Uniform temporal convergence of numerical schemes for incompressible miscible displacement
Provides theoretical convergence guarantees for a broad class of numerical methods used in porous media flow, addressing a gap in long-time behavior analysis.
The paper proves uniform-in-time convergence of HMM discretisations for the concentration variable in incompressible miscible displacement models, extending previous results that were limited to finite time intervals.
The Hybrid Mimetic Mixed (HMM) family of discretisations includes the Hybrid Finite Volume method, the Mimetic Finite Difference method and the Mixed Finite Volume method. This note demonstrates that HMM discretisations of the equations describing the single-phase, miscible displacement through a porous medium of one incompressible fluid by another converge uniformly in time for the concentration variable.