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Numerical approximation of water–air two-phase flow by the mixed finite element method |
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| Authors: | Johannes Korsawe Eugen Perau Susanne Potthoff Gerhard Starke |
| Affiliation: | a Institut für Angewandte Mathematik, Universität Hannover, 30167, Hannover, Germany b Fachbereich Bauwesen, Universität Duisburg-Essen, 45117, Essen, Germany c Fachbereich Bauwesen, Universität Duisburg-Essen, 45117, Essen, Germany d Institut für Angewandte Mathematik, Universität Hannover, 30167, Hannover, Germany |
| Abstract: | A new model for two-phase flow of water and air in soil is presented. This leads to a system of two mass balance equations and two equations representing conservation of momentum of fluid and gas, respectively. This paper is concerned with the verification of this model for the special case of a rigid soil skeleton by computational experiments. Its numerical treatment is based on the Raviart–Thomas mixed finite element method combined with an implicit Euler time discretization. The feasibility of the method is illustrated for some test examples of one- and two-dimensional two-phase flow problems. |
| Keywords: | Two-phase flow model Capillarity Compressed air Tunneling Mixed finite element methods Raviart–Thomas |
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