In the spring semester of 2021, amidst the upheaval of remote education, the members of class 2.29 “Numerical Fluid Mechanics” navigated the challenges of online learning with grace and resilience. Led by their dedicated Professor Pierre Lermusiaux, supported by TA’s Aaron Charous and Corbin Foucart and administrative assistant Lisa Maxwell, the class embraced virtual tools to foster engagement and collaboration. Throughout the semester, they engaged actively in discussions and presentations using digital platforms. Despite the challenges of distance, the class maintained a sense of camaraderie and enthusiasm. During the final project presentations, Lisa’s ukulele performance added a memorable touch. Singing the lyrics she penned, Lisa’s song served as a heartfelt reminder of their shared journey through remote learning.

The 2.29 Song

Oh yeah we're 2.29
We had our whole class online
In the Spring of '21
Pierre taught twice a week
In a Zoom room he would speak
Can't believe the semester's gone!

Pierre buzzed like a bee
to keep us awake...THAT'S SO MIT!
Where were you at 11:35...?
Crank Nicholson's a finite
Dynamics you're dynamite
It's pahDAY (not PAHday)
you need to derive!

There were equations Euler
(that's quasilinear!),
Taylor Tables and fluid flow...
The first derivative? Give me a sedative!
Let me say (implicitly and explicitly)
where you can go!

That's right we're 2.29!
We had class all online
in the Spring of '21.
We learned lots and lots,
now we're dynamics Hot Shots!
Thanks for being so much fun!

Numerical modeling of ocean physics is essential for multiple applications. However, the large range of scales and interactions involved in ocean dynamics make numerical modeling challenging and expensive. Many regional ocean models resort to a hydrostatic (HS) approximation that reduces the computational burden. However, a challenge is to capture and study ocean phenomena involving complex dynamics over a wider range of scales and processes, from regional to small scales (e.g., thousands of kilometers to meters), resolving submesocales, nonlinear internal waves, subduction, and overturning where they occur. Many such local dynamics require non-hydrostatic (NHS) ocean models. The main computational cost for NHS models arises from solving a globally coupled elliptic PDE for the NHS pressure. Our main research thrust is to optimally reduce these costs so that the NHS dynamics are resolved where needed.

We start from a high-order hybridizable discontinuous Galerkin (HDG) finite element NHS ocean solver, which is well suited for multidynamics systems. We present a new adaptive algorithm to decompose a domain into NHS and HS dynamics subdomains and solve their corresponding equations, thereby reducing the cost associated with the NHS pressure solution step. The NHS/HS subdomains are adapted based on new numerical NHS estimators, such that NHS dynamics is used only where needed. Since the choice of boundary condition imposed on the internal boundaries between subdomains is crucial to maintain accuracy, we explore and compare different choices. To evaluate the computational costs and accuracy of the adaptive NHS-HS solver, we first complete several analyses using internal solitary waves (e.g. Vitousek and Fringer 2011). We then complete more realistic NHS-HS simulations of Rayleigh-Taylor instability-driven subduction events by nesting with our MSEAS realistic and operational data-assimilative HS ocean modeling system.