Maseeh Mathematics and Statistics Colloquium: Modeling Multiphase Porous Flows

Speaker: Dr. Noel Walkington
Carnegie Mellon University

Title: Modeling Multiphase Porous Flows

Abstract: In order to model many geological flows of contemporary interest it is necessary to include the thermodynamics of the underlying processes. Examples include CO_2 sequestration and the release of greenhouse gasses dissolved in melting permafrost. Tractable models of such problems can only involve gross (macroscopic) properties, since a precise description of the physical system is neither available nor computationally tractable.

This talk will first briefly review the role thermodynamics plays in classical continuum mechanics; in particular, how dissipation principles give rise to bounds above and beyond the natural conservation properties. The development of macroscopic models of geological flows involving multiple components undergoing changes of phase will then be considered. These models involve an amalgamation of classical and continuum thermodynamics to yield systems of conservation laws which inherit natural dissipation principles. The convexity (concavity) of the free energy (entropy) functions is essential for the development of stability estimates of solutions to these equations, and the development of stable numerical schemes.

Biography: Noel Walkington is a numerical analyst and professor of mathematics at Carnegie Mellon University. He holds degrees in mechanical engineering and mathematics and enjoys working at the interface of the two. His research interests center around the development and analysis of algorithms for the solution of partial differential equations (PDEs) that arise in engineering and science. He is particularly interested in bringing new tools to bear upon challenging problems that arise in the numerical approximation of PDEs, including the design and analysis of 2D and 3D mesh generation algorithms that resolve difficult geometric features.