A New Robust Carbuncle-Free Roe Scheme for Strong Shock

A New Robust Carbuncle-Free Roe Scheme for Strong Shock J Sci Comput https://doi.org/10.1007/s10915-018-0747-1 A New Robust Carbuncle-Free Roe Scheme for Strong Shock 1 1 1 Shu-sheng Chen · Chao Yan · Bo-xi Lin · Yan-su Li Received: 18 April 2017 / Revised: 13 May 2018 / Accepted: 26 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract The paper devises a new robust carbuncle-free Roe Riemann solver for strong shock, different from hybrid method, entropy fix, Liou’s conjecture (J Comput Phys 160:623–648, 2000) and artificial viscosity (Rodionov in J Comput Phys 345:308–329, 2017). Roe scheme encounters carbuncle phenomenon, violates entropy condition and lacks positiv- ity property. The remedy integrates shear viscosity into momentum flux to damp undesirable perturbation and prevents unstable vorticity mode from triggering shock instability. Com- pared to HLL scheme, shear viscosity is properly established through dimensional analysis and analogy method. The non-linear wave speeds are slightly modified by incorporating the neighboring cell information for positive conservation. The pressure-based sensing function is applied to preserve shear layer while keeping shock robustness. The resulting scheme is very easily implemented by converting the existing Roe code. The matrix stability analysis confirms that this approach is shock-stable and more robust than entropy fix. A series http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Scientific Computing Springer Journals

A New Robust Carbuncle-Free Roe Scheme for Strong Shock

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Algorithms; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Theoretical, Mathematical and Computational Physics
ISSN
0885-7474
eISSN
1573-7691
D.O.I.
10.1007/s10915-018-0747-1
Publisher site
See Article on Publisher Site

Abstract

J Sci Comput https://doi.org/10.1007/s10915-018-0747-1 A New Robust Carbuncle-Free Roe Scheme for Strong Shock 1 1 1 Shu-sheng Chen · Chao Yan · Bo-xi Lin · Yan-su Li Received: 18 April 2017 / Revised: 13 May 2018 / Accepted: 26 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract The paper devises a new robust carbuncle-free Roe Riemann solver for strong shock, different from hybrid method, entropy fix, Liou’s conjecture (J Comput Phys 160:623–648, 2000) and artificial viscosity (Rodionov in J Comput Phys 345:308–329, 2017). Roe scheme encounters carbuncle phenomenon, violates entropy condition and lacks positiv- ity property. The remedy integrates shear viscosity into momentum flux to damp undesirable perturbation and prevents unstable vorticity mode from triggering shock instability. Com- pared to HLL scheme, shear viscosity is properly established through dimensional analysis and analogy method. The non-linear wave speeds are slightly modified by incorporating the neighboring cell information for positive conservation. The pressure-based sensing function is applied to preserve shear layer while keeping shock robustness. The resulting scheme is very easily implemented by converting the existing Roe code. The matrix stability analysis confirms that this approach is shock-stable and more robust than entropy fix. A series

Journal

Journal of Scientific ComputingSpringer Journals

Published: Jun 1, 2018

References

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