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High-order entropy-stable discontinuous Galerkin methods for the compressibleEuler and Navier-Stokes equations require the positivity of thermodynamicquantities in order to guarantee their well-posedness. In this work, weintroduce a positivity limiting strategy for entropy-stable discontinuousGalerkin discretizations constructed by blending high order solutions with alow order positivity-preserving discretization. The proposed low orderdiscretization is semi-discretely entropy stable, and the proposed limitingstrategy is positivity preserving for the compressible Euler and Navier-Stokesequations. Numerical experiments confirm the high order accuracy and robustnessof the proposed strategy.

A positivity preserving strategy for entropy stable discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations