论文标题
主动通量扩展到任意准确性顺序
Extensions of Active Flux to arbitrary order of accuracy
论文作者
论文摘要
Active Flux是最近开发的用于双曲线保护定律的数值方法。它的经典自由度是细胞界面处的细胞平均值和点值。后者在相邻细胞之间共享，导致全球连续重建。点值的更新包括上风，但没有解决Riemann问题。单元平均值的更新需要在单元格接口处进行通量正交，可以使用点值立即执行。本文探讨了主动通量的不同扩展到任意高度准确性，同时保持了全球连续性的想法。我们建议在保持相同的自由度的同时增加模板，或者增加点值的数量，或者包括更高的矩作为新的自由度。这些扩展具有不同的特性，并反映了有限体积，有限差异和有限元方法的家族的关系的不同看法。
Active Flux is a recently developed numerical method for hyperbolic conservation laws. Its classical degrees of freedom are cell averages and point values at cell interfaces. These latter are shared between adjacent cells, leading to a globally continuous reconstruction. The update of the point values includes upwinding, but without solving a Riemann Problem. The update of the cell average requires a flux quadrature at the cell interface, which can be immediately performed using the point values. This paper explores different extensions of Active Flux to arbitrarily high order of accuracy, while maintaining the idea of global continuity. We propose to either increase the stencil while keeping the same degrees of freedom, or to increase the number of point values, or to include higher moments as new degrees of freedom. These extensions have different properties, and reflect different views upon the relation of Active Flux to the families of Finite Volume, Finite Difference and Finite Element methods.
