Lukas Lundgren: Modeling subglacial ice ocean interaction using a conservative high-order finite element method

Abstract

In this talk, we present a practical approach to modeling complex ocean dynamics, using a continuous finite element method applied to the non-hydrostatic Boussinesq approximation of the Navier-Stokes equations. This approach is well-suited for applications such as coastal ocean dynamics and ice-ocean interactions. We introduce a modification to the gravity force term that improves energy conservation in numerical simulations without requiring a strict divergence-free condition. This enhancement allows for more accurate energy estimates, covering both kinetic and potential energy.

Additionally, we propose a new symmetric viscosity operator, specifically designed for modeling turbulence in stratified flow, ensuring conservation of angular momentum while dissipating kinetic energy. The viscosity coefficients are determined using a residual-based method, making the method high-order accurate. We demonstrate the effectiveness of this approach through numerical tests, including a simulation of ocean circulation and basal melting beneath the ice tongue of the Ryder Glacier and the adjacent Sherard Osborn fjord. Our method, implemented on a fully unstructured mesh, shows better resolution of turbulent flow features and reduced artificial diffusion when compared to traditional ocean models.