Reservoir Simulation

With MacCormack (1969) scheme being an explicit scheme, while simple to implement and which does not require inversion of large matrices; and which remains to be second-order accurate in both space and time, whether, for characterizing heterogeneous hydrocarbon reservoirs with non-linear hyperbolic equations, to what extent, MacCormack scheme would remain to be efficient numerically (as closed form solutions remain available only for idealized cases of non-linear hyperbolic equations)?

Will this scheme would efficiently capture shock?

Will there be a need for iterations, when the capillary pressure between oil and brine remains to be larger?

With such a two-level predictor corrector scheme, can we have a relatively longer distance steps that could be used to obtain the same accuracy as that obtained using first-order schemes (although, MacCormack scheme must satisfy CFL condition for stability)? Won’t it produce numerical oscillations @ or near the oil-brine front/interface? If so, then, whether, such oscillations (caused by the dispersive errors) could remain to be dampened by introducing artificial viscosity?

Dr Suresh Kumar Govindarajan

Professor [HAG]

IIT Madras

14-March-205