A new modified skew upwind differencing scheme for convective flows

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 ${10}^{-15},$ 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.

Disclosure statement

The author confirms that there is no any conflict of interest in this submitted work and there has been no any financial support for this work.