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

TL;DRAbstract

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, in particular the Eulerian-Lagrangian localized adjoint method (ELLAM). We present a procedure for exact analytical particle tracking, given a lowest-order Raviart-Thomas velocity field v(x,y,t) on a rectangular spatial grid, with linear interpolation of v from the beginning to the end of a time step. Thus, on each cell, the x-component of v is bilinear in x and t and constant in y; the y-component is constant in x and bilinear in y and t; also, the spatial normal component is continuous across every cell edge at all times. Analytical tracking with this spatial discretization was consi

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