Numerical method for modeling photosynthesis of algae on pulsing soft corals

This paper presents a numerical method to study the pulsing behavior of soft corals. Evidence indicates that the pulsing behavior of soft corals in the family Xeniidae facilitates photosynthesis of their symbiotic algae. One way to investigate this complex behavior is through mathematical modeling and numerical simulations. The immersed boundary method is used to model the interaction of the tentacles with the surrounding fluid. The flow is then coupled with a photosynthesis model. The photosynthesis is modeled by advecting and diffusing oxygen, the byproduct of photosynthesis, where the coral tentacles act as a moving source of the oxygen. This study develops a methodology for solving a partial differential equation with boundary conditions on a moving immersed elastic boundary. In this study, the Reynolds and Peclet numbers are varied in the simulations to gain an understanding of how these parameters affect the mixing and photosynthesis. The mixing is quantified using both the fluid flow and oxygen concentration dynamics. The results show that for the biologically relevant Peclet number, the fluid dynamics significantly affect the photosynthesis and that the biologically relevant Reynolds number is advantageous for mixing and photosynthesis.