3-D Modeling of Light, Flow, Mass and Heat Transfer in Coral Colonies

Martinez Jimenez Fernan David1, Murthy Swathi2, Picioreanu Cristian1, Kühl Michael2
1King Abdullah University of Science and Technology (KAUST), Water Desalination and Reuse Center, Biological and Environmental Science and Engineering Division, Thuwal 23955-6900, Saudi Arabia
2Marine Biology Section, Department of Biology, University of Copenhagen, Strandpromenaden 5, 3000 Helsingør, Denmark
Published in 2023

Corals are symbiotic marine organisms greatly dependent on the dynamic gradients of light, temperature and chemical species, all affected by the water flow in their surroundings. We developed a multiphysics modelling approach to simulate the microscale spatial distribution of light, temperature and dissolved oxygen in and around a coral fragment, with morphology determined by 3-D scanning techniques (Figure 1). The geometry of the coral fragment (with and without tissue) was determined by a structured light 3-D scanner, then a watertight mesh model of the coral geometry was exported as an STL file. The field of photon scalar irradiance was determined by calculating the radiative transfer using the Monte Carlo approach implemented in the software ValoMC, considering absorption, scattering and refraction in various tissue layers and skeleton. Optical properties were assigned as a function of the calculated wall distance in COMSOL Multiphysics®. Due to the stochastic nature of the light simulations, the scalar irradiation field had to be smoothened in COMSOL Multiphysics® by solving a Poisson equation in weak form. The COMSOL® model geometry then consisted of a solid domain (i.e., the 3-D scan of the coral fragment), enclosed by water in a box matching the dimensions of the flow chamber used experimentally. In a sequence of stationary steps, we calculated first the water velocity field around the coral in the laminar flow according to experiments. Secondly, the water flow was used in solving the oxygen mass transport in water, coral tissues and skeleton, with spatially-dependent convection, diffusion and source terms (i.e., local production and consumption due to photosynthesis and respiration in different tissue layers and skeleton). Finally, the heat transfer by convection and conduction in water, coral tissue and skeleton was computed accounting for the heat source corresponding to light absorption. The solution strategy consisted of a sequence of stationary steps: smoothening the imported light radiation field, computing water flow, computing wall distance, then oxygen transfer and finally the heat transfer. In particular, two cases were assumed for flow at the coral surface: zero-velocity (without ciliary movement) and a set velocity (with ciliary movement included as induced flow by assuming an oscillating horizontal velocity component). The model results show that the morphology of the coral skeleton leads to hotspots and shadowed regions of light in the colony and strongly affects the water flow field. This in turn impacts the radiation-driven O2 and heat production and, thus, the distribution of oxygen and temperature within the coral. The simulated light, oxygen and temperature distribution showed a fairly good match with our local measurements done by microsensors in similar flow and light conditions. The model allows studies on the effects of coral morphology and light scattering on the internal light environment, as well as the combined contribution of light, water flow and ciliary movement on O2 and temperature distributions in the coral. These are all important effects when studying the coral resilience to the rapid changing of the marine environment due to global warming and seawater acidification.