A Numerical Scheme to Reduce Numerical Diffusion for Advection-Dispersion Modeling: Validation and Application

Abstract

Advection-dispersion is an essential process in most fluid dynamics problems such as tracer test for reservoir characterization. Many numerical schemes have been developed to simulate this process. However, numerical diffusion encountered in these schemes causes inaccuracy in simulation results, and efforts to reduce numerical diffusion usually lead to other problems such as instability of schemes and oscillation in results. We present a new scheme, named Intra-Cell Advection Tracking (ICAT), to minimize numerical diffusion as well as preserve stability and monotonicity for advection-dispersion modeling. In this new scheme, the key idea is to track scalar transport in each discretized cell by introducing a queue in this cell to connect the inflow and outflow interfaces. We use a sequential transport rule to temporally track the scalar transport in the queue, and use a flow distribution mechanism to spatially track the scalar transport among queues in different cells. Two test cases are performed to investigate the capability of ICAT. Compared with the results obtained from other numerical schemes, the results from ICAT have less 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.