近年来，为了保证常微分方程解的一个全局泛函的保存，人们发展了各种逐次近似法。我们推广了这种方法来保证有限多凸函数(熵)的局部熵不等式，并将其应用于可压缩Euler方程和Navier-Stokes方程。基于采用部分求和和同时逼近项算符的熵保守或耗散半离散的非结构化hp自适应SSDC框架，我们针对可压缩的计算流体动力学开发了第一个离散化方法，该方法是主要保守的，局部熵在完全稳定的情况下稳定在通常的CFL条件下具有离散意义，除了每个元素具有单个标量方程的可并行求解之外，其他条件都是明确的，并且在时空上任意高阶精确。我们针对一组复杂性不断增加的测试案例展示了全离散显式局部熵稳定求解器的准确性和鲁棒性。

原文题目：Fully-Discrete Explicit Locally Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations

原文：Recently, relaxation methods have been developed to guarantee the preservation of a single global functional of the solution of an ordinary differential equation. We generalize this approach to guarantee local entropy inequalities for finitely many convex functionals (entropies) and apply the resulting methods to the compressible Euler and Navier-Stokes equations. Based on the unstructured hp-adaptive SSDC framework of entropy conservative or dissipative semidiscretizations using summation-by-parts and simultaneous-approximation-term operators, we develop the first discretizations for compressible computational fluid dynamics that are primary conservative, locally entropy stable in the fully discrete sense under a usual CFL condition, explicit except for the parallelizable solution of a single scalar equation per element, and arbitrarily high-order accurate in space and time. We demonstrate the accuracy and the robustness of the fully-discrete explicit locally entropy-stable solver for a set of test cases of increasing complexity.

原文作者：Hendrik Ranocha, Lisandro Dalcin, Matteo Parsani

原文地址：https://arxiv.org/abs/2003.08831