This study seeks to reduce the degree of uncertainty that often arises in computational fluid dynamics simulations about the computed accuracy of functional outputs. An error estimation methodology based on discrete adjoint sensitivity analysis is developed to provide a quantitative measure of the error in computed outputs. The developed procedure relates the local residual errors to the global error in output function via adjoint variables as weight functions. The three major steps in the error estimation methodology are: (1) development of adjoint sensitivity analysis capabilities; (2) development of an efficient error estimation procedure; (3) implementation of an output-based grid adaptive scheme. Each of these steps are investigated. For the first step, parallel discrete adjoint capabilities are developed for the variable Mach version of the U2NCLE flow solver. To compare and validate the implementation of adjoint solver, this study also develops direct sensitivity capabilities. A modification is proposed to the commonly used unstructured flux-limiters, specifically, those of Barth-Jespersen and Venkatakrishnan, to make them piecewise continuous and suitable for sensitivity analysis. A distributed-memory message-passing model is employed for the parallelization of sensitivity analysis solver and the consistency of linearization is demonstrated in sequential and parallel environments. In the second step, to compute the error estimates, the flow and adjoint solutions are prolongated from a coarse-mesh to a fine-mesh using the meshless Moving Least Squares (MLS) approximation. These error estimates are used as a correction to obtain highlyurate functional outputs and as adaptive indicators in an iterative grid adaptive scheme to enhance the accuracy of the chosen output to a prescribed tolerance. For the third step, an output-based adaptive strategy that takes into account the error in both the primal (flow) and dual (adjoint) solutions is implemented. A second adaptive strategy based on physics-based feature detection is implemented to compare and demonstrate the robustness and effectiveness of the output-based adaptive approach. As part of the study, a general-element unstructured mesh adaptor employing h-refinement is developed using Python and C++. Error estimation and grid adaptation results are presented for inviscid, laminar and turbulent flows.

This thesis deals with the development of a new adaptive algorithm for three-dimensional fluid flows based on a residual error estimator. The residual, known as the R –parameter has been successfully extended to three dimensions using a novel approach for arbitrary grid topologies. The computation of the residual error estimator in three dimensions is based on a least-squares based reconstruction and the order of accuracy of the latter is critical in obtaining a consistent estimate of the error. The R –parameter can become inconsistent on three–dimensional meshes depending on the grid quality. A Zero Mean Polynomial(ZMP) which is k–exact, and which preserves the mean has been used in this thesis to overcome the problem. It is demonstrated that the ZMP approach leads to a more accurate estimation of solution derivatives as opposed to the conventional polynomial based least-squares method. The ZMP approach is employed to compute the R –parameter which is the n used to derive the criteria for refinement and derefinement. Studies on three different complex test problems involving inviscid, laminar and turbulent flows demonstrate that the new adaptive algorithm is capable of detecting the sources of error efficiently and lead to accurate results independent of the grid topology.

A numerical technique is developed to simulate the vortices associated with stationary and flapping wings. The Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations are used over an unstructured grid. The present work assesses the locations of the origins of vortex generation, models those locations and develops a systematic mesh refinement strategy to simulate vortices more accurately using the URANS model. The vortex center plays a key role in the analysis of the simulation data. A novel approach to locating a vortex center is also developed referred to as the Max-Max criterion. Experimental validation of the simulated vortex from a stationary NACA0012 wing is achieved. The tangential velocity along the core of the vortex falls within five percent of the experimental data in the case of the stationary NACA0012 simulation. The wing surface pressure coefficient also matches with the experimental data. The refinement techniques are then focused on unsteady simulations of pitching and dual-mode wing flapping. Tip vortex strength, location, and wing surface pressure are analyzed. Links to vortex behavior and wing motion are inferred.

Unsteady flowfields are integral to high-speed applications, demanding precise modelling to characterize their unsteady features accurately. The simulation of unsteady supersonic and hypersonic flows is inherently computationally expensive, requiring a highly refined mesh to capture these unsteady effects. While anisotropic metric-based adaptive mesh refinement has proven effective in achieving accuracy with much less complexity, current algorithms are primarily tailored for steady flow fields. This thesis presents a novel approach to address the challenges of anisotropic grid adaptation of unsteady flows by leveraging a data-driven technique called Dynamic Mode Decomposition (DMD). DMD has proven to be a powerful tool to model complex nonlinear flows, given its links to the Koopman operator, and also its easy mathematical implementation. This research proposes the integration of DMD into the process of anisotropic grid adaptation to dynamically adjust the mesh in response to evolving flow features. The effectiveness of the proposed approach is demonstrated through numerical experiments on representative unsteady flow configurations, such as a cylinder in a subsonic flow and a cylinder in a supersonic channel flow. Results indicate that the incorporation of DMD enables an accurate representation of unsteady flow dynamics. Overall, this thesis contributes to making advances in the adaptation of unsteady flows. The novel framework proposed makes it computationally tractable to track the evolution of the main coherent features of the flowfield without losing out on accuracy by using a data-driven method. / Master of Science / Simulating unsteady, high-speed fluid flows around objects like aircraft and rockets poses a significant computational challenge. These flows exhibit rapidly evolving, intricate pattern structures that demand highly refined computational meshes to capture accurately. However, using a statically refined mesh for the entire simulation is computationally prohibitive. This research proposes a novel data-driven approach to enable efficient anisotropic mesh adaptation for such unsteady flow simulations. It leverages a technique called Dynamic Mode Decomposition (DMD) to model the dominant coherent structures and their evolution from snapshot flow field data. DMD has shown powerful capabilities in identifying the most energetic flow features and their time dynamics from numerical or experimental data. By integrating DMD into the anisotropic mesh adaptation process, the computational mesh can be dynamically refined anisotropically just in regions containing critical time-varying flow structures. The efficacy of this DMD-driven anisotropic adaptation framework is demonstrated in representative test cases - an unsteady subsonic flow over a circular cylinder and a supersonic channel flow over a cylinder. Results indicate that it enables accurate tracking and resolution of the key unsteady flow phenomena like vortex shedding using far fewer computational cells compared to static mesh simulations. In summary, this work makes anisotropic mesh adaptation computationally tractable for unsteady flow simulations by leveraging data-driven DMD modelling of the evolving coherent structures. The developed techniques pave the way for more accurate yet efficient unsteady CFD simulations.

The resolution of the complex physics of rotating configurations is critical for any engineering analysis that requires multiple frames of reference. Two well-known applications are in the rotorcraft and wind energy industries. Rotor wake impingement from rotor-fuselage and wind turbine-tower interactions impact structural and acoustic characteristics. Additionally, parasite drag resulting from rotorcraft hubs may result in severe limitations on forward flight vehicle performance. Complex turbulent wakes from rotors and hubs impinging on downstream empennage can create adverse aeroelastic behavior and can affect handling qualities. Numerical simulations of these flows require state-of-the-art Navier Stokes methods using dynamic overset grids. However, many current methods typically used in industry result in wakes that dissipate essential features. In order to address these concerns, two advancements are introduced in this thesis. Feature-based grid adaptation on dynamic overset grids has been developed and demonstrated with an unstructured Navier Stokes solver. The unique feature of the adaptation technique is that it is applied globally on the overset grid system except within the boundary layer. In concert with grid adaptation, an efficient parallelized search algorithm for solution interpolation over massively distributed systems has been created. This results in cost-effective interpolation that retains the numerical order of accuracy and has been verified in both space and time. The improvements have been demonstrated for rotor-fuselage interaction and a generic rotating hub. Detailed analysis of convergence of the methodology and sensitivity of the results to relevant parameters have also been included.

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The present work deals with the extension of Acoustic Flux Vector Splitting (AFVS) scheme for the Compressible Viscous flow computations. Accurate viscous flow computations require much finer grids with adequate clustering of grid points in certain regions. Viscous flow computations are performed on unstructured triangulated grids. Solving Navier-Stokes equations involves the inviscid Euler part and the viscous part. The inviscid part of the fluxes are computed using the Acoustic Flux Vector Splitting scheme and the viscous part which is diffusive in nature does not require upwinding and is taken care using a central difference type of scheme. For these computations both the cell centered and the cell vertex finite volume methods are used. Higher order accuracy on unstructured meshes is achieved using the reconstruction procedure. Test cases are chosen in such a way that the performance of the scheme can be evaluated for different range of mach numbers. We demonstrate that higher order AFVS scheme in conjunction with a suitable grid adaptation strategy produce results that compare well with other well known schemes and the experimental data. An assessment of the relative performance of the AFVS scheme with the Roe scheme is also presented.