The powerful tropical cyclones generate various destructive forces, including storm surges, heavy winds, and inland flooding, especially in coastal areas. The low-lying coastal areas are particularly susceptible to the devastating effects of coastal flooding caused by storm surges. The mathematical models are often employed to forecast cyclonic wind speed, surge height and coastal inundation to facilitate effective planning and evacuation measures, especially for real-time events. These models provide valuable insights into the potential impacts and help authorities make informed decisions to mitigate the risks posed by storm surges. Most of the existing models mainly suffer from computational cost and numerical instability. In this context, a mathematical model called IROMS-iS2D (Integrated River Ocean Modelling System – inertial Surge two-Dimensional) is developed based on the solution of the local-inertial shallow water equations to significantly improve computational time without encountering numerical instability problems. The performance of the developed model is thoroughly investigated by comparing wind speed and storm surges with observed data and reported results from three historical cyclones along the Bay of Bengal region. Then, the application of the model is demonstrated by simulating the Sidr cyclone and probable storm surges along the Tamil Nadu coast. The IROPMS-iS2D model is found to be significantly faster than the 2D models. Overall, it is found that by leveraging mathematical models like IROMS-iS2D, authorities can enhance their preparedness and response strategies, ultimately minimizing the potential damage and loss of life caused by these hazardous weather phenomena.