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 based on convex limiting. The key ingredient in the limiting procedure is a low order positivity-preserving discretization based on graph viscosity terms. The proposed limiting strategy is both positivity preserving and discretely entropy-stable for the compressible Euler and Navier-Stokes equations. Numerical experiments confirm the high order accuracy and robustness of the proposed strategy.

翻译：在这项工作中,我们引入了基于 convex 限制的对可压缩的 Euler 和 Navier-Stokes 等式的高序诱导性可不连续的 Galerkin 方法,这需要热力量的假设性,以保障其稳妥性。在这项工作中,我们引入了基于 convex 限制的对可压缩的 Euler 和 Navier-Stokes 等式的对准性限制战略。限制程序的关键成分是基于图形粘度术语的低顺序相对性保持离散性。拟议的限制战略是,既保存正态性,又对可压缩的 Euler 和 Navier-Stokes 等式的离散性调节性。数字实验证实了拟议战略的高度顺序准确性和稳健。