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We design a numerical approximation of a system of partial differentialequations modelling the miscible displacement of a fluid by another in a porousmedium. The advective part of the system is discretised using a characteristicmethod, and the diffusive parts by a finite volume method. The scheme isapplicable on generic (possibly non-conforming) meshes as encountered inapplications. The main features of our work are the reconstruction of a Darcyvelocity, from the discrete pressure fluxes, that enjoys a local consistencyproperty, an analysis of implementation issues faced when tracking, via thecharacteristic method, distorted cells, and a new treatment of cells near theinjection well that accounts better for the conservativity of the injectedfluid.

An HMM--ELLAM scheme on generic polygonal meshes for miscible incompressible flows in porous media