Numerical study of the solution to the dam problem

Abstract

The flow of a laminar fluid that filters through a porous medium is considered. This behavior leads to the formulation of a mathematical model that, through the Baiocchi transformation, allows it to be expressed as a free boundary problem. In this we wish to evaluate the pressure gradient of the fluid in the medium. The present work consists of the following: i) variational formulation of the problem il) study of
the existence and uniqueness of the solution and iii) numerical resolution of the problem of
generated convex minimization. To find the numerical solution of the variational inequality, the Finite Element method and the Uzawa algorithm have been used.
In the numerical simulation of the dam problem, the domain has been considered
of computational calculation, a rectangular IR geometry, assuming as known boundaries, the impermeable zone, the one in contact with the air and the one that coexists with the fluid. The free (or unknown) boundary is generated by the curve that separates the dry zone from the wet zone. The numerical technique that has been
performed to solve this problem is very effective and is recommended in other problems
of a non-linear type, because the mathematical treatment is extensible and because of the speed of computational convergence in the process.