems described by sets of DAEs with uncertainties in both initial conditions and system parameters. The algorithm is based on VALENCIA-IVP, which has been developed recently for the computation of verified enclosures of the solution sets of initial...

A Numerical Approach of the sentinel method for distributed parameter systems

Aboubakari Traore, Benjamin Mampassi, Bisso Saley (2007)

Open Mathematics

In this paper we consider the problem of detecting pollution in some non linear parabolic systems using the sentinel method. For this purpose we develop and analyze a new approach to the discretization which pays careful attention to the stability of the solution. To illustrate convergence properties we give some numerical results that present good properties and show new ways for building discrete sentinels.

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