Evolution of phase transitions in methane hydrate

• Main Authors: Nathan L Gibson, F Patricia Medina, Malgorzata Peszynska, Ralph E Showalter
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Subjects: Methane hydrate
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1076.9369; http://math.oregonstate.edu/%7Empesz/documents/publications/GMPS13.pdf

Abstract. We consider a simplified model of methane hydrates which we cast as a nonlinear evolution problem. For its well-posedness we extend the existing theory to cover the case in which the problem involves a measurable family of graphs. We represent the nonlinearity as a subgradient and prove a useful comparison principle, thus optimal regularity results follow. For the numerical solution we apply a fully implicit scheme without regularization and use semismooth Newton algorithm for a solver, and the graph is realized as a complementarity constraint (CC). The algorithm is very robust and we extend it to define an easy and superlinearly convergent fully implicit scheme for Stefan problem and other multivalued examples.