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动力学至关重要，更精确高效的格式始终处于发展之中。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至关重要。本文的主要目标是针对通量形式的不可压缩平流问题，确定新的、约束性更弱的单调性保持充分条件。我们首先识别了通量形式不可压缩平流保持单调性的额外必要条件，证明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区域约束更弱。基于此，我们提出了两个适用于通量形式不可压缩平流的、更广义的新型限制器区域。