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Title: | A Linear Domain Decomposition Method for Non-equilibrium Two-Phase Flow Models | Authors: | LUNOWA, Stephan POP, Sorin Koren, Barry |
Issue Date: | 2021 | Publisher: | Springer | Source: | Vermolen, Fred; Vuik, Cornelis (Ed.). Numerical Mathematics and Advanced Applications ENUMATH 2019, Springer, p. 145 -153 | Series/Report: | Lecture Notes in Computational Science and Engineering | Series/Report no.: | 139 | Abstract: | We consider a model for two-phase flow in a porous medium posed in a domain consisting of two adjacent regions. The model includes dynamic capillarity and hysteresis. At the interface between adjacent subdomains, the continuity of the normal fluxes and pressures is assumed. For finding the semi-discrete solutions after temporal discretization by the θ-scheme, we proposed an iterative scheme. It combines a (fixed-point) linearization scheme and a non-overlapping domain decomposition method. This article describes the scheme, its convergence and a numerical study confirming this result. The convergence of the iteration towards the solution of the semi-discrete equations is proved independently of the initial guesses and of the spatial discretization, and under some mild constraints on the time step. Hence, this scheme is robust and can be easily implemented for realistic applications. | Document URI: | http://hdl.handle.net/1942/34094 | ISBN: | 9783030558734 9783030558741 |
DOI: | 10.1007/978-3-030-55874-1_13 | Category: | C1 | Type: | Proceedings Paper |
Appears in Collections: | Research publications |
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