标题： 利用傅里叶变换分析多维半离散Active Flux方法 显示英文标题

标题： Analysis of the multi-dimensional semi-discrete Active Flux method using the Fourier transform

摘要： Active Flux 的自由度包括单元平均值和单元边界上的点值，这些点值在相邻单元之间共享，从而产生全局连续的重构。半离散的 Active Flux 方法利用其自由度来获取用于点值更新的空间导数的有限差分近似。平均值通过通量的求积公式进行更新，并利用点值作为求积点。时间积分采用标准的龙格-库塔方法。我们证明了这种在二维和三维空间中对 Active Flux 方法的推广，在笛卡尔网格上对于线性声学是稳态保持的，并且分析了数值扩散和稳定性。 显示英文摘要

摘要： The degrees of freedom of Active Flux are cell averages and point values along the cell boundaries. These latter are shared between neighbouring cells, which gives rise to a globally continuous reconstruction. The semi-discrete Active Flux method uses its degrees of freedom to obtain Finite Difference approxi\-mations to the spatial derivatives which are used in the point value update. The averages are updated using a quadrature of the flux and making use of the point values as quadrature points. The integration in time employs standard Runge-Kutta methods. We show that this generalization of the Active Flux method in two and three spatial dimensions is stationarity preserving for linear acoustics on Cartesian grids, and present an analysis of numerical diffusion and stability.