Numerical Methods- DNS & LES
The major thrust of all activity is geared towards developing high accuracy computing methods for DNS and LES using finite difference methods.
Higher Order Explicit Upwinding Methods: In the first phase, during 1988- 2000, the activities were focused on developing and using explicit higher order upwinding schemes for solving unsteady flow problems. Some representative works were reported in:
- Sengupta & Sengupta (1994) solved the bluff-body flow past a circular cylinder using a 3rd order upwind scheme. Spectral analysis of the scheme was also presented to show the spectral accuracy and numerical dissipation of the scheme. A brief introduction to spectral analysis is provided here below that enabled us to view explicit schemes.
Details of the spectral method of analysis as developed under Prof. Sengupta’s guidance at IIT Kanpur is now available in the book:
Foundation of Computational Fluid Dynamics: Tapan Kumar Sengupta, Universities Press, Hyderabad (India), 2004.
- In Sengupta & Nair (1997) flow past elliptic cylinder was studied using 3rd and 5th order upwind schemes. Some of the properties of explicit schemes were compared in this paper.
The numerical aspect of work on explicit upwinding schemes was summarized in IJNMF paper, where the connection between higher order upwind schemes was established with LES.
High Accuracy Compact Schemes :
After 2001, Prof. Sengupta and his associates have started working in the area of compact difference schemes. A host of new schemes have been developed that have been presented, published and used for solving flow problems. In fact, this is the major tool that has been used for most of the high accuracy computing performed in the CFD lab under the guidance of Prof. Sengupta since 2001. In developing new schemes and their interpretation, once again the spectral framework is adopted. A brief description of this follows:
Some representative schemes have been analyzed and reported in Sengupta et al. (JCP, vol. , pp (2003)) and details on CD schemes have been discussed in chapter 11 of the book: Foundation of CFD by T.K. Sengupta (2004).
Typical results of such an analysis are shown below:
THESE ARE ALL STABLE SCHEMES AS COMPARED TO THE OTHER SCHEMES SHOWN BEFORE. THESE SCHEMES ALSO HAVE MORE SPECTRAL RESOLUTION.
SOME APPLICATIONS OF THESE SCHEMES WILL BE SHOWN ELSEWHERE.