Session S20 - Applied Math and Computational Methods and Analysis across the Americas

Friday, July 16, 16:00 ~ 16:30 UTC-3

Numerics and nonlinear wave analysis of geochemical injection for multicomponent two phase flow in porous media

Amaury Alvarez Cruz

Federal University of Rio de Janeiro, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Since there exists no general theory for the existence and uniqueness of solutions to systems of conservation laws, finding a numerical approximation to this solution is still a current challenge. In this work we propose a method to find approximated solutions of such systems by combining semi-analytical and numerical algorithms. We study a particular system arising from the analysis of the transport of chemical species, which poses a classical problem in Geochemical transport in porous media. Our analysis focuses on solving a Riemann problem of a system of four conservation laws of chemical species. Bifurcation and inflection surfaces lead us to propose a  "more likely" solution that must appear in the numerical solution. Due to the structure of flux and accumulation functions, an n-dimensional analysis of the existence of waves on the system is possible in this case. Finite element methods and finite difference schemes such as Backward-Euler and Crank-Nicolson are used for solving the system of conservation laws. Coefficients of the system are obtained from chemical data. The analysis of the existence of generalized solutions is studied.

Joint work with I. S. Ledoino(Laboratório Nacional de Computação Científica), D. Marchesin (IMPA) and J. Bruining (Delft Institute).

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