Positivity-preserving flux limiters for high-order conservative schemes

Details Positivity-preserving flux limiters for high-order conservative schemes Positivity-preserving flux limiters for high-order conservative schemes

2012-03-07

arxiv.org/abs/1203.1540v1

Physics

Fluid Dynamics

Scientific paper

In this work a very 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. Similarly to previous works a restrictive time-step size condition is required to maintain the formal order of accuracy. The time-step limit can be relaxed largely, however, if only preserving positivity is of concern. A number of numerical examples suggest that this method can be used to prevent positivity failure when the flow involves vacuum or near vacuum and very strong discontinuities.

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