Description
We explore the use of mimetic finite differences as an alternative numerical method to solve the partial differential equations that model the mass transport and concentration profiles of geologically sequestered carbon dioxide. We study the mathematical foundations and the underlying algorithms to construct higher-order one-dimensional mimetic operators, and we extend this knowledge to enable systematic derivations of their higher-dimensional counterparts. This work is then used as the theoretical foundation for the Mimetic Methods Toolkit (MTK); a C++ API implementing mimetic discretization and quadrature schemes on logically-rectangular grids. We discuss the API's design, structure, and usage philosophy, as well as its parallel programming aspects, and the related utility APIs. We also introduce a matrix storage scheme and provide preliminary tests of its performance. The resulting method can be used to compute the concentrations of multiple solutes in distributed-memory computers. Our applications focus on the simulation of long-term geologic sequestration of carbon dioxide.
