Kalita, Jiten Ch.2015-09-302023-10-202015-09-302023-10-202001ROLL NO. 0974602https://gyan.iitg.ac.in/handle/123456789/612Supervisors: Durga Charan Dalal and Anoop Kumar DassThis work is concerned with higher-order compact (HOC) schemes for convection-diffusion equations in general and incompressible viscos flows in particular. A fully compact and fully higher-order accurate scheme is developed for the standard buoyancy driven square cavity problem through O(h4) compact approximation of the derivative source term and zero-gradient temperature boundary conditions of identical accuracy at the adiabatic walls. The scheme produces highly accurate results even for very high laminar Rayleigh numbers for which no other HOC results are seen. ...enMATHEMATICSThesis