Research

My research interests broadly revolve arounds high-order numerical methods and mathematical algorithms. In particular, I am interested in Computational Math, Scientific Computing and Numerical algorithms.

High-order finite volume WENO solver in MOM6

A high-order finite volume WENO (Weighted Essentially Non-Oscillatory) solver for tracer transport in ocean models provides an efficient and accurate way to simulate the movement of tracers, such as temperature and salinity, within ocean currents. Using high-order discretization, the solver can accurately capture tracer concentration gradients, even in sharp fronts or discontinuities that often arise in oceanic flows. The WENO scheme enhances stability near these discontinuities, reducing numerical oscillations and dissipation. This makes it particularly effective for large-scale ocean simulations, where accurately capturing tracer dynamics is essential for understanding circulation patterns, mixing processes, and nutrient transport. See a comparison between the Piecewise Parabolic Method (PPM) based solver (the current solver used in MOM6 for the tracer transport) and the 7th-order WENO-based solver ( the newly implemented solver).

Discontinuous Galerkin methods for ocean modelling

Discontinuous Galerkin methods offer a highly effective approach for solving PDEs numerically, particularly for hyperbolic PDEs, where they provide excellent accuracy per degree of freedom. These methods also offer high locality and flexibility, making them well-suited for high-performance computing and large-scale problems such as ocean simulations. We apply the discontinuous Galerkin method to simulate large-scale ocean circulation to demonstrate this. Specifically, we use a high-order nodal discontinuous Galerkin method to solve multilayer shallow water equations, addressing key properties like well-balancedness and unstructured meshes. Check out the videos below and explore more details in our papers.