AbstractsEngineering

The thesis deals with the development of a new residual error estimator and adaptive algorithms based on the error estimator for steady and unsteady fluid flows in a finite volume framework. The aposteriori residual error estimator referred to as R – parameter, is a measure of the local truncation error and is derived from the imbalance arising from the use of an exact operator on the numerical solution for conservation laws. A detailed and systematic study of the R – parameter on linear and non – linear hyperbolic problems, involving continuous flows and discontinuities is performed. Simple theoretical analysis and extensive numerical experiments are performed to establish the fact that the R – parameter is a valid estimator at limiter – free continuous flow regions, but is rendered inconsistent at discontinuities and with limiting. The R – parameter is demonstrated to work equally well on different mesh topologies and detects the sources of error, making it an ideal choice to drive adaptive strategies. The theory of the error estimation is also extended for unsteady flows, both on static and moving meshes. The R – parameter can be computed with a low computational overhead and is easily incorporated into existing finite volume codes with minimal effort. Adaptive refinement algorithms for steady flows are devised employing the residual error estimator. For continuous flows devoid of limiters, a purely R – parameter based adaptive algorithm is designed. A threshold length scale derived from the estimator determines the refinement/derefinement criterion, leading to a self – evolving adaptive algorithm devoid of heuristic parameters. On the other hand, for compressible flows involving discontinuities and limiting, a hybrid adaptive algorithm is proposed. In this hybrid algorithm, error indicators are used to flag regions for refinement, while regions of derefinement are detected using the R – parameter. Two variants of these algorithms, which differ in the computation of the threshold length scale are proposed. The disparate behaviour of the R – parameter for continuous and discontinuous flows is exploited to design a simple and effective discontinuity detector for compressible flows. For time – dependent flow problems, a two – step methodology is proposed for adaptive grid refinement. In the first step, the ``best" mesh at any given time instant is determined. The second step involves predicting the evolution of flow phenomena over a period of time and refines regions into which the flow features would progress into. The latter step is implemented using a geometric – based ``Refinement Level Projection" strategy which guarantees that the flow features remain in adapted zones between successive adaptive cycles and hence uniform solution accuracy. Several numerical experiments involving inviscid and viscous flows on different grid topologies are performed to illustrate the success of the proposed adaptive algorithms. Appendix 1 Candidate's response to the comments/queries of the examiners The…