Accurate transport algorithms are crucial for computational fluid dynamics and more accurate and efficient schemes are always in development. One dimensional limiting is commonly employed 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. We identify additional necessary conditions for incompressible flux form advection to be monotonic, demonstrating that the Spekreijse limiter region is not sufficient for incompressible flux form advection to remain monotonic. 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力学至关重要，更精确、更高效的格式一直在不断发展。一维限制技术常被用于抑制非物理振荡，但此类限制器的应用可能降低计算精度。确定限制器所需的最弱充分条件集合对于开发成功的数值算法具有重要意义。本文的主要目标是针对通量形式不可压缩平流问题，识别新的、限制性更弱的单调性保持充分条件。我们首先确定了通量形式不可压缩平流保持单调性所需的额外必要条件，证明了Spekreijse限制器区域不足以保证通量形式不可压缩平流的单调性。随后，通过凸组合论证推导出新的充分条件，这些条件比满足离散最大值原理的Sweby区域限制更弱。基于此，我们提出了两个适用于通量形式不可压缩平流的、更普适的新限制器区域。