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  • J Reuther, A Jameson, J J Alonso, M J Rimlinger, D Sauders, M J Rimiinger +2 others
  • 2001
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)
This paper describes the formulation of optimization techniques based on control theory for aerodynamic shape design in viscous compressible flow, modelled by the Navier-Stokes equations. It extends previous work on optimization for inviscid flow. The theory is applied to a system defined by the partial differential equations of the flow, with the boundary(More)
An efficient, high-order, conservative method named the spectral difference method has been developed recently for conservation laws on unstructured grids. It combines the best features of structured and unstructured grid methods to achieve high-computational efficiency and geometric flexibility; it utilizes the concept of discontinuous and high-order local(More)
The flux reconstruction approach to high-order methods is robust, efficient, simple to implement, and allows various high-order schemes, such as the nodal discontinu-ous Galerkin method and the spectral difference method, to be cast within a single unifying framework. Utilizing a flux reconstruction formulation, it has been proved (for one-dimensional(More)
While second order methods for computational simulations of fluid flow provide the basis of widely used commercial software, there is a need for higher order methods for more accurate simulations of turbulent and vortex dominated flows. The discontinuous Galerkin (DG) method is the subject of much current research toward this goal. The spectral difference(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)
This article outlines some of the principal issues in the development of numerical methods for the prediction of flows over aircraft and their use in the design process. These include the choice of an appropriate mathematical model, the design of shock-capturing algorithms, the treatment of complex geometric configurations, and shape modifications to(More)
The Flux Reconstruction (FR) approach unifies several well-known high-order schemes for unstructured grids, including a collocation-based nodal discontinuous Galerkin (DG) method and all types of Spectral Difference (SD) methods, at least for linear problems. The FR approach also allows for the formulation of new families of schemes. Of particular interest(More)
The flux reconstruction (FR) approach unifies various high-order schemes, including collocation based nodal discontinuous Galerkin (DG) methods, and all spectral difference methods (at least for a linear flux function), within a single framework. Recently a new range of linearly stable FR schemes have been identified, henceforth referred to as(More)