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.
Beirao da Veiga, L., Pichler, A., Vacca, G. (2021). A virtual element method for the miscible displacement of incompressible fluids in porous media. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 375(1 March 2021) [10.1016/j.cma.2020.113649].
A virtual element method for the miscible displacement of incompressible fluids in porous media
Beirao da Veiga L.
;Vacca G.
2021
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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