Analytical Tracking Along Streamlines in Temporally Linear Raviart- Thomas Velocity Fields

摘要

Numerical simulators of ground-water flow and transport are frequently used to determine streamlines and to estimate travel times and pathways of contaminant movement. These items are often obtained by tracking conceptual water particles through the computational grid using model- calculated flow velocities. Such tracking is also an important component of the Lagrangian part of many methods for transport modeling, in particular the Eulerian-Lagrangian localized adjoint method (ELLAM). A procedure for exact analytical particle tracking is presented, given a lowest-order Raviart-Thomas velocity field v on a rectangular spatial grid, with linear temporal interpolation of v from the beginning to the end of a time step. This includes xt- and yt-bilinearity in the x- and y-components, respectively, of v. Previous authors assumed that v was steady, or that its time derivative was constant in space. Transience in v allows a particle to reverse its direction during a time step. The added effect of bilinearity can be significant, especially when v varies in time due to changes in well pumping rates or variable recharge. These effects are discussed qualitatively and illustrated with test problems that compare the accuracy of the tracking methods.