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Full-Text Articles in Engineering
The Solution Of A Singular Integral Equation Arising From A Lifting Surface Theory For Rotating Blades, Mark H. Dunn
The Solution Of A Singular Integral Equation Arising From A Lifting Surface Theory For Rotating Blades, Mark H. Dunn
Mathematics & Statistics Theses & Dissertations
A technique is presented for the solution of a linear, two dimensional, singular, Volterra integral equation of the first kind. The integral equation, originally developed by Farassat and Myers, is derived from the basic equations of linearized acoustics and models the lifting force experienced by an infinitesimally thin surface moving tangent to itself. As a particular application, the motion of modern high speed aircraft propellers (Advanced Technology Propellers) is considered. The unknown propeller blade surface pressure distribution is approximated by a piecewise constant function and the integral equation is solved numerically by the method of collocation. Certain simplifying assumptions applied …
An Extension Of Essentially Non-Oscillatory Shock-Capturing Schemes To Multi-Dimensional Systems Of Conservation Laws, Jay Casper
Mathematics & Statistics Theses & Dissertations
In recent years, a class of numerical schemes for solving hyperbolic partial differential equations has been developed which generalizes the first-order method of Godunov to arbitrary order of accuracy. High-order accuracy is obtained, wherever the solution is smooth, by an essentially non-oscillatory (ENO) piecewise polynomial reconstruction procedure, which yields high-order pointwise information from the cell averages of the solution at a given point in time. When applied to piecewise smooth initial data, this reconstruction enables a flux computation that provides a time update of the solution which is of high-order accuracy, wherever the function is smooth, and avoids a Gibbs …