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- W1968373018 abstract "This work focuses on high-order numerical schemes for conservation laws with emphasis on problems that admit discontinuous solutions. We will investigate several enabling techniques with the aim to construct robust methods for unstructured meshes capable of reliably producing globally high-order accurate results even in the presence of discontinuities. We use spectral and pseudo-spectral schemes in connection with such techniques as Gibbs-complementary reconstruction to recover high-order accuracy near discontinuities. I. Introduction Computational aerodynamics has been dominated by schemes which are higher than first-order accurate only in smooth regions, where they are typically restricted to second, or perhaps third order accuracy. The presence of discontinuities in transonic aerodynamics has greatly hampered the success of high-order accurate methods. In the vicinity of discontinuities the typical scheme uses restrictive limiters to damp out high-frequency oscillatory modes. While low-order schemes have been very successful due to their robustness and relative eciency, many fields of research, such as aeroacoustics, large-eddy simulation (LES), and unsteady nonperiodic flow require highly accurate numerical methods. For many applications a high-order accurate scheme for solutions with discontinuities that retains its nominal accuracy everywhere would be quite welcome. In this paper we will explore one possible route to such a scheme. We will start from a most promising new numerical scheme for unstructured meshes, namely the Spectral Dierence method," @default.
- W1968373018 created "2016-06-24" @default.
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- W1968373018 date "2005-06-06" @default.
- W1968373018 modified "2023-09-26" @default.
- W1968373018 title "High-Order Accurate Methods for High-Speed Flow" @default.
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- W1968373018 doi "https://doi.org/10.2514/6.2005-5251" @default.
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