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arXiv · 1907.13080

A virtual element method for the miscible displacement of incompressible fluids in porous media

Lourenco Beirao da Veiga·Alexander Pichler·Giuseppe Vacca
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Abstract

In the present contribution, we construct a virtual element (VE) discretization for the problem of miscible displacement of one incompressible fluid by another, described by a time-dependent coupled system of nonlinear partial differential equations. Our work represents a first study to investigate the premises of virtual element methods (VEM) for complex fluid flow problems. We combine the VEM discretization with a time stepping scheme and develop a complete theoretical analysis of the method under the assumption of a regular solution. The scheme is then tested both on a regular and on a more realistic test case.

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Lourenco Beirao da Veiga, Alexander Pichler, Giuseppe Vacca. 2019-07-30. A virtual element method for the miscible displacement of incompressible fluids in porous media. https://arxiv.org/abs/1907.13080

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