Affordable, high order simulations of turbulent flows on unstructured grids for very high Reynolds’ number flows require wall models for efficiency. However, different wall models have different accuracy and stability properties. Here, we develop a kinetic energy stability estimate to investigate stability of wall model boundary conditions. Using this norm, two wall models are studied, a popular equilibrium stress wall model, which is found to be unstable and the dynamic slip wall model which is found to be stable. These results are extended to the discrete case using the Summation-by-parts (SBP) property of the discontinuous Galerkin method. Numerical tests show that while the equilibrium stress wall model is accurate but unstable, the dynamic slip wall model is inaccurate but stable.

对于非雷诺数很高的非结构化网格，要进行可承受的，高阶湍流模拟，需要使用壁模型来提高效率。但是，不同的墙模型具有不同的精度和稳定性。在这里，我们开发了一个动能稳定性估计值，以研究壁模型边界条件的稳定性。使用该规范，研究了两个墙模型，一个是流行的平衡应力墙模型，该模型被发现是不稳定的，另一个是动态滑墙模型，被发现是稳定的。使用不连续Galerkin方法的“部分求和”（SBP）属性将这些结果扩展到离散情况。数值试验表明，虽然平衡应力墙模型是准确的但不稳定的，而动力滑移墙模型是不准确的但稳定的。