Tutorial Title: Metrics of High Performance Computing: Dispersion Relation by Spectral Analysis


Tapan K. Sengupta

09:10:00 - 10:20:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Over the last one decade, significant improvements have taken place which makes DNS possible, where some flows can be simulated from the onset of instability to fully developed turbulent stage. It is emphasized that this DNS is distinct from those practised by many in different disciplines, where governing equations are modified by many artifices. In this talk we explain how true DNS has been made possible by developing: (i) Spectral analysis tool for full domain; (ii) High accuracy compact difference scheme; (iii) A correct theory for error dynamics (replacing the celebrated von Neumann analysis) and (iv) Various upwind and adaptive multi-dimensional filters - all these have been developed at High Performance Computing Laboratory, IIT Kanpur slowly over the last decade. We will explain centrality of these concepts in developing the correct numerical dispersion relation and identify the major sources of errors. With the help of correct error propagation equation, one develops dispersion relation preserving (DRP) numerical methods for solving full Navier- Stokes equation. We will also discuss about various formulations of Navier-Stokes equation used for DNS of 2D and 3D flows. All the analysis tools developed are explained with the help of figures and animations showing various flow instabilities in internal and external flows, including DNS for 2D and 3D disturbance fields for turbulent flows. All these herald a beginning for DNS of transitional and turbulent flows.