Almost all engineering CFD applications are turbulent, but one usually does not use DNS but RANS or LES simulations. Why are Direct Numerical Simulations of Turbulence so computationally expensive. Here are the notes: github.com/Ceyron/machine-lea...
Turbulence is one example of multiscale physics, physical phenomena where certain aspects appear in small spatial and temporal sizes and others in larger, with the big problem the different scales affect each other. Turbulence Closure Models in RANS and Subgrid Scale Models in LES are just examples of how one tries to alleviate the computational cost of resolving all scales.
In this video, we will investigate why Dircect Numerical Simulations (DNS) of Turbulence are often quoted as being on a complexity of O(Re³) with Re being the Reynolds number.
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Timestamps:
00:00 Introduction
01:06 What is Turbulence?
01:55 Multi-Scale Physics
02:51 Turbulence in Engineering
03:11 When is a flow turbulent?
04:20 The Reynolds Number
05:17 Convective and Diffusive Transport
06:48 Limit Cases: Euler & Stokes Equations
07:13 Non-Linear Convection causing turbulence
08:26 Transition to Turbulence
09:29 Computing the Reynolds Number
10:12 When is Re high?
12:05 Re for Engineering CFD
14:59 Measuring the scales of turbulence - Kolmogorov scales
16:49 Turbulence scales dictate discretization sizes
19:26 Assessing the computational cost
22:03 Explicit vs Implicit Timestepping
27:31 Total Cost of DNS Turbulence Simulation
29:18 Aerospace example
29:49 Top 500 fastest supercomputers
31:08 Computational Runtime
31:38 Design Exploration & Optimization
32:24 Moore's law
33:13 Electricity Consumption for Computation
33:58 Higher Re examples
34:40 Summary & Important Take-Away
34:57 Outro
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