A virtual element method for the miscible displacement of incompressible fluids in porous media
L. Beirão da Veiga, Alexander Pichler, Giuseppe Vacca
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.
Topics & Concepts
DiscretizationCompressibilityDisplacement (psychology)Porous mediumPartial differential equationNonlinear systemMathematicsVirtual workScheme (mathematics)Finite element methodFluid dynamicsFlow (mathematics)Incompressible flowMathematical analysisApplied mathematicsCalculus (dental)MechanicsGeometryPhysicsEngineeringPorosityStructural engineeringGeotechnical engineeringQuantum mechanicsMedicinePsychologyPsychotherapistDentistryAdvanced Numerical Methods in Computational MathematicsElectromagnetic Simulation and Numerical MethodsAdvanced Mathematical Modeling in Engineering