A high-order TVD transport method for hybrid meshes on complex geological geometry

Abstract

The paper presents a new implicit pressure-implicit saturation higher-order accurate in space and second-order accurate in time advection-dispersion scheme for the hyperbolic transport equations in porous media with discrete three-dimensional representation of material interfaces. We develop adaptive time differencing methods to use time steps greater than the mesh Courant number (Courant-Friedrich-Levy condition, CFL). The paper pays special attention to hybrid discretization of subsurface geometry, placing emphasis on the multiphase flow in fractured petroleum reservoirs. We also introduce numerical iso-parametric double mapping integration method for node-centred hybrid meshes and use it ..