| 14 Sep 2026
Mimetic interpolation for finite-time Lyapunov exponent computation near irregular domain boundaries
Abstract. Finite-time Lyapunov exponents (FTLEs) are widely used to identify Lagrangian coherent structures (LCS) in geophysical flows. Applying FTLEs to numerical model output requires reconstructing continuous velocity fields from discrete model grids, thus the resulting flow structures are sensitive to the interpolation method. This issue is particularly important for models with staggered-grid discretisations and complex solid boundaries, such as buildings, terrain and coastlines, where velocity components are defined at different locations and no-through-flow conditions must be respected. Most existing FTLE workflows assume co-located velocity components and do not explicitly account for fluid-solid boundaries during interpolation. Interpolating staggered velocities to cell centres before trajectory integration can therefore violate boundary conditions, producing unphysical particle paths, including trajectories that enter solid regions. Here, we present a flux-conservative, mimetic vector interpolation scheme that removes the co-location assumption while ensuring no-through-flow conditions at fluid-solid interfaces. We demonstrate the method using large eddy simulations of a wildfire plume in urban terrain. Compared with conventional interpolation, the mimetic approach produces boundary-aware trajectories and reveals coherent-structure geometries shaped by urban topography that are otherwise obscured. These results show that interpolation is not merely a numerical preprocessing step, but can directly affect inferred LCS geometries and their physical interpretation in staggered-grid simulations with complex boundaries.
This is an interesting paper that shows significant sensitivity in finite-time Lyapunov exponent (FTLE) calculations between linear and conservative interpolation of velocity fields on staggered CFD grids. I think it should be published with a few minor amendments:
1. For people not that familiar with FTLE (such as myself!), it might be worth adding a brief overview rather than relegating this to a reference. For example, saying this is the scalar value of the maximum eigenvalue, mentioning what the 'finite time' is in this context etc.
2. Ghost cells can be constructed to cancel the velocity field on the interface, i.e. taking a opposite value rather than being zero everywhere as described here. I guess these are not as robust as mimetic interpolation? I think a brief discussion of other interpolation methods, rather than just the most basic ghost cell method, and their disadvantages compared to the mimetic approach should be included.
3. In Fig. 6 is the fire in the centre of the domain at ~ coordinates 250, 250? If so I think this should be marked and highlighted. It looks like this is a source of the FTLE structures so some commentary on this could be added.
4. It would be good to have some more information or detail on why these FTLE are important in the fire context - I know the paper does cover this somewhat, but I was thinking some discussion around the differences in ember transport between the two methods at the WUI.
5. Along the same lines as the previous point, a zoomed in close-up of a region near the urban interface would be useful in seeing the differences in fine-scale flow dynamics at around structures.