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The theory of non-oscillatory scalar schemes is developed in this paper in terms of the local extremum diminishing (LED) principle that maxima should not increase and minima should not decrease. This principle can be used for multi-dimensional problems on both structured and unstructured meshes, while it is equivalent to the total variation diminishing(More)
An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity CFD, geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to(More)
The effect of artificial diffusion on discrete shock structures is examined for a family of schemes which includes scalar diffusion, convective upwind and split pressure (CUSP) schemes, and upwind schemes with characteristic splitting. The analysis leads to conditions on the diffusive flux such that stationary discrete shocks can contain a single interior(More)
New versions of implicit algorithms are proposed for the efficient solution of the Euler equations of com-pressible flow. The methods are based on a pre-conditioned, Lower-Upper (LU) implementation of a nonlinear, Symmetric Gauss-Seidel (SGS) algorithm for use as a smoothing algorithm in a multi-grid method. The methods have been implemented for flows in(More)
Implicit methods for hyperbolic equations are analyzed using LU de-compositions. It is shown that the inversion of the resulting tridiagonal matrices is usually stable even when diagonal dominance is lost. Furthermore, these decompositions can be used to construct stable algorithms in multi-dimensions. When marching to a steady state, the solution is(More)