Evolution of phase transitions in methane hydrate
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...
| Main Authors: | , , , |
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| Format: | Text |
| Language: | English |
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| Online Access: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1076.9369 http://math.oregonstate.edu/%7Empesz/documents/publications/GMPS13.pdf |
| Summary: | 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. |
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