![Fig. 11 Numerical Schlieren contours computed in this work (top) and obtained by experiments of Sembian et al. [48] (bottom) for the shock-wave interaction with a water column at M = 2.4](https://www.researchgate.net/publication/356083440/figure/fig19/AS:1088525088882707@1636536013933/Numerical-Schlieren-contours-computed-in-this-work-top-and-obtained-by-experiments-of_Q320.jpg)
![Plots of density a1ρ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_{1} \rho _{1}$$\end{document} for the isolated sharp-material interface at t=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t=2$$\end{document} obtained with WENO3 and CWENO3 schemes, and compared with the reference exact solution. It can be noticed that the the WENO3 is producing some oscillations near the material interface, while they are absent from the CWENO3 obtained solution](https://www.researchgate.net/publication/356083440/figure/fig2/AS:1088462535041026@1636521099912/Plots-of-density-a1r1documentclass12ptminimal-usepackageamsmath_Q320.jpg)
![Plots of density a1ρ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_{1} \rho _{1}$$\end{document}, pressure and velocity for the isolated sharp-material interface at t=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t=2$$\end{document} obtained with the CWENO3 scheme with primitive and conservative variables reconstruction, and comparison with the exact solution. The primitive variable reconstruction is producing an oscillation-free solution for both pressure and velocity](https://www.researchgate.net/publication/356083440/figure/fig3/AS:1088462535041027@1636521099985/Plots-of-density-a1r1documentclass12ptminimal-usepackageamsmath_Q320.jpg)
![Plot of density a1ρ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_{1} \rho _{1}$$\end{document}, pressure and velocity for the isolated sharp-material interface at t=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t=2$$\end{document} obtained with several CWENO schemes where it can be noticed that all the schemes provide the correct solution with no oscillations, and normalised pressure and velocity error at the t=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t=2$$\end{document} where it can be seen that the minute oscillations are close to machine precision](https://www.researchgate.net/publication/356083440/figure/fig4/AS:1088462539231241@1636521100225/Plot-of-density-a1r1documentclass12ptminimal-usepackageamsmath_Q320.jpg)
December 2021
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311 Reads
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44 Citations
Journal of Scientific Computing
In this paper we extend the application of unstructured high-order finite-volume central-weighted essentially non-oscillatory (CWENO) schemes to multicomponent flows using the interface capturing paradigm. The developed method achieves high-order accurate solution in smooth regions, while providing oscillation free solutions at discontinuous regions. The schemes are inherently compact in the sense that the central stencils employed are as compact as possible, and that the directional stencils are reduced in size, therefore simplifying their implementation. Several parameters that influence the performance of the schemes are investigated, such as reconstruction variables and their reconstruction order. The performance of the schemes is assessed under a series of stringent test problems consisting of various combinations of gases and liquids, and compared against analytical solutions, computational and experimental results available in the literature. The results obtained demonstrate the robustness of the new schemes for several applications, as well as their limitations within the present interface-capturing implementation.