论文标题
剩余分布和主动通量公式的组合或一类新的方案，这些方案可以结合相同双曲问题的几种著作：应用于1d Euler方程
A combination of Residual Distribution and the Active Flux formulations or a new class of schemes that can combine several writings of the same hyperbolic problem: application to the 1D Euler equations
论文作者
论文摘要
我们展示了如何以一种自然的方式（即没有任何测试或切换）组合的保守和非保守的配方，该制度具有保守形式的双曲线系统。这是从两种不同类别的方案中启发的：剩余分布一个\ cite {MR4090481}和Active Flux配方\ Cite {AF1，AF3，AF3，AF4，AF4，AF5，ROEAF}。该解决方案在全球连续，并且如在活动通量方法中，通过点值和平均值的组合描述。与“经典”的活动通量方法不同，点心和牢房平均的自由度的含义不同，因此遵循不同形式的PDE：它是单元平均值的保守版本，对于点，可能是不保守的。事实证明，这种新的方案可以满足像定理这样的宽松的Wendroff。我们还开发了执行非线性稳定性的方法。我们说明了几个基准的行为，有些具有挑战性。
We show how to combine in a natural way (i.e. without any test nor switch) the conservative and non conservative formulations of an hyperbolic system that has a conservative form. This is inspired from two different class of schemes: the Residual Distribution one \cite{MR4090481}, and the Active Flux formulations \cite{AF1, AF3, AF4,AF5,RoeAF}. The solution is globally continuous, and as in the active flux method, described by a combination of point values and average values. Unlike the "classical" active flux methods, the meaning of the pointwise and cella averaged degrees of freedom is different, and hence follow different form of PDEs: it is a conservative version of the cell average, and a possibly non conservative one for the points. This new class of scheme is proved to satisfy a Lax-Wendroff like theorem. We also develop a method to perform non linear stability. We illustrate the behaviour on several benchmarks, some quite challenging.
