Open AccessThe Influence of Velocity Field Approximations in Tracer Injection Processes
Author(s) -
Yoisell R. Núñez,
Cristiane Oliveira de Faria,
Sandra M. C. Malta,
Abimael F. D. Loula
Publication year - 2018
Publication title -
tema
Language(s) - English
Resource type - Journals
eISSN - 2179-8451
pISSN - 1677-1966
DOI - 10.5540/tema.2018.019.02.347
Subject(s) - spurious relationship , mathematics , galerkin method , finite element method , field (mathematics) , mathematical optimization , petrov–galerkin method , darcy's law , mathematical analysis , physics , porous medium , statistics , pure mathematics , thermodynamics , geotechnical engineering , porosity , engineering
Although the concentration is the most important variable in tracer injection processes, an efficient and accurate velocity field approximation is crucial to obtain a good physical behaviour for the problem. In this paper we analyse a Stabilized Dual Hybrid Mixed (SDHM) method to solve the Darcy's system in the velocity and pressure variables that involves the conservation of mass and Darcy's law. This approach is locally conservative, free of compromise between the finite element approximation spaces and capable of dealing with heterogeneous media with discontinuous properties. The tracer concentration is solved via a combination of the Streamline Upwind Petrov-Galerkin (SUPG) method in space with an implicit finite difference scheme in time. We also employ a semi-analytical approach (Abbaszadeh-Dehghani analytical solution) to integrate the transport equation. A numerical comparative study using the SDHM formulation, the Galerkin method and a post-processing technique to calculate the velocity field in combination with those concentration approximation methodologies are presented. In all comparisons, the SDHM formulation appears as the most efficient, accurate and almost free of spurious oscillations.