Characteristic adaptive subdomain methods for reservoir flow problems

Abstract

Abstract The simulation of multiphase and multicomponent fluid flows often requires the solution of large, coupled systems of nonlinear partial differential equations of convection‐advection type. The equations are usually advection dominated with small but important local diffusive effects. An operator‐splitting technique is used to address these different phenomena. A modified method of characteristics is used to try to eliminate the nonsymmetry in the operators due to advection. Although this method does not completely symmetrize the problem with nonlinear, nonconvex flux functions, the remaining operator is almost symmetric and can be stabilized via Petrov‐Galerkin techniques with optimal or near optimal test functions. Effective localized test functions are descrbed. A coarse grid is defined to treat the slow variation of the fluid velocity away from fronts. A substructuring of this grid gives a proper frontal resolution via local patch grid refinement. Preconditioning techniques are presented to efficiently solve the resulting composite‐grid problem. Error estimates for the total approximation procedure are presented. Finally, certain two‐dimensional computations are described.