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In the modelling of turbulent flows, DNS is often too computationally expensive.

Therefore, we take a 'statistical' approach and use mean flow equations, which require closure on account of the Reynolds stress. One way to do that is through the Eddy Viscosity Hypothesis, and one of the ways of determining this is "Eddy Viscosity" is the k-ε model.

Why is the former more computationally expensive than the latter? I know that for high Re, the smallest eddy sizes are very small – but don't you need to calculate the equations (Navier-Stokes or k-ε) at these small scales whether using DNS or k-ε?

Thanks

Therefore, we take a 'statistical' approach and use mean flow equations, which require closure on account of the Reynolds stress. One way to do that is through the Eddy Viscosity Hypothesis, and one of the ways of determining this is "Eddy Viscosity" is the k-ε model.

Why is the former more computationally expensive than the latter? I know that for high Re, the smallest eddy sizes are very small – but don't you need to calculate the equations (Navier-Stokes or k-ε) at these small scales whether using DNS or k-ε?

Thanks

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