The Influence of Velocity Field Approximations in Tracer Injection Processes - Núñez, Yoisell R.; Faria, Cristiane Oliveira; Malta, Sandra M. C.; Loula, Abimael F. D. (Trends in Computational and Applied Mathematics, 2018)
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.