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.
翻译:在这项工作中,我们引入了一种假设性限制战略,即通过混合高顺序溶液和低顺序活性分解而制造的可压缩尤勒和纳维-斯托克斯等式的高序可不连续的加热金方法,这需要热力活性数量的假设性,以保障其稳妥性。在这项工作中,我们引入了一种假设性限制战略,即通过混合高顺序溶液和低顺序活性分解而制造的、低顺序溶解和低顺序活性分解。拟议的低顺序分解法是半分立的酶稳定,而拟议的限制战略是为可压缩尤勒和纳维埃-斯托克斯等式等式保准性。数字实验证实了拟议战略的高度顺序准确性和稳健性。