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, which gives rise to 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.