The numerical study of aeroacoustic problems places stringent demands on the choice of a computational algorithm, particularly when shock waves are involved, Because of their dual capacity for high-order accuracy and ...
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The numerical study of aeroacoustic problems places stringent demands on the choice of a computational algorithm, particularly when shock waves are involved, Because of their dual capacity for high-order accuracy and high-resolution shock capturing, the recently developed class of essentially nonoscillatory (ENO) schemes has generated considerable interest in regard to such problems. The use of ENO schemes for aeroacoustic applications is investigated, with particular attention to the control of the adaptivestenciling procedure. A modification of previously developed stencil-biasing procedures is proposed. This nonlinear stencil biasing allows a freer adaptation near discontinuities than is allowed by the previous biasing methods, without disturbing the biased, stable stencils that are desired in smooth regions. The accuracy of these new methods is validated through the study of a shocked nozzle flow. An axisymmetric shock-vortex interaction is then investigated, Numerical results indicate a reduction in error when compared with results in which other stencil-biasing procedures are used.
The finite volume and finite difference implementations of high-order accurate essentially nonoscillatory shock-capturing schemes are discussed and compared. Results obtained with fourth-order accurate algorithms base...
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The finite volume and finite difference implementations of high-order accurate essentially nonoscillatory shock-capturing schemes are discussed and compared. Results obtained with fourth-order accurate algorithms based on both formulations are examined for accuracy, sensitivity to grid irregularities, resolution of waves that are oblique to the mesh, and computational efficiency. Some algorithm modifications that may be required for a given application are suggested. Conclusions that pertain to the relative merits of both formulations are drawn, and some circumstances for which each might be useful are noted.
The computational qualities of spatially high-order accurate methods for the finite-volume solution of the Euler equations are presented. Multidimensional reconstruction operators discussed include versions of the k-e...
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The computational qualities of spatially high-order accurate methods for the finite-volume solution of the Euler equations are presented. Multidimensional reconstruction operators discussed include versions of the k-exact and essentially nonoscillatory (ENO) algorithms. The ENO schemes utilized are the reconstruction-via-primitive-function scheme and a dimensionally split ENO reconstruction. High-order operators are compared in terms of reconstruction and solution accuracy, computational cost, and oscillatory behavior in supersonic flows with shocks. Inherent steady-state convergence difficulties are demonstrated for the implemented adaptive-stencilalgorithms. An exact solution to the heat equation is used to determine reconstruction error, and the computational intensity is reflected through operation counts. The standard variable-extrapolation method (MUSCL) is included for comparison. Numerical experiments include the Ringleb flow for numerical accuracy and a shock-reflection problem. A vortex-shock interaction demonstrates the ability of the ENO scheme to excel in simulating unsteady high-frequency flow physics.
We continue the study of the finite-volume application of high-order-accurate, essentially nonoscillatory shock-capturing schemes to two-dimensional initial-boundary-value problems. These schemes achieve high-order sp...
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We continue the study of the finite-volume application of high-order-accurate, essentially nonoscillatory shock-capturing schemes to two-dimensional initial-boundary-value problems. These schemes achieve high-order spatial accuracy, in smooth regions, by a piecewise polynomial approximation of the solution from cell averages. In addition, this spatial operation involves an adaptivestencil algorithm, in order to avoid the oscillatory behavior that is associated with interpolation across steep gradients. High-order Runge-Kutta methods are employed for time integration, thus making these schemes best suited for unsteady problems. Schemes are developed which use fifth- and sixth-order-accurate spatial operators in conjunction with a fourth-order time operator. Under a sufficient time-step restriction, numerical results suggest that these schemes converge according to the higher-order spatial accuracy, for unsteady problems. Second-, third-, and fifth-order algorithms are applied to the Euler equations of gasdynamics and tested on a problem that models a shock-vortex interaction.
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