Numerical Modeling of Multiphysics Systems

University Of Pittsburgh, Pittsburgh PA

Investigators

Abstract

The main objectives of the proposed research are to design, analyze, and implement accurate, robust, and efficient numerical methods for partial differential equations which model complex multiscale multiphysics systems arising in science and engineering applications. In particular, the research will focus on several critical components of the mathematical and numerical modeling of coupled free fluid and porous media flows: identification of a correct mathematical model, especially appropriate interface conditions, analysis of the well-posedness of the model, design and analysis of stable and accurate numerical discretization methods, including finite element methods on non-matching grids, interior convergence and postprocessing, and a posteriori error estimation and adaptivity, and development of efficient solution algorithms such as parallel domain decomposition and Newton-Krylov-multigrid solvers and preconditioners. The numerical techniques to be developed in this research are general and address fundamental questions of numerical analysis of partial differential equations. Applications to coupling of groundwater and surface water flows, as well as modeling of the cardiovascular system will be emphasized. Computer modeling of subsurface and surface flow and transport can provide reliable and cost-effective solutions to environmental and energy problems such as contaminant surface water and groundwater remediation and enhanced oil recovery. Current simulators do not take into account the complex multiscale interaction between subsurface and surface geosystems. This research will model this interaction, which is crucial for the accurate prediction of fluid behavior. The research will result in the development of robust and flexible software tools for performing accurate realistic multiprocessor simulations of contaminant remediation of wetlands, lakes and estuaries. Mathematical and computational modeling of the cardiovascular system is a relatively new but rapidly growing area of research. This application has a vast importance to society. For example, the heart attacks and strokes that result from atherosclerosis are the major cause of death in industrial nations. The aim of the proposed research in this area is to model computationally atherosclerosis taking into account the recently discovered, but critical effect of inflammation. Coupled macroscopic models of blood flow within the artery and its wall will be combined with cellular level models of acute inflammatory response. The research will lead to the development of optimized simulation tools which will advance prevention, detection, and therapy of atherosclerosis.