General Notices

The Campus Community is invited to attend a research seminar entitled Numerical Solvers for 3D Navier–Stokes Equations in Concentric Toroidal Shells by Dr. Vishal Siewnarine from 1:00 p.m. to 2:00 p.m. on Thursday, April 30, 2026 at FST Room C1 or via Zoom.

Venue & Access Information

The seminar will be conducted both in person and virtually via Zoom.

In Person: FST C1, First Floor, C4 Building

Virtual Attendance (Zoom): Click here to join

Abstract

This talk will discuss the development and testing of efficient numerical solvers for the three-dimensional Navier–Stokes equations in toroidal geometries, specifically for fluid flow between concentric toroidal shells. Motivated by Taylor–Couette instability studies in toroidal systems, the presentation will explore two approaches: an ADI-based finite difference solver for low Reynolds numbers and a high-order spectral solver with Runge–Kutta time stepping for higher Reynolds number flows.

The spectral method, using Fourier and Chebyshev representations, achieves high accuracy and reveals previously unresolved instability patterns, currently observed to be primarily two-dimensional. The solver is also applied to flows between oscillating toroidal shells, capturing complex dynamics and enabling torque calculations, with implications for engineering applications such as mechanical damping systems.

Keywords: Navier–Stokes equations, toroidal shells, numerical fluid dynamics, mechanical damping.