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arXiv · 1811.11108

Artificial viscosity to cure the shock instability in high-order Godunov-type schemes

Alexander V. Rodionov
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Abstract

The artificial viscosity approach for curing the carbuncle phenomenon (a numerical problem, also known as the shock instability) in shock-capturing methods has been recently presented and successfully tested on the first-order schemes in two- and three-dimensional simulations. The present study extends the proposed approach to the case of using high-order Godunov-type schemes. Several implementations of well-known schemes were selected for the study. They involve the MUSCL and WENO data reconstructions in space along with the Runge-Kutta and Hancock-type time stepping techniques. Numerous computations of the Quirk-type test problems and other popular tests were performed to examine and tune the artificial viscosity approach as applied to the selected schemes. As a result of this study (1) the principal coefficient in the artificial viscosity model was adjusted and (2) some methodological suggestions for substantial weakening of the post-shock oscillations were stated.

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Alexander V. Rodionov. 2018-12-24. Artificial viscosity to cure the shock instability in high-order Godunov-type schemes. https://arxiv.org/abs/1811.11108

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