The life and times of Pteridinium simplex
Darroch, Simon et al. (2022), The life and times of Pteridinium simplex, Dryad, Dataset, https://doi.org/10.5061/dryad.0rxwdbs1g
COMSOL (.mph) and.gif files providing/illustrating fluid dynamics simulations of modeled Pteridinium simplex in a variety of different orientations and fluid velocities. The following text is cut/pasted from the methods section of the in-review manuscript:
Model building. – We constructed three-dimensional digital models of Pteridinium (Figure 9) using Rhinoceros 3D v.6. Models were simplified representations of the organism’s morphology, which were scaled to the lengths and widths of typical fossil specimens recorded during fieldwork. Due to both the uncertainty surrounding the relative height of the central vane and a need to test the effect of specific morphological features on flow patterns, we constructed three idealized models in which we varied key anatomical features. Based on our interpretations of collected and field specimens and published reconstructions (e.g., Meyer et al., 2014a), our base model consists of a hollow half-ellipsoid with a long-axis medial vane raised above the cavity opening (Figure 9a). We additionally developed two null models: (1) a hollow half-ellipsoid with a long-axis medial vane flush with the cavity opening (Figure 9b); and (2) a filled half-ellipsoid without a medial vane (Figure 9c). Models were exported from Rhinoceros 3D as non-uniform rational B-spline (NURBS) geometries (see Supplementary Models).
Setup of fluid flow simulations. – Digital models were imported into COMSOL Multiphysics v. 5.6 for use in computer simulations of fluid flow. We adopted a standardized setup in all our analyses, using a hexahedron (400 x 200 x 40 cm) as the flow domain, with the Pteridinium model placed just upstream of the approximate center of the domain (Supp. Fig. 1). The domain was scaled large enough to ensure that the flow fully developes in both the individual and population-level simulations (see Gibson et al., 2021). We selected boundary conditions to accommodate a time-dependent analysis using a Large Eddy Simulation (LES) turbulence model. While previous CFD studies of Ediacaran taxa (Rahman et al., 2015; Darroch et al., 2017; Gibson et al., 2019; Cracknell et al., 2021) have relied on stationary solvers using the Reynolds-averaged Navier–Stokes (RANS) Shear Stress Transport (SST) turbulence closure, time-dependent LES offers the potential for more accurate simulation of turbulence by not relying on the Reynolds stress tensor (see Gibson et al., 2021). The upper surface of the flow domain was assigned a slip condition, the lower surface of the domain (i.e. the floor) and all surfaces corresponding to the model of Pteridinium were assigned no-slip conditions. All remaining surfaces of the domain were assigned periodic boundary conditions with their respective opposing, parallel surface. A pressure point constraint located on the no-slip lower surface was used as a reference pressure, and a pressure differential (specific to the desired velocity) was applied across the upstream and downstream periodic boundaries to drive flow through the domain (Supp. Table 1). To determine the pressure differentials for our three desired velocities (see below), we first conducted preliminary stationary analyses of laminar flow with upstream inlet boundary conditions that modeled fully developed flow at the desired velocities and downstream outlet conditions that suppressed backflow. In simulations that were too unsteady (and thus non-linear) for a laminar flow regime, we used the RANS Spalart–Allmaras turbulence closure because of its ability to quickly approximate flow field conditions (Bardina et al., 1997; Blazek, 2001). In all the preliminary CFD simulations, the surfaces of the domain parallel to flow were assigned slip boundary conditions (same as the upper surface), and the lower domain surface and Pteridinium model were assigned no-slip boundaries. Using these preliminary solutions, we differenced the absolute averaged pressures across the upstream (inlet) and downstream (outlet) surfaces to determine the necessary pressure to drive flow in our LES analyses. To ensure that our simulations initialized with physically realistic conditions, and thereby minimize the computation time, we used the preliminary stationary flow field solutions as the initial conditions for our LES analyses. LES simulations were solved with COMSOL’s dynamic timestepping for 30 s of flow time with data outputs at every 0.01 s. Far field time averaged velocity (U) was plotted to ensure flow fields followed the “Law of the Wall” (Gibson et al., 2021).We conducted a mesh sensitivity analysis using the most morphologically complex model (hollow half-ellipsoid with a long-axis medial vane raised above the cavity opening) oriented perpendicular to flow and the highest simulated inlet velocity (0.85 m/s), in which we solved our LES analyses under progressively finer meshes (Supp. Table 2; using the pre-defined mesh sizes in COMSOL, e.g. “Coarse”, “Normal”, “Fine”, etc.). We then integrated drag forces across the lower, external faces of the Pteridinium model at each timestep, and time averaged these values to compare between mesh sizes. Based on this analysis, we selected the “Normal” pre-defined mesh size as the best compromise between computational speed and the accuracy of fluid flow results (Supp. Table 2).
.mph files give the set-up parameters for CFD simulaitons, and require COMSOL Multiphysics software to run.
National Science Foundation, Award: NSF-NERC EAR-2007928
Natural Environment Research Council, Award: NE/V010859/1
Natural Sciences and Engineering Research Council of Canada, Award: RGPIN 435402
Alexander von Humboldt-Stiftung, Award: NA