13 research outputs found

    Numerical computation of transonic flows by finite-element and finite-difference methods

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    Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined

    The Sixth Copper Mountain Conference on Multigrid Methods, part 2

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    The Sixth Copper Mountain Conference on Multigrid Methods was held on April 4-9, 1993, at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth

    Lectures on Computational Numerical Analysis of Partial Differential Equations

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    From Chapter 1: The purpose of these lectures is to present a set of straightforward numerical methods with applicability to essentially any problem associated with a partial differential equation (PDE) or system of PDEs independent of type, spatial dimension or form of nonlinearity.https://uknowledge.uky.edu/me_textbooks/1002/thumbnail.jp

    Compact integrated radial basis function modelling of particulate suspensions

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    The present Ph.D. thesis is concerned with the development of computational procedures based on Cartesian grids, point collocation, immersed boundary method, and compact integrated radial basis functions (CIRBF), for the simulation of heat transfer and steady/unsteady viscous flows in complex geometries, and their applications for the prediction of macroscopic rheological properties of particulate suspensions. The thesis consists of three main parts. In the first part, integrated radial basis function approximations are developed into compact local form to achieve sparse system matrices and high levels of accuracy together. These stencils are employed for the discretisation of the Navier-Stokes equation in the pressurevelocity formulation. The use of alternating direction implicit (ADI) algorithms to enhance the computational efficiency is also explored. In the second part, compact local IRBF stencils are extended for the simulation of flows in multiply-connected domains, where the direct forcing-immersed boundary (DFIB) method is adopted to handle such complex geometries efficiently. In the third part, the DFIB-CIRBF method is applied for the investigation of suspensions of rigid particles in a Newtonian liquid, and the prediction of their bulk viscosity and stresses. The proposed computational procedures are verified successfully with several test problems in Computational Fluid Dynamics and Computational Rheology. Accurate results are achieved using relatively coarse grids

    Meshless methods: theory and application in 3D fracture modelling with level sets

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    Accurate analysis of fracture is of vital importance yet methods for effetive 3D calculations are currently unsatisfactory. In this thesis, novel numerical techniques are developed which solve many of these problems. This thesis consists two major parts: firstly an investigation into the theory of meshless methods and secondly an innovative numerical framework for 3D fracture modelling using the element-free Galerkin method and the level set method. The former contributes to some fundamental issues related to accuracy and error control in meshless methods needing to be addressed for fracture modelling developed later namely, the modified weak form for imposition of essential boundary conditions, the use of orthogonal basis functions to obtain shape functions and error control in adaptive analysis. In the latter part, a simple and efficient numerical framework is developed to overcome the difficulties in current 3D fracture modelling. Modelling cracks in 3D remains a challenging topic in computational solid mechanics since the geometry of the crack surfaces can be difficult to describe unlike the case in 2D where cracks can be represented as combinations of lines or curves. Secondly, crack evolution requires numerical methods that can accommodate the moving geometry and a geometry description that maintains accuracy in successive computational steps. To overcome these problems, the level set method, a powerful numerical method for describing and tracking arbitrary motion of interfaces, is used to describe and capture the crack geometry and forms a local curvilinear coordinate system around the crack front. The geometry information is used in the stress analysis taken by the element-Free Galerkin method as well as in the computation of fracture parameters needed for crack propagation. Examples are tested and studied throughout the thesis addressing each of the above described issues

    Compact non-symmetric and symmetric stencils based on integrated radial basis functions for differential problems

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    This PhD project is concerned with the development of compact local stencils based on integrated radial basis functions (IRBFs) for both spatial and temporal discretisations of partial differential equations (PDEs), and their applications in heat transfer and fluid flows. The proposed approximation stencils are effective and efficient since (i) Cartesian grids are employed to represent both rectangular and non-rectangular domains; (ii) high levels of accuracy of the solution and sparseness of the resultant algebraic system are achieved together; and (iii) time derivatives are discretised with high order approximation. For spatial discretisation, a compact non-symmetric flat-IRBF stencil is developed. Significant improvements in the matrix condition number, solution accuracy and convergence rate with grid refinement over the usual approaches are obtained. Furthermore, IRBFs are used for Hermite interpolation in the solution of PDEs, resulting in symmetric stencils defined on structured/random nodes. For temporal discretisation, a compact IRBF stencil is proposed, where the time derivative is approximated in terms of, not only nodal function values at the current and previous time levels, but also nodal derivative values at the previous time level. When dealing with moving boundary problems (e.g. particulate suspensions and fluid structure interacting problems), to avoid the grid regeneration issue, an IRBF-based domain embedding method is also developed, where a geometrically-complex domain is extended to a larger, but simpler shaped domain, and a body force is introduced into the momentum equations to represent the moving boundaries. The proposed methods are verified in the solution of differential problems defined on simply- and multiply-connected domains. Accurate results are achieved using relatively coarse Cartesian grids and relatively large time steps. The rate of convergence with grid refinement can be up to the order of about 5. Converged solutions are obtained in the simulation of highly nonlinear fluid flows and they are in good agreement with benchmark/well-known existing solutions

    Aeronautical engineering: A continuing bibliography with indexes (supplement 291)

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    This bibliography lists 757 reports, articles, and other documents introduced into the NASA scientific and technical information system in May. 1993. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment, and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics
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