Numerical diffusion for flow-aligned unstructured grids with application to estuarine modeling

摘要

The benefits of unstructured grids in hydrodynamic models are well understood but in many cases lead to greater numerical diffusion compared with methods available on structured grids. The flexible nature of unstructured grids, however, allows for the orientation of the grid to align locally with the dominant flow direction and thus decrease numerical diffusion. We investigate the relationship between grid alignment and diffusive errors in the context of scalar transport in a triangular, unstructured, 3-D hydrodynamic code. Analytical results are presented for the 2-D anisotropic numerical diffusion tensor and verified against idealized simulations. Results from two physically realistic estuarine simulations, differing only in grid alignment, show significant changes in gradients of salinity. Changes in scalar gradients are reflective of reduced numerical diffusion interacting with the complex 3-D structure of the transporting flow. We also describe a method for utilizing flow fields from an unaligned grid to generate a flow-aligned grid with minimal supervision.