CENTRAL SCHEMES FOR POROUS MEDIA FLOW

Abstract

We are concerned with numerical schemes for solving scalar hyperbolic conservation laws arising in the simulation of multiphase flows in heterogeneous porous media. These schemes are non-oscillatory and enjoy the main advantage of Godunov-type central schemes: simplicity, i.e., they employ neither characteristic decomposition nor pproximate Riemann solvers. This makes them universal methods that can be applied to a wide variety of physical problems, including hyperbolic systems. We compare the Kurganov-Tadmor (KT) [1] semi-discrete central scheme with the Nessyahu-Tadmor (NT) [2] central scheme. The KT scheme uses more precise information about the local speeds of propagation together with integration over nonuniform control volumes, which contain the Riemann fans. The numerical dissipation in the (KT) scheme is smaller than in the original NT scheme, however the NT scheme can use larger time steps. Numerical simulations are presented for two-phase flow problems in very heterogeneous formations. We find the KT scheme to be considerably less diffusive, particularly in the presence of viscous fingers, which lead to strong restrictions on the time step selection. REFERENCES [1] Kurganov, A. & Tadmor, E., 2000. New high-resolution central schemes for nonlinear conser- vation laws and convection-diffusion equations. Journal of Computational Physics, vol. 160, pp. 241­282. [2] Nessayahu, H. & Tadmor, E., 1990. Non-oscillatory central differencing for hyperbolic conser- vation laws. Journal of Computational Physics, vol. 87, n. 2, pp. 408­463.