Spectral Method in Turbulence — Lesson 1

This lesson covers the spectral method used in turbulence, a fundamental concept in fluid dynamics. It explains how to simulate hydrodynamic flow and compute energy transfer. The lesson also discusses the advantages and disadvantages of various methods such as finite difference, finite volume, finite elements, and vortex method, with a focus on the spectral method. It further elaborates on how to compute fluxes, the concept of Fourier transform, and the importance of energy transfer in different scales. The lesson also introduces the concept of Kolmogorov theory and explains how to solve equations in spectral space. Towards the end, it introduces the TARANG code developed for solving general PDE spectral problems.

Video Highlights

01:02 - Explanation of the spectral method for simulation and its advantages and disadvantages
04:12 - Discussion on the importance of choosing the right number of Fourier modes in the initial condition
09:21 - Explanation of the process of time stepping in the spectral method
24:51 - Discussion on the importance of computing the non-linear term in the spectral method
43:01 - Explanation of the process computing energy transfer in spectral method

Key Takeaways

- The spectral method captures scale by scale flows or flows at different scales.
- Fourier transform allows capturing the amplitude of the flow at different scales.
- The spectral method requires very idealized geometry and is not suitable for all types of flows.
- The method of collocation is used in the spectral method.
- The energy transfer from one Fourier mode to another is crucial in the spectral method.