Abstract In this article, a new modified skew upwind differencing scheme (MSUDS) for convective flow is presented. This scheme is tested by pure advection test cases such as Step, Sine-square, Semi-ellipse, and Smith-Hutton test profiles. The benchmark lid-driven cavity flow problem is also solved with this MSUDS scheme. All the results are well plotted and validated. All the data regarding overshoots/undershoots are presented in tabular form for each test case. The maximum value of overshoot/undershoot using this scheme is of the order of about which is quite insignificant and that may be smoothened during iteration. The presented MSUDS scheme offers a range of choices depending on the convection problem. It is observed that the results obtained with the application of the presented MSUDS scheme is as good as that obtained with the other schemes such as high resolution equi-gradient scheme and higher order schemes developed till so far for solving convection problems. Its implementation is simple with less computational effort.

中文翻译：

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一种新的改进的对流逆风差分方案

摘要 在本文中，提出了一种新的改进的对流逆风差分方案（MSUDS）。该方案通过纯平流测试用例（例如 Step、Sine-square、Semi-ellipse 和 Smith-Hutton 测试配置文件）进行测试。该 MSUDS 方案也解决了基准盖驱动腔流动问题。所有的结果都很好地绘制和验证。对于每个测试用例，所有关于过冲/下冲的数据都以表格形式呈现。使用该方案的过冲/下冲的最大值大约是非常微不足道的数量级，并且可以在迭代过程中平滑。所提出的 MSUDS 方案根据对流问题提供了一系列选择。可以看出，应用所提出的 MSUDS 方案获得的结果与使用其他方案获得的结果一样好，例如高分辨率等梯度方案和迄今为止为解决对流问题而开发的高阶方案。它的实现很简单，计算量更少。