Accurate transport algorithms are crucial for computational fluid dynamics and more accurate and efficient schemes are always in development. One dimensional limiting is a commonly employed technique used to suppress nonphysical oscillations. However, the application of such limiters can reduce accuracy. It is important to identify the weakest set of sufficient conditions required on the limiter as to allow the development of successful numerical algorithms. The main goal of this paper is to identify new less restrictive sufficient conditions for flux form in-compressible advection to remain monotonic. First, we identify conditions in which the Spekreijse limiter region can fail to be monotonic for incompressible flux form advection and demonstrate this numerically. Then a convex combination argument is used to derive new sufficient conditions that are less restrictive than the Sweby region for a discrete maximum principle. This allows the introduction of two new more general limiter regions suitable for flux form incompressible advection.

翻译：精确的输运算法对于计算流体动力学至关重要，且更精确高效的算法方案始终在发展中。一维限制是常用技术，用于抑制非物理振荡。然而，此类限制器的应用可能降低精度。识别限制器所需的最弱充分条件集对于开发成功的数值算法具有重要意义。本文主要目标是识别通量形式不可压缩平流保持单调性的新且限制性更弱的充分条件。首先，我们识别了Spekreijse限制器区域在不可压缩通量形式平流中可能失去单调性的条件，并通过数值实验加以验证。随后，采用凸组合论证推导出新的充分条件，该条件相比Sweby区域对离散最大原理的限制更弱。由此引入两种适用于通量形式不可压缩平流的更通用新型限制器区域。