My Current research work encompasses:
1. Finite Difference Approximations of the solutions of Navier-Stokes equations in both continuous and discontinuous domains. Different formulations of Navier-Stokes equations like primitive variable, stream-function vorticity, pure stream-function are exploited for applications. They encompass:
a. Analyzing wake structures and heat convection for flow past oscillating/non-oscillating circular, ellipse shaped cylinders using our developed schemes.
b. Analyzing the rheology of deformable fluid particles like drops and bubbles in various fluid environments using our developed schemes. The applications include examining the behavior of star shaped/ellipse shaped bubbles oscillating to stationary circular shape at equilibrium, deforming circular bubbles under shear flows.
2. Development of asymptotic Numerical Methods like Time Perturbation and Resummation techniques for solutions of partial differential equations. It includes comparison with classic finite difference schemes for equations like Burgers, Navier-Stokes and level set evolution equations.
3. Risk Assessment of accidental Oil Spills in Red Sea: This study investigates the risk from oil spills along the main shipping lane in the Red Sea based on simulated oil trajectories using the MOHID oil spill model forced by the outputs of validated high resolution met-ocean data that have been generated for the Red Sea. The presented maps in this study provide valuable insight into the risk of oil pollution and a comprehensive information about the direction of the spill and the coastal resources likely to be affected.

MA 2032 : Numerical Analysis (Jan - Aug '22)