Numerical Methods for Modeling the Fluid Flow of Pulsing Soft Corals and the Photosynthesis of their Symbiotic Algae
This dissertation presents a novel 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 coral 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 oxygen. This work develops a methodology for solving a system of partial differential equations with boundary conditions on a moving immersed elastic boundary. Two-dimensional numerical simulations are presented where the Reynolds and Péclet numbers are varied in the simulations to understand 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 Péclet number, the fluid dynamics significantly affect the photosynthesis and that the biologically relevant Reynolds number is advantageous for mixing and photosynthesis. The models and methods developed have been contributed to the open-source software library implementation of the immersed boundary method, IB2d. Three-dimensional numerical simulations of soft coral pulsing are also presented using the IBAMR software library. A three-dimensional mixing analysis of the flow is presented. Further, preliminary results of the three-dimensional corals pulsing with a background oxygen concentration are presented with the methodology for modeling the three-dimensional coral tentacles as a sink or source of a concentration.