Preconditioned iterative methods for solving elliptic partial differential equations

Preconditioned iterative methods for solving elliptic partial differential equation

The AGE iterative methods for solving large linear systems occurring in differential equations

The work presented in this thesis is wholly concerned with the Alternating Group Explicit (AGE) iterative methods for solving large linear systems occurring in solving Ordinary and Partial Differential Equations (ODEs and PDEs) using finite difference approximations. [Continues.

Navier-Stokes flowfield computation of wing/rotor interaction for a tilt rotor aircraft in hover

The download on the wing produced by the rotor-induced downwash of a tilt rotor aircraft in hover is of major concern because of its severe impact on payload-carrying capability. A method has been developed to help gain a better understanding of the fundamental fluid dynamics that causes this download, and to help find ways to reduce it. In particular, the method is employed in this work to analyze the effect of a tangential leading edge circulation-control jet on download reduction. Because of the complexities associated with modeling the complete configuration, this work focuses specifically on the wing/rotor interaction of a tilt rotor aircraft in hover. The three-dimensional, unsteady, thin-layer compressible Navier-Stokes equations are solved using a time-accurate, implicit, finite difference scheme that employs LU-ADI factorization. The rotor is modeled as an actuator disk which imparts both a radical and an azimuthal distribution of pressure rise and swirl to the flowfield. A momentum theory blade element analysis of the rotor is incorporated into the Navier-Stokes solution method. Solution blanking at interior points of the mesh has been shown here to be an effective technique in introducing the effects of the rotor and tangential leading edge jet. Results are presented both for a rotor alone and for wing/rotor interaction. The overall mean characteristics of the rotor flowfield are computed including the flow acceleration through the rotor disk, the axial and swirl velocities in the rotor downwash, and the slipstream contraction. Many of the complex tilt rotor flow features are captured including the highly three-dimensional flow over the wing, the recirculation fountain at the plane of symmetry, wing leading and trailing edge separation, and the large region of separated flow beneath the wing. Mean wing surface pressures compare fairly well with available experimental data, but the time-averaged download/thrust ratio is 20-30 percent higher than the measured value. The discrepancy is due to a combination of factors that are discussed. Leading edge tangential blowing, of constant strength along the wing span, is shown to be effective in reducing download. The jet serves primarily to reduce the pressure on the wing upper surface. The computation clearly shows that, because of the three-dimensionality of the flowfield, optimum blowing would involve a spanwise variation in blowing strength

Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology

Transonic flow studies

Major emphasis was on the design of shock free airfoils with applications to general aviation. Unsteady flow, transonic flow, and shock wave formation were examined

A compendium of computational fluid dynamics at the Langley Research Center

Through numerous summary examples, the scope and general nature of the computational fluid dynamics (CFD) effort at Langley is identified. These summaries will help inform researchers in CFD and line management at Langley of the overall effort. In addition to the inhouse efforts, out of house CFD work supported by Langley through industrial contracts and university grants are included. Researchers were encouraged to include summaries of work in preliminary and tentative states of development as well as current research approaching definitive results

Numerical techniques for predicting aerodynamic characteristics of bodies

Two methods are presented characteristics of bodies SUMMARY for predicting the aerodynamic in inviscid and irrotational flow. The first method is limited to incompressible flow and makes use of panels of ring sources to approximate the body surface. The technique is dedicated to single, axisymmetric body configurations in either uniform longitudinal or rectilinear motion. The versatility of the method is due to the use of sources as singularities placed on the body surface, allowing discontinuous body profiles to be analysed. The method has been compared for accuracy and efficiency with experimental and theoretical results. Further investigation showed that at present there existed no numerical technique which could predict the aerodynamic behaviour of multiple bodies in compressible flow. Hence, a fully three-dimensional method was developed which made use of the Full Potential Equation (F.P.E.) in conservative form. A computational mesh is placed around the body configuration and at each mesh node the F.P.E. is satisfied ~n finite difference form. The method is able to give a complete description of the flow around the bodies at transonic mach numbers. Comparisons to test the accuracy and efficiency of the method are limited to either, purely subsonic flow for two body configurations or zero incidence for transonic flow around a single body.Ph

Sensitivity Analysis and Optimization of Aerodynamic Configurations with Blend Surfaces

A novel (geometrical) parametrization procedure using solutions to a suitably chosen fourth order partial differential equation is used to define a class of airplane configurations. Inclusive in this definition are surface grids, volume grids, and grid sensitivity. The general airplane configuration has wing, fuselage, vertical tail and horizontal tail. The design variables are incorporated into the boundary conditions, and the solution is expressed as a Fourier series. The fuselage has circular cross section, and the radius is an algebraic function of four design parameters and an independent computational variable. Volume grids are obtained through an application of the Control Point Form method. A graphic interface software is developed which dynamically changes the surface of the airplane configuration with the change in input design variable. The software is made user friendly and is targeted towards the initial conceptual development of any aerodynamic configurations. Grid sensitivity with respect to surface design parameters and aerodynamic sensitivity coefficients based on potential flow is obtained using an Automatic Differentiation precompiler software tool ADIFOR. Aerodynamic shape optimization of the complete aircraft with twenty four design variables is performed. Unstructured and structured volume grids and Euler solutions are obtained with standard software to demonstrate the feasibility of the new surface definition