Transient Semi-Circular Lid-Driven Cavity Flow using Non- Uniform Structured Grid Method with Upwind Scheme

Abstract

In this article, two-dimensional lid-driven cavity flow in a semi-circular cavity is simulated using a non-uniform finite different method with structured grid. NavierStokes and continuity equations are simplified using a non-dimensional streamfunctionvorticity approach. A Reynolds number of 1000 is used and the vorticity and streamfunction contour plot is monitored with convergence criteria of 1x10 -7 set to both the vorticity and the streamfunction value. The result shows that the primary vortex moves from the upper left cavity corner to the upper right corner, while the magnitude of the streamfunction grows at the primary vortex center. The primary vortex size decreases steadily as the time increases. This phenomenon is greatly affected by the increasing size of the secondary vortex at the lower left. Slight changes of vortex size are observed as the flow achieves a steady state condition. Validation of the simulation results shows the current value deviation from the established result is less than 5%. In future, it is recommended to use a better numerical method so that the simulation is more stable and so that the calculation time can be reduced.

Four-Sided Lid-Driven Cavity Flow using Time Splitting Method of Adams-Bashforth Scheme

“…The flow inside a square cavity has been widely used to demonstrate fluid flow using simple geometry. The flow structure in a one-sided lid-driven cavity problem has been reported by many researchers (Ghia, Ghia, & Shin, 1982;Idris, Ammar, Tuan Ya, & Amin, 2013;Idris, Irwan, & Ammar, 2012;Musa, Abdullah, Azwadi, & Zulkifli, 2011;Rosdzimin, Zuhairi, & Azwadi, 2010;Sidik & Attarzadeh, 2011). Later, research on different cavity geometries has been reported, such as a deep cavity (Patil, Lakshmisha, & Rogg, 2006), semi-circular cavity (Yang, Shi, Guo, & Sai, 2012), trapezoidal cavity (Zhang, Shi, & Chai, 2010) and triangular cavity (González, Ahmed, Kühnen, Kuhlmann, & Theofilis, 2011).…”