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Jung, Chang-Yeol
Analysis and computational methods Lab
Research Interests
  • Analysis, singular perturbations, uncertainty, numerical methods

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Fine structures for the solutions of the two-dimensional Riemann problems by high-order WENO schemes

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Title
Fine structures for the solutions of the two-dimensional Riemann problems by high-order WENO schemes
Author
Jung, Chang-YeolNguyen, Thien Binh
Keywords
2D Riemann problem; Euler equations; Shock-capturing methods; Weighted essentially non-oscillatory (WENO) schemes; WENO-𝜃
Issue Date
201802
Publisher
SPRINGER
Citation
ADVANCES IN COMPUTATIONAL MATHEMATICS, v.44, no.1, pp.147 - 174
Abstract
The two-dimensional Riemann problem with polytropic gas is considered. By a restriction on the constant states of each quadrant of the computational domain such that there is only one planar centered wave connecting two adjacent quadrants, there are nineteen genuinely different initial configurations of the problem. The configurations are numerically simulated on a fine grid and compared by the 5th-order WENO-Z5, 6th-order WENO-6, and 7th-order WENO-Z7 schemes. The solutions are very well approximated with high resolution of waves interactions phenomena and different types of Mach shock reflections. Kelvin-Helmholtz instability-like secondary-scaled vortices along contact continuities are well resolved and visualized. Numerical solutions show that WENO-6 outperforms the comparing WENO-Z5 and WENO-Z7 in terms of shock capturing and small-scaled vortices resolution. A catalog of the numerical solutions of all nineteen configurations obtained from the WENO-6 scheme is listed. Thanks to their excellent resolution and sharp shock capturing, the numerical solutions presented in this work can be served as reference solutions for both future numerical and theoretical analyses of the 2D Riemann problem.
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DOI
http://dx.doi.org/10.1007/s10444-017-9538-8
ISSN
1019-7168
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