What is it about?
In the name of DNS i.e. solution of the Navier-Stokes equation, some researchers have been reporting results for the solution of turbulence problem with methods that are adulterated with artifiacts of hyper-viscosity etc. This paper shows that it is possible to solve the Navier-Stokes equation by analysing adopted numerical methods by global spectral analysis (GSA).
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Why is it important?
This and some additional papers cited in this, shows the true story of the solution of 2D Taylor-Green vortex problem by the pseudo-spectral method with higher order Runge-Kutta method. This also shows why 2D turbulence theory, that presupposes an inertial range, are not at all relevant to this problem. This heralds a new and correct direction for DNS.
Perspectives
We have recovered the lost ground of DNS by a true analysis technique, namely the GSA, for the periodic problems like homogeneous isotropic turbulence and Taylor-Green vortex. a correct guideline is established for DNS.
Professor Tapan Kumar Sengupta
Indian Institute of Technology Kanpur
Read the Original
This page is a summary of: Direct simulation of two-dimensional flows by pseudo-spectral method: Special features and validations by Taylor–Green vortex problem, Computers & Fluids, September 2025, Elsevier,
DOI: 10.1016/j.compfluid.2025.106754.
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