Model adaptivity for porous media

Oregon State University, Corvallis OR

Investigators

Abstract

The theory of error estimation is of paramount importance to the computational sciences. Local temporal and spatial grid adaptivity help to minimize the discretization error at a low computational cost. In this project the investigator and graduate students pursue a study of model adaptivity in which the original model represented by a coupled system of partial differential equations is replaced by another one which is easier to solve. The main idea of model adaptivity is to use an appropriate splitting of the total error so that the discretization and the modeling error are estimated a-posteriori and controlled locally and globally. Realization of these ideas depends on a particular application and its numerical approximation as well as on the relevant quantities of interest which guide both the grid and model adaptivity. This project will focus on applications in porous media, in particular on those of multiscale and preferential type, and on their various conforming and non-conforming finite element formulations. The researchers will prove new theoretical results as well as will develop new adaptive algorithms whose prototype implementations will be available in public domain. The project will lay foundations for a new class of fast and accurate computational methods for simulation of natural phenomena occuring under the Earth's surface such as flow of contaminated water through and over complex geological formations. While traditional methods use a fixed model of such phenomena as a basis for computational simulations, the novel ideas proposed in this research project will allow to discard those elements of a model which are computationally costly but which do not have significant impact on the solutions. The new methods proposed in the project will be evaluated from both theoretical as well as from practical point of view and can be used in place of costly sensitivity and parameter studies. The results of the project will be also applicable to other disciplines such as engineering design of multiscale materials, large scale simulations of neutron transport and biomedical applications. Undergraduate and graduate students will be involved in research and will be trained in the new and traditional adaptive computational methods and their applications.