Fully Locally Conservative Characteristic Methods for Transport Problems

University Of Texas At Austin, Austin TX

Investigators

Abstract

The transport of a chemical tracer within an ambient fluid (such as a contaminant in groundwater), can be approximated by Eulerian-Lagrangian numerical methods. These methods conserve tracer mass locally, but not the mass of the ambient fluid. They therefore compute inaccurate densities, which can seriously degrade the quality of the solution over time. The PI and coworker recently defined the Volume Corrected Characteristics-Mixed Method (VCCMM) for the simplest transport problem, by considering the transport problem not as a single hyperbolic equation for the tracer, but rather as a system of two equations describing the motion of both the tracer and ambient fluids, each of which must be conserved locally. This project will: (1) Complete the development of VCCMM, by placing it on a sound theoretical footing and developing a parallel version of the software; (2) Improve and extend VCCMM to more complex flows; (3) Develop a grid adapted version; and (4) Develop methods for nonlinear transport problems, including miscible, compressible flows, and two-phase, immiscible flows, for which the solution may contain shocks and rarefactions. The project is expected to result in significant improvement in the approximation of transport problems for long time simulation, because the discrete approximation will have less numerical diffusion and preserve important physical principles. The project is expected to have broader impacts, including: (1) Developing a scientific software tool that can be applied to a wide range of practical problems; (2) The training of one Ph.D. student in a multidisciplinary environment; and (3) Societal benefits by allowing better modeling of, e.g., geologic basin formation, long-lived radio-isotope decay, miscible fingering, and two-phase flows. The ability to predict the movement of a chemical specie, called a tracer, within another, ambient fluid is important in many applications. For example, the need arises in ground-water contaminant migration studies. This project investigates ways to improve the prediction of tracer transport through computer simulation. State-of-the-art numerical algorithms of Lagrangian type simulate tracer transport by explicitly calculating the movement of individual particles within small regions of space. Tracer mass is conserved, meaning that no mass is artificially created or destroyed by the numerical calculations. This is a critical property for studies involving, e.g., contaminants, since even small concentrations can be toxic to humans, and any creation or degradation of the tracer must be due to physical and chemical processes and not to numerical artifacts. However, Lagrangian methods do not conserve the mass of the ambient fluid. This results in inaccurate tracer densities. That is, although tracer mass is conserved, its concentration is incorrectly computed, which can lead to serious inaccuracies in reaction dynamics and degradation in the predicted movement over time. The approach taken by the PI to resolve these difficulties is to consider the transport of both the tracer and ambient fluids, each of which must be conserved. The research is expected to result in significant improvement in the approximation of transport problems for long time simulation, and the training of at least one Ph.D. student in a multidisciplinary environment. This work has potential societal benefits as applied to problems in the contamination of ground-water, petroleum and natural gas production, and CO2 sequestration.