High-order methods for conservation laws can be very efficient, in particular on modern hardware. However, it can be challenging to guarantee their stability and robustness, especially for under-resolved flows. A typical approach is to combine a well-working baseline scheme with additional techniques to ensure invariant domain preservation. To obtain good results without too much dissipation, it is important to develop suitable baseline methods. In this article, we study upwind summation-by-parts operators, which have been used mostly for linear problems so far. These operators come with some built-in dissipation everywhere, not only at element interfaces as typical in discontinuous Galerkin methods. At the same time, this dissipation does not introduce additional parameters. We discuss the relation of high-order upwind summation-by-parts methods to flux vector splitting schemes and investigate their local linear/energy stability. Finally, we present some numerical examples for shock-free flows of the compressible Euler equations.

翻译：守恒律的高阶方法在现代硬件上可以非常高效，然而保证其稳定性和鲁棒性具有挑战性，尤其在欠分辨流动中。典型方法是将性能良好的基础格式与额外技巧结合以确保不变域保持性。为在不过度耗散的情况下获得良好结果，开发合适的基础方法至关重要。本文研究此前主要应用于线性问题的迎风求和分部算子。与间断伽辽金方法仅在单元界面处引入耗散不同，这类算子自带全局固有耗散，且无需引入额外参数。我们讨论了高阶迎风求和分部法与通量矢量分裂法的关联，并研究其局部线性/能量稳定性。最后给出可压缩欧拉方程无激波流动的数值算例。