论文标题
熵稳定，高阶逐个局部离散，而无需接口处罚
Entropy-stable, high-order summation-by-parts discretizations without interface penalties
论文作者
论文摘要
该论文介绍了由逐个组合（SBP）运算符构建的高阶精度，能量和熵稳定的离散化。值得注意的是，与以前使用不连续的SBP离散化的努力不同，离散化组装了全球SBP运营商并使用连续解决方案。研究基于衍生物的耗散和局部预测稳定（LPS）作为稳定基线离散化的选择。这些稳定在一个维度上等于乘法常数，但只有LPS仍适合一般的多维SBP操作员。此外，LPS能够利用$ 2P $对角色所需的其他节点，从而导致具有界光谱半径的元素 - 位置稳定。通过在熵变量上应用投影，可以轻松获得熵稳定的LPS版本。使用线性化和EULER方程的数值实验证明了稳定离散化的准确性，效率和鲁棒性，并且连续方法与更常见的不连续SBP方法进行了比较。
The paper presents high-order accurate, energy-, and entropy-stable discretizations constructed from summation-by-parts (SBP) operators. Notably, the discretizations assemble global SBP operators and use continuous solutions, unlike previous efforts that use discontinuous SBP discretizations. Derivative-based dissipation and local-projection stabilization (LPS) are investigated as options for stabilizing the baseline discretization. These stabilizations are equal up to a multiplicative constant in one dimension, but only LPS remains well conditioned for general, multidimensional SBP operators. Furthermore, LPS is able to take advantage of the additional nodes required by degree $2p$ diagonal-norms, resulting in an element-local stabilization with a bounded spectral radius. An entropy-stable version of LPS is easily obtained by applying the projection on the entropy variables. Numerical experiments with the linear-advection and Euler equations demonstrate the accuracy, efficiency, and robustness of the stabilized discretizations, and the continuous approach compares favorably with the more common discontinuous SBP methods.
