Areas of Research

1. Mathematical Modelling on Water Wave Phenomena (Surface Wave Dynamics)
2. Integral Equations
3. Partial Differential Equations
4. Numerical Method and Simulation

Research Interests:

1. Very Large Floating Structures
2. Water wave scattering by plates, barriers, cylindrical structures and bottom topography
3. Hydrodynamic loading
4. Perturbation techniques
5. Fluid flow through porous medium
6. Fluid Flow in a Channel
7. Linear and Nonlinear Waves

• Surface Wave Dynamics

• In this study of scattering of surface waves by structure, mixed boundary value problems are set up for the determination of a velocity potential where the governing partial differential equation happens to be Laplace's equation in two dimensions for normal incidence and in three dimensions for oblique incidence within the fluid with a mixed boundary condition on the free surface and a condition on the bottom boundary. As the fluid domain extends to infinity, a far-field condition or an infinity condition arises to ensure uniqueness of the problem. Depending upon the problem, we apply different analytical methods such as perturbation analysis, Green's function technique, application of Green's integral theorem, Fourier transform technique and application of residue theorem, Finite cosine transform technique and eigenfunction expansion technique to solve the mixed boundary value problem. The effects of system parameters are analysed through graphs and tables.

• Linear and Nonlinear Fluid Flow in Channel

• In this study, the irrotational flow in single layer, two layer and three layer is modelled and solved using linear theory. The nonlinear irrotational flow is also modelled in single layer and solved using integral equation approach.

• Integral Equation

• In this study, we have solved Fredholm integral equations of second kind analytically and numerically for its approximate numerical solutions. Also such integral equations which arise in various areas of mathematical physics are solved numerically.