Positivity-preserving flux limiters for high-order conservative schemes

TL;DR

This paper introduces a simple flux limiter method that ensures positivity of density and pressure in high-order conservative schemes, effectively preventing negative values in challenging flow conditions.

Contribution

The proposed method preserves the original scheme's accuracy while effectively enforcing positivity without overly restrictive time-step constraints.

Findings

Prevents negative density and pressure in simulations involving vacuum.

Maintains high-order accuracy with a less restrictive time-step condition.

Effective for flows with strong discontinuities and near vacuum conditions.

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.