Positivity-preserving flux limiters for high-order conservative schemes

X. Y. Hu; N. A. Adams; C. -W. Shu

doi:10.1016/j.jcp.2013.01.024

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arXiv · 1203.1540

Positivity-preserving flux limiters for high-order conservative schemes

X. Y. Hu·N. A. Adams·C. -W. Shu

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Abstract

In this work a simple method to enforce the positivity-preserving property for general high-order conservative schemes is proposed. The method keeps the original scheme unchanged and detects critical numerical fluxes which may lead to negative density and pressure, and then imposes a cut-off flux limiter to satisfy a sufficient condition for preserving positivity. Though an extra time-step size condition is required to maintain the formal order of accuracy, it is less restrictive than those in previous works. A number of numerical examples suggest that this method, when applied on an essentially non-oscillatory base scheme, can be used to prevent positivity failure when the flow involves vacuum or near vacuum and very strong discontinuities.

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X. Y. Hu, N. A. Adams, C. -W. Shu. 2012-03-07. Positivity-preserving flux limiters for high-order conservative schemes. https://doi.org/10.1016/j.jcp.2013.01.024

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