Incorporating the multigrid method with the adaptive local grid refinement to solve 3-D subsurface density-dependent flow and transport equations

This paper presents an approach combining the multigrid method and the adaptive local grid refinement to solve 3-D density-dependent flow and transport equations in the subsurface. This combination is to provide a collaborated numerical strategy which is computationally efficient and accurate. With the multigrid method, the computational efficiency is achieved through its O(n) computations in solving a matrix equation with n unknowns. With the adaptive local grid refinement, the computational accuracy is improved without introducing unaffordable efforts by only refining the non-smooth region. In addition, the computational efficiency is accomplished without wasting computing time on the smooth region. To determine the rough region for mesh refinement, we examine the mesh Peclet number during each nonlinear iteration in the flow module, and check the smoothness of the Lagrangian concentrations over elements in the Lagrangian step of the transport module. With the rough elements detected in each module, a modular setting of grid generation is employed to perform the local zooming grid and prepare the information for the multigrid application. We have used this approach to adapt the 3DSALT model to its adaptive multigrid version, 3DMGZMFT. One example is given to demonstrate the success of this approach.