arXiv subjects

Eugenio Aulisa

Publications and source records attributed to Eugenio Aulisa.

21 records · Page 2Linked to original sources

arXiv2013

Geometric framework for modeling nonlinear flows in porous media, and its applications in engineering

This work represents an application of constant mean curvature graphs (as solutions of the mean curvature PDE) to non-linear non-Darcy flows in porous media. It relates time invariant pressure distribution graphs to graphs of constant mean curvature surfaces. This differential geometric interpretation provides an important tool for evaluating technological parameters in reservoir engineering.

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arXiv2013

Geometric Methods in the Analysis on Non-linear Flows in Porous Media (Preliminary Version)

Over the past few years, we developed a mathematically rigorous method to study the dynamical processes associated to nonlinear Forchheimer flows for slightly compressible fluids. We have proved the existence of a geometric transformation which relates constant mean curvature surfaces and time-invariant pressure distribution graphs constrained by the Darcy-Forchheimer law. We therein established a direct relationship between the CMC graph equation and a certain family of equations which we call $g$-Forchheimer equations. The corresponding results, on fast flows and their geometric interpretation, can be used as analytical tools in evaluating important technological parameters in reservoir engineering.

math.DG↗

arXiv2013

Constructing isothermal curvature line coordinates on surfaces which admit them

Isothermic parameterizations} are synonyms of isothermal curvature line parameterizations, for surfaces immersed in Euclidean spaces. We provide a method of constructing isothermic coordinate charts on surfaces which admit them, starting from an arbitrary chart. One of the primary applications of this work consists of numerical algorithms for surface visualization.

math.DG↗