论文标题
非线性问题的主动通量方案
The Active Flux scheme for nonlinear problems
论文作者
论文摘要
活动通量方案是有限体积方案，其沿细胞边界分布的其他点值。它是准确的三阶，不需要Riemann求解器。取而代之的是，给定重建，解决点值位置的初始值问题。然后，通过正交沿细胞边界的进化值获得互晶石通量。对于线性问题，确切的进化运算符可用，对于非线性问题，人们需要求助于近似进化运算符。本文在多个空间维度中为非线性双曲系统和非线性标量方程式提供了这种近似运算符。通过将波速估算到足够的准确性顺序来获得它们。此外，还引入了熵修复程序，并提出了新的限制策略。该方案的能力在各种平稳和不连续的设置上进行评估。
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.
