Abstract The primary contribution of this article is a linear stability analysis of the two-dimensional Cartesian grid Active Flux method. For the advection equation we show that stability for CFL ≤ 1 requires a more accurate flux computation than previously assumed. For the acoustic equations we confirm the expected stability for CFL ≤ 1 2 . Furthermore, we introduce a nonlinear limiting based on a bound preserving multi-dimensional reconstruction. Numerical results for advection and Burgers’ equation illustrate the performance of this limiting technique.

中文翻译：

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笛卡尔网格有源通量方法：线性稳定性和边界保持限制

摘要 本文的主要贡献是二维笛卡尔网格有源通量方法的线性稳定性分析。对于平流方程，我们表明 CFL ≤ 1 的稳定性需要比之前假设的更准确的通量计算。对于声学方程，我们确认了 CFL ≤ 1 2 的预期稳定性。此外，我们引入了基于边界保留多维重建的非线性限制。对流和伯格斯方程的数值结果说明了这种限制技术的性能。