Mitigating horizontal divergence “checker-board” oscillations on unstructured triangular C-grids for nonlinear hydrostatic and nonhydrostatic flows

- Triangular C-grids have “checker-board” horizontal divergence noise.
- Horizontal divergence errors propagate into the vertical velocity and primary flow.
- Implicit and explicit filters are proposed to mitigate horizontal divergence errors.
- Explicit filters and nonhydrostatic pressure are insufficient to constrain the noise.
- The implicit second-order nodal filter performs best for the fully unstructured grid.

A complication of finite-volume triangular C-grid methods is the numerical emergence of horizontal divergence errors that lead to grid-scale oscillations in vertical velocity. Nonlinear feedback via advection of momentum can lead to numerical instability in velocity modes via positive feedback with spurious vertical velocities induced by horizontal divergence truncation error. Existing strategies to mitigate divergence errors such as direct divergence averaging and increased diffusion do not completely mitigate horizontal vertical velocity oscillations. We present a novel elliptic filtering approach to mitigate this spurious error and more accurately represent vertical velocities via improved calculation of horizontal divergences. These results are applied to laminar curved channel flows, demonstrating the applicability of the method to reproduce secondary flow features.