Higher order compact schemes for incompressible viscous flows on geometries beyond rectangular
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In this dissertation, we have proposed a new class of higher order compact (HOC) finite difference schemes for solving the two-dimensional (2D) incompressible viscous flows through geometries beyond rectangular. The proposed schemes are developed for both steady-state and transient flows which are governed by the Navier-Stokes (N-S) equations. All these schemes are fourth order accurate in space while the ones for the transient flows are implicit, and first or second order accurate in time depend- ing on the choice of a weighted average parameter. We have employed these schemes not only on problems having analytical solutions to verify their order of accuracy, ef- ficiency, effectiveness and robustness but also to explore new flow phenomena of some other complicated problems, namely, the lid-driven cavity flow, channel flow with forward and backward constriction, flow in a lateral and symmetric dilated channels, flow through constricted tube etc. They are seen to efficiently capture both steady- state and transient solutions with Dirichlet as well as Neumann boundary conditions. Apart from including all the features of existing HOC schemes, the formulation has the added advantage of capturing transient viscous flows involving free and wall bounded shear layers which invariably contain spatial scale variation. We present both quali- tative and quantitative results produced by our schemes on relatively coarser grid for all the test cases and compare them with theoretical predictions, analytical as well as established numerical and experimental results available in the literature. Excellent agreement is obtained in all the cases..
Supervisors: Durga Charan Dalal and Jiten Chandra Kalita