Of the surface capturing schemes, the levelset and multi-phase models are implemented and extensively examined. First, the levelset method is shown, and its weaknesses are identified; a mis- appropriation of changes in momentum, a strong dependence on the density by the eigenvalues of the inviscid flux Jacobian, and a prescribed density transition. These weaknesses are specifically addressed and overcome by the formulation of the multi-phase model. Consequently, the multi-phase model is chosen for this work. Previous surface fitting techniques simply absorb the gravitational source term into the pressure. It must be noted that this absorbtion is valid only for single density flows; since the surface fitting approach is solving only one side of the interface, there is no significant change in the density througout the domain. Consequently, absorbing the gravitational source into the pressure term is not possible in a surface capturing scheme in which both sides of the interface are solved. Thus, a new treatment of the gravitational source term is required and is presented in this work. A multi-phase model is implemented into a parallel, three-dimensional, unsteady, incompressible Navier-Stokes flow solver for the purpose of examining free surface flows on unstructured meshes. The reasons for choosing this model above others are presented, and the multi-phase model is discussed. The base algorithm is briefly examined with emphasis given to the areas which require additional care. The construction of the gravity source term which drives the formation of the waves is explained in detail, and its effects on the rest of the algorithm are identified. Finally, the method is carefully compared with available data on a submerged NACA 0012 airfoil, the Wigley Hull, the Series 60 Cb=0.6 ship, and the DTMB 5415 ship.

The primary objective of this study is to develop a sliding interface method for simulations involving relative rotational grid motion suitable for unstructured grid topologies. The present method alleviates computationally expensive grid deformation, remeshing, and hole cutting procedures. Rotational motion is accomplished by rigidly rotating a subdomain representing the moving component. At the subdomain interface boundary, the faces along the interfaces are extruded into the adjacent subdomain to create new volume elements and provide a one-cell overlap. These new volume elements close the control volumes for the nodes on the interface surface and allow a flux to be computed across the subdomain interface. An interface flux is computed independently for each subdomain. The values of the solution variables and other quantities for the nodes created by the extrusion process are found by interpolation. The extrusion is done so that the interpolation will maintain information as localized as possible. A parallel implementation of the neighbor search is used to find the extruded points in the adjacent subdomain. The method has been implemented in a parallel, node-centered finite volume, high-resolution viscous flow solver. The method does not impose any restrictions on the subdomain interface aside from the axisymmetric limitation required for rotational motion. In addition, the grid on the subdomain interface is arbitrary. The boundary surfaces between the two subdomains can have independent grids from one another. They do not have to connect in a one-to-one manner and there are no symmetry or pattern restrictions placed on the surface grid. A variety of numerical simulations were performed on several small-scale model problems to examine conservation of the interface flux. Overall flux conservation errors were found to be comparable to that for fully connected and fully conservative simulations. In addition, excellent agreement was obtained with both theoretical and experimental results. Three large-scale applications were also used to validate the method and highlight some of the advantages of the sliding interface method compared to the current state-of- the-art for unstructured grid applications. This sliding interface method requires no geometric modifications and has significantly shorter run times Furthermore, there were no apparent adverse effects on the numerical solutions by not strictly enforcing flux conservation at the subdomain boundary.

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No description available.

The first two steps in the development of an integrated multidisciplinary design optimization procedure capable of analyzing the nonlinear fluid flow about geometrically complex aeroelastic configurations have been accomplished in the present work. For the first step, a three-dimensional unstructured grid approach to aerodynamic shape sensitivity analysis and design optimization has been developed. The advantage of unstructured grids, when compared with a structured-grid approach, is their inherent ability to discretize irregularly shaped domains with greater efficiency and less effort. Hence, this approach is ideally suited fro geometrically complex configurations of practical interest. In this work the time-dependent, nonlinear Euler equations are solved using an upwind, cell-centered, finite-volume scheme. The discrete, linearized systems which result from this scheme are solved iteratively by a preconditioned conjugate-gradient-like algorithm known as GMRES for the two-dimensional cases and a Gauss-Seidel algorithm for the three-dimensional; at steady-state, similar procedures are used to solve the accompanying linear aerodynamic sensitivity equations in incremental iterative form. As shown, this particular form of the sensitivity equation makes large-scale gradient-based aerodynamic optimization possible by taking advantage of memory efficient methods to construct exact Jacobian matrix-vector products. Various surface parameterization techniques have been employed in the current study to control the shape of the design surface. Once this surface has been deformed, the interior volume of the unstructured grid is adapted by considering the mesh as a system of interconnected tension springs. Grid sensitivities are obtained by differentiating the surface parameterization and the grid adaptation algorithms with ADIFOR, an advanced automatic-differentiation software tool. To demonstrate the ability of this procedure to analyze and design complex configurations of practical interest, the sensitivity analysis and shape optimization has been performed for several two- and three-dimensional cases. In two-dimensions, an initially symmetric NACA-0012 airfoil and a high-lift multi-element airfoil were examined. For the three-dimensional configurations, an initially rectangular wing with uniform NACA-0012 cross-sections was optimized; in additions, a complete Boeing 747-200 aircraft was studied. Furthermore, the current study also examines the effect of inconsistency in the order of spatial accuracy between the nonlinear fluid and linear shape sensitivity equations. The second step was to develop a computationally efficient, high-fidelity, integrated static aeroelastic analysis procedure. To accomplish this, a structural analysis code was coupled with the aforementioned unstructured grid aerodynamic analysis solver. The use of an unstructured grid scheme for the aerodynamic analysis enhances the interactions compatibility with the wing structure. The structural analysis utilizes finite elements to model the wing so that accurate structural deflections may be obtained. In the current work, parameters have been introduced to control the interaction of the computational fluid dynamics and structural analyses; these control parameters permit extremely efficient static aeroelastic computations. To demonstrate and evaluate this procedure, static aeroelastic analysis results for a flexible wing in low subsonic, high subsonic (subcritical), transonic (supercritical), and supersonic flow conditions are presented. / Ph. D.

Computational solutions are presented for flows ranging from incompressible viscous flows to inviscid transonic flows. The viscous flow problems are solved using the incompressible Navier-Stokes equations while the inviscid solutions are attained using the full potential equation. Results for the viscous flow problems focus on turbulence modeling when separation is present. The main focus for the inviscid results is the development of an unstructured solution algorithm. The subject dealing with turbulence modeling for separated flows is discussed first. Two different test cases are presented. The first flow is a low-speed converging-diverging duct with a rapid expansion, creating a large separated flow region. The second case is the flow around a stationary hydrofoil subject to small, oscillating hydrofoils. Both cases are computed first in a steady state environment, and then with unsteady flow conditions imposed. A special characteristic of the two problems being studied is the presence of strong adverse pressure gradients leading to flow detachment and separation. For the flows with separation, numerical solutions are obtained by solving the incompressible Navier-Stokes equations. These equations are solved in a time accurate manner using the method of artificial compressibility. The algorithm used is a finite volume, upwind differencing scheme based on flux-difference splitting of the convective terms. The Johnson and King turbulence model is employed for modeling the turbulent flow. Modifications to the Johnson and King turbulence model are also suggested. These changes to the model focus mainly on the normal stress production of energy and the strong adverse pressure gradient associated with separating flows. The performance of the Johnson and King model and its modifications, along with the Baldwin-Lomax model, are presented in the results. The modifications had an impact on moving the flow detachment location further downstream, and increased the sensitivity of the boundary layer profile to unsteady flow conditions. Following this discussion is the numerical solution of the full potential equation. The full potential equation assumes inviscid, irrotational flow and can be applied to problems where viscous effects are small compared to the inviscid flow field and weak normal shocks. The development of a code is presented which solves the full potential equation in a finite volume, cell centered formulation. The unique feature about this code is that solutions are attained on unstructured grids. Solutions are computed in either two or three dimensions. The grid has the flexibility of being made up of tetrahedra, hexahedra, or prisms. The flow regime spans from low subsonic speeds up to transonic flows. For transonic problems, the density is upwinded using a density biasing technique. If lift is being produced, the Kutta-Joukowski condition is enforced for circulation. An implicit algorithm is employed based upon the Generalized Minimum Residual method. To accelerate convergence, the Generalized Minimum Residual method is preconditioned. These and other problems associated with solving the full potential equation on an unstructured mesh are discussed. Results are presented for subsonic and transonic flows over bumps, airfoils, and wings to demonstrate the unstructured algorithm presented here. / Ph. D.

Visualization of large amounts of simulation data is important for the understanding of most physical phenomena. The limited capabilities of desktop machines make them unsuitable for handling excessive amounts of simulation data. The present day high speed networks have made it possible to remotely visualize the data being generated by a supercomputer in real time. In order for such a system to be reliable, a robust communication protocol and an efficient compression mechanism are needed. This work presents a remote visualization system that addresses these issues, and emphasizes the design and implementation of the application level network protocol. A control theory based adaptive rate control algorithm is presented for UDP streams that maximizes the effective throughout experienced by the stream while minimizing the packet loss. The algorithm is shown to make the system responsive to changing network conditions. This makes the system deployable over any network, including the Internet. / Master of Science

This thesis’ aim is to explore improvements to, and applications of, a fundamental quantum algorithm invented by Grover. Grover’s algorithm is a basic tool that can be applied to a large number of problems in computer science, creating quantum algorithms that are polynomially faster than fastest known and fastest possible classical algorithms that solve the same problems. Our goal in this thesis is to make these techniques readily accessible to those without a strong background in quantum physics: we achieve this by providing a set of tools, each of which makes use of Grover’s algorithm or similar techniques, that can be used as subroutines in many quantum algorithms. The tools we provide are carefully constructed: they are easy to use, and they are asymptotically faster than the best tools previously available. The tools that we supersede include algorithms by Boyer, Brassard, Hoyer and Tapp, Buhrman, Cleve, de Witt and Zalka and Durr and Hoyer. After creating our tools, we create several new quantum algorithms, each of which is faster than the fastest known classical algorithm that accomplishes the same aim, and some of which are faster than the fastest possible classical algorithm. These algorithms come from graph theory, computational geometry and dynamic programming. We discuss a breadth-first search that is faster than (edges) (the classical limit) in a dense graph, maximum-points-on-a-line in (N3/2 lgN) (faster than the fastest classical algorithm known), as well as several other algorithms that are similarly illustrative of solutions in some class of problem. Through these new algorithms we illustrate the use of our tools, working to encourage their use and the study of quantum algorithms in general.

This thesis aim is to explore improvements to, and applications of, a fundamental quantum algorithm invented by Grover. Grovers algorithm is a basic tool that can be applied to a large number of problems in computer science, creating quantum algorithms that are polynomially faster than fastest known and fastest possible classical algorithms that solve the same problems. Our goal in this thesis is to make these techniques readily accessible to those without a strong background in quantum physics: we achieve this by providing a set of tools, each of which makes use of Grovers algorithm or similar techniques, that can be used as subroutines in many quantum algorithms. The tools we provide are carefully constructed: they are easy to use, and they are asymptotically faster than the best tools previously available. The tools that we supersede include algorithms by Boyer, Brassard, Hoyer and Tapp, Buhrman, Cleve, de Witt and Zalka and Durr and Hoyer. After creating our tools, we create several new quantum algorithms, each of which is faster than the fastest known classical algorithm that accomplishes the same aim, and some of which are faster than the fastest possible classical algorithm. These algorithms come from graph theory, computational geometry and dynamic programming. We discuss a breadth-first search that is faster than (edges) (the classical limit) in a dense graph, maximum-points-on-a-line in (N3/2 lgN) (faster than the fastest classical algorithm known), as well as several other algorithms that are similarly illustrative of solutions in some class of problem. Through these new algorithms we illustrate the use of our tools, working to encourage their use and the study of quantum algorithms in general.

In this thesis, an approach is presented for the generation of grids suitable for the simulation of high Reynolds number viscous flows in complex three-dimensional geometries. The automatic and reliable generation of such grids is today on the biggest bottlenecks in the industrial CFD simulation environment. In the proposed approach, unstructured tetrahedral grids are employed for the regions far from the viscous boundaries of the domain, while semi-structured layers of high aspect ratio prismatic and hexahedral elements are used to provide the necessary grid resolution inside the boundary layers and normal to the viscous walls. The definition of the domain model is based on the STEP ISO standard and the topological information contained in the model is used for applying the hierarchical grid generation parameters defined by the user. An efficient, high-quality and robust algorithm is presented for the generation of the unstructured simplicial (triangular of tetrahedral) part of the grid. The algorithm is based on the Delaunay triangulation and the internal grid points are created following a centroid or frontal approach. For the surface grid generation, a hybrid approach is also proposed similar to the volume. Semi-structured grids are generated on the surface grid (both on the edges and faces of the domain) to improve the grid resolution around convex and concave ridges and corners, by aligning the grid elements in the directions of high solution gradients along the surface. A method is also developed for automatically setting the grid generation parameters related to the surface grid generation based on the curvature of the surface in order to obtain an accurate and smooth surface grid. Finally, a semi-structured prismatic/hexahedral grid generation algorithm is presented for the generation of the part of grid close to the viscous walls of the domain. The algorithm is further extended with improvements meant to increase the grid quality around concave and convex ridges of the domain, where the semi-structured grids are known to be inadequate. The combined methodology is demonstrated on a variety of complex examples mainly from the automotive and aeronautical industry.