Solvers for Incompressible Immiscible Flow
Knut‐Andreas Lie · Cambridge University Press eBooks · 2019
This chapter teaches you how to simulate incompressible, two-phase flow using a sequential formulation that splits the equation system into an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. We discuss fluid objects, the sequential solution procedure, and explicit and implicit transport solvers in some detail. The second part of the chapter is devoted to a number of simulation examples that highlight typical flow behavior. Examples include gravity segregation, homogeneous quarter five-spots, heterogeneous quarter five-spots with viscous fingering, and buoyant migration of CO2 in a sloping aquifer. Furthermore, we discuss water coning, gravity override, capillary fringes, and a simplified simulation of the Norne field model. We end the chapter by a discussion of various sources of numerical errors, including splitting and grid-orientation errors.