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Immersed Boundary Finite Element Method Simulates Swimming Patterns in Blue Blubber Jellyfish

By Lina Sorg

Researchers in the computational fluid dynamics (CFD) community commonly generate numerical simulations to understand jellyfish swimming behaviors. These studies typically utilize simplified models that simulate the jellyfish bell and neglect the oral arms. However, some species of medusa—such as the blue blubber jellyfish—have prominent oral arms (see Figure 1); when measured together, these arms comprise nearly the same diameter as the bell. Experimental results indicate that blue blubber jellyfish, which pulse in a staccato-like rhythm, have a relatively high propulsive efficiency when compared to other species. As such, models that neglect the oral arms will yield overly idealized fluid dynamics.

During a minsymposium presentation at the 2023 SIAM Conference on Computational Science and Engineering, which is currently take place in Amsterdam, the Netherlands, Matea Santiago of the University of Arizona employed the immersed boundary finite element (IBFE) method to simulate muscle-driven swimming in blue blubber jellyfish with oral arms.

Figure 1. The blue blubber jellyfish, which has prominent oral arms, has a relatively high propulsive efficiency when compared to other species. Figure courtesy of Steven Johnson under the GNU Free Documentation License.
To create her model, Santiago began with an armless jellyfish bell. She and her team purchased oral arms online, smoothed them out, used Autodesk’s Fusion 360 design software to merge them with the bell, and meshed them via hexagonal elements in Coreform Cubit. The elastic force that Santiago applied to the model relates to the stress tensor, which can decompose into passive and active elasticity. Passive elasticity models the jellyfish body—comprised of tissue and hence elastic—as a neo-Hookean material. To model muscle contraction, Santiago applied active tension in strategic spots that corresponded with the location of jellyfish muscles. An activation function allows the jellyfish bell to open when tension is released.

Next, Santiago applied the Navier-Stokes equations—which account for variables such as fluid velocity, fluid pressure, fluid viscosity, fluid density, and external force density—to model fluid flow. She then utilized the IBFE method to solve the resulting fluid-structure interaction. “This is a different flavor of the classical immersed boundary method,” Santiago said. “It allows us to model a three-dimensional (3D) object in a 3D fluid.” 

Because 3D simulations—while more biologically relevant than the alternative—are computationally expensive to conduct, Santiago and her team relied on a 3D software library called Immersed Boundary Method Adaptive Mesh Refinement Software Infrastructure (IBAMR). Like the name suggests, IBAMR allows for an adaptive, parallelizable implementation of the immersed boundary method. Santiago subsequently shared several simulated scenarios. When tension is applied to an armless bell that is tethered in place, the bell contracts and exhibits vertical velocity. A downward jet is consequently visible — an expected product of an upward-swimming organism. However, the same jet disappeared when Santiago added oral arms to the simulation. It remained absent even after she shrunk the size of the arms, suggesting the presence of underlying elastic properties that are worthy of consideration.

Next, Santiago shared a side-by-side swimming comparison of a jellyfish bell with and without oral arms. The armless bell could easily swim upwards, but the addition of arms hindered the swimming process. “Having these oral arms obviously makes a pretty big difference in the dynamics,” she said. “Understanding how they relate to swimming is pretty important.”

Since the project is still a work in progress, Santiago concluded her presentation with a brief discussion of several model limitations. While she currently considers the oral arms as one large mass, doing so is not biologically realistic. She also had to smooth the arms significantly to initially mesh them with the bell; in IBFE, gaps and small structures lead to more refined fluid grid. “If we were to create the model and mesh it appropriately, it would be really difficult to run these simulations in a timely manner,” Santiago said.

Lina Sorg is the managing editor of SIAM News.
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