Executive Summary : | This project pertains to further developing a higher order compact scheme for generalized convection-diffusion equation in domains under continuous time deformation. As evident from the literature, such a scheme finds wide application in various fields of study related to fluid flow with and without thermal effect. They also find application in fluid-structure interaction problems. We are particularly interested in simulating incompressible viscous flow and in areas of heat transfer. Our previous experiences suggest the superior performance of compact schemes in diverse flow configurations. The main emphasis will be discretization of the Navier-Stokes equation and the Boussinesq equation in a deformable domain using a compact scheme. In this context, it is crucial to design numerical methods capable of adapting to changing flow geometries and is the main point of investigation in this project. Here, it is also pertinent to develop adequate grid deformation strategies, and a part of our effort in this project will be devoted to this cause. Further, extension to fluid-structure interaction problems is also envisaged. |