High-order entropy-stable discontinuous Galerkin methods for the compressible
Euler and Navier-Stokes equations require the positivity of thermodynamic
quantities in order to guarantee their well-posedness. In this work, we
introduce a positivity limiting strategy for entropy-stable discontinuous
Galerkin discretizations constructed by blending high order solutions with a
low order positivity-preserving discretization. The proposed low order
discretization is semi-discretely entropy stable, and the proposed limiting
strategy is positivity preserving for the compressible Euler and Navier-Stokes
equations. Numerical experiments confirm the high order accuracy and robustness
of the proposed strategy