Locally Conservative Algorithms for Flow

Locally mass conservative methods for subsurface ow are presented and applied to the unstable miscible displacement problem arising in porous media. The pressure equation is solved either by the discontinuous Galerkin method or the mixed nite element method. The concentration equation is solved using a higher order Godunov method. Theoretical estimates are given for the approximation of the pressure obtained by the discontinuous Galerkin method. A velocity projection method based on the discontinuous Galerkin method is introduced. Numerical simulations comparing the two methods are presented. 1.1 INTRODUCTION In either surface water or subsurface water environmental quality modeling, the ow and multi-species transport may be solved separately using diierent numerical methods and grids due to diierences in time and length scales involved. For example, in surface water, the ow grid usually needs to incorporate high resolution near land boundaries and should extend into the ocean to avoid spurious boundary eeects. The transport code may only simulate transport over a small portion of the ow domain, and may use much coarser resolution. Therefore, for eecient coupling of ow and transport codes, it is critical to be able to take velocities from an arbitrary ow grid, and project them onto an arbitrary transport grid. For accurate multi-species transport, it is desirable for the velocities to be locally conservative on the transport grid.