Abstract
The advection-dispersion equation for scalar transport is essential for the numerical modeling of many fluid dynamics problems. However, solutions from numerical schemes always suffer from numerical diffusion and/or oscillation. In this study, we develop an Intra-Cell Advection Tracking (ICAT) scheme to minimize numerical diffusion and preserve monotonicity for advection-dispersion modeling. The key idea is to introduce “queues” in each discretized cell, and using a sequential transport rule and a flow distribution mechanism to track the scalar transport in these queues temporally and spatially. The capability and limitations of ICAT are first investigated through three test cases. Compared with the results obtained from other numerical schemes, the results from ICAT show substantially reduced numerical diffusion and agree better with analytical solutions. We also employ ICAT to simulate the transport process of a conservative tracer in a fracture with a highly heterogeneous aperture distribution. Discrete flow channels in the fracture are better discerned by ICAT than by other numerical schemes, indicating the suitability of ICAT for modeling tracer transport in channelized flow fields.
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