The Active Flux scheme is a finite volume scheme with additional point values distributed along the cell boundary. It is third order accurate and does not require a Riemann solver. Instead, given a reconstruction, the initial value problem at the location of the point value is solved. The intercell flux is then obtained from the evolved values along the cell boundary by quadrature. Whereas for linear problems an exact evolution operator is available, for nonlinear problems one needs to resort to approximate evolution operators. This paper presents such approximate operators for nonlinear hyperbolic systems in one dimension and nonlinear scalar equations in multiple spatial dimensions. They are obtained by estimating the wave speeds to sufficient order of accuracy. Additionally, an entropy fix is introduced and a new limiting strategy is proposed. The abilities of the scheme are assessed on a variety of smooth and discontinuous setups.

中文翻译：

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非线性问题的有源通量方案

主动通量方案是有限体积方案，其附加点值沿单元边界分布。它是三阶精确的，不需要Riemann求解器。取而代之的是，在给定重构的情况下，解决了点值位置处的初始值问题。然后，通过沿正交方向从沿单元边界的演化值获得单元间通量。对于线性问题，可以使用精确的进化算子，而对于非线性问题，则需要求助于近似的进化算子。本文提出了一维非线性双曲系统的近似算子和多维空间维的非线性标量方程。通过将波速估计到足够的精度等级来获得它们。此外，引入了熵修正并提出了一种新的限制策略。