The development of a shape optimization solver using the existing Computational Fluid Dynamics (CFD) codes is taken up as topic of research in this thesis. A shape optimizer was initially developed based on Genetic Algorithm (GA) coupled with a CFD solver in an earlier work. The existing CFD solver is based on Kinetic Flux Vector Splitting and uses least squares discretization. This solver requires a cloud of points and their connectivity set, hence this CFD solver is a meshless solver. The advantage of a meshless solver is utilised in avoiding re-gridding (only connectivity regeneration is required) after each shape change by the shape optimizer. The CFD solver is within the optimization loop, hence evaluation of CFD solver after each shape change is mandatory. Although the earlier shape optimizer developed was found to be robust, but it was taking enoromous amount of time to converge to the optimum solution (details in Appendix). Hence a new evolving method, Ant Colony Optimization (ACO), is implemented to replace GA. A shape optimizer is developed coupling ACO and the meshless CFD solver. To the best of the knowledge of the present author, this is the first time when ACO is implemented for aerodynamic shape optimization problems. Hence, an exhaustive validation has become mandatory. Various test cases such as regeneration problems of (1) subsonic - supersonic nozzle with a shock in quasi - one dimensional flow (2) subsonic - supersonic nozzle in a 2-dimensional flow field (3) NACA 0012 airfoil in 2-dimensional flow and (4) NACA 4412 airfoil in 2-dimensional flow have been successfully demonstrated. A comparative study between GA and ACO at algorithm level is performed using the travelling salesman problem (TSP). A comparative study between the two shape optimizers developed, i.e., GA-CFD and ACO-CFD is carried out using regeneration test case of NACA 4412 airfoil in 2-dimensional flow. GA-CFD performs better in the initial phase of optimization and ACO-CFD performs better in the later stage. We have combined both the approaches to develop a hybrid GA-ACO-CFD solver such that the advantages of both GA-CFD and ACO-CFD are retained with the hybrid method. This hybrid approach has 2 stages, namely, (Stage 1) initial optimum search by GA-CFD (coarse search), the best members from the optimized solution from GA-CFD are segregated to form the input for the fine search by ACO-CFD and (Stage 2) final optimum search by ACO-CFD (fine search). It is observed that this hybrid method performs better than either GA-CFD or ACO- CFD, i.e., hybrid method attains better optimum in less number of CFD calls. This hybrid method is applied to the following test cases: (1) regeneration of subsonic-supersonic nozzle with shock in quasi 1-D flow and (2) regeneration of NACA 4412 airfoil in 2-dimensional flow. Two applications on shape optimization, namely, (1) shape optimization of a body in strongly rotating viscous flow and (2) shape optimization of a body in supersonic flow such that it enhances separation of binary species, have been successfully demonstrated using the hybrid GA-ACO-CFD method. A KFVS based binary diffusion solver was developed and validated for this purpose. This hybrid method is now in a state where industrial shape optimization applications can be handled confidently.

This work deals with discretizing viscous fluxes in the context of unstructured data based finite volume and meshless solvers, two competing methodologies for simulating viscous flows past complex industrial geometries. The two important requirements of a viscous discretization procedure are consistency and positivity. While consistency is a fundamental requirement, positivity is linked to the robustness of the solution methodology. The following advancements are made through this work within the finite volume and meshless frameworks. Finite Volume Method: Several viscous discretization procedures available in the literature are reviewed for: 1. ability to handle general grid elements 2. efficiency, particularly for 3D computations 3. consistency 4. positivity as applied to a model equation 5. global error behavior as applied to a model equation. While some of the popular procedures result in inconsistent formulation, the consistent procedures are observed to be computationally expensive and also have problems associated with robustness. From a systematic global error study, we have observed that even a formally inconsistent scheme exhibits consistency in terms of global error i.e., the global error decreases with grid refinement. This observation is important and also encouraging from the view point of devising a suitable discretization scheme for viscous fluxes. This study suggests that, one can relax the consistency requirement in order to gain in terms of robustness and computational cost, two key ingredients for any industrial flow solver. Some of the procedures are analysed for positivity as applied to a Laplacian and it is found that the two requirements of a viscous discretization procedure, consistency(accuracy) and positivity are essentially conflicting. Based on the review, four representative schemes are selected and used in HIFUN-2D(High resolution Flow Solver on UNstructured Meshes), an unstructured data based cell center finite volume flow solver, to simulate standard laminar and turbulent flow test cases. From the analysis, we can advocate the use of Green Gauss theorem based diamond path procedure which can render high level of robustness to the flow solver for industrial computations. Meshless Method: An Upwind-Least Squares Finite Difference(LSFD-U) meshless solver is developed for simulating viscous flows. Different viscous discretization procedures are proposed and analysed for positivity and the procedure which is found to be more positive is employed. Obtaining suitable point distribution, particularly for viscous flow computations happens to be one of the important components for the success of the meshless solvers. In principle, the meshless solvers can operate on any point distribution obtained using structured, unstructured and Cartesian meshes. But, the Cartesian meshing happens to be the most natural candidate for obtaining the point distribution. Therefore, the performance of LSFD-U for simulating viscous flows using point distribution obtained from Cartesian like grids is evaluated. While we have successfully computed laminar viscous flows, there are difficulties in terms of solving turbulent flows. In this context, we have evolved a strategy to generate suitable point distribution for simulating turbulent flows using meshless solver. The strategy involves a hybrid Cartesian point distribution wherein the region of boundary layer is filled with high aspect ratio body-fitted structured mesh and the potential flow region with unit aspect ratio Cartesian mesh. The main advantage of our solver is in terms of handling the structured and Cartesian grid interface. The interface algorithm is considerably simplified compared to the hybrid Cartesian mesh based finite volume methodology by exploiting the advantage accrue out of the use of meshless solver. Cheap, simple and robust discretization procedures are evolved for both inviscid and viscous fluxes, exploiting the basic features exhibited by the hybrid point distribution. These procedures are also subjected to positivity analysis and a systematic global error study. It should be remarked that the viscous discretization procedure employed in structured grid block is positive and in fact, this feature imparts the required robustness to the solver for computing turbulent flows. We have demonstrated the capability of the meshless solver LSFDU to solve turbulent flow past complex aerodynamic configurations by solving flow past a multi element airfoil configuration. In our view, the success shown by this work in computing turbulent flows can be considered as a landmark development in the area of meshless solvers and has great potential in industrial applications.