Why is DNS more computationally expensive than k-ε?

In summary, DNS is more computationally expensive because it requires resolving all length and time scales, while models like the k-epsilon model only require resolving the mean turbulence structures.
  • #1
humphreybogart
22
1
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
 
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  • #2
Simply put: in DNS, you need to resolve all the length and time scales. In Large Eddy Simulations, you resolve the largest scales and you have a model for the small ones (all scales smaller than the grid size are modeled). In Reynolds Stress Models, you have a lumped model for all turbulence scales and you assume that turbulence is governed by a single length and time scale. That is why for k-epsilon simulations, you only need to resolve the mean turbulence structures.
 

1. Why is DNS more computationally expensive than k-ε?

DNS (Direct Numerical Simulation) is more computationally expensive than k-ε turbulence modeling because it solves the Navier-Stokes equations directly without any simplifications or assumptions. This means that DNS requires a much finer resolution for accurate results, leading to a larger number of grid points and longer computation times.

2. What is the difference between DNS and k-ε turbulence modeling?

The main difference between DNS and k-ε turbulence modeling is the level of complexity in their respective approaches to solving the Navier-Stokes equations. DNS solves the equations directly without any assumptions, while k-ε turbulence modeling uses simplified equations and models to approximate the turbulent flow.

3. How does the computational cost of DNS compare to k-ε?

The computational cost of DNS is significantly higher than k-ε turbulence modeling. This is because DNS requires a much finer grid resolution to accurately capture the turbulent flow, leading to a larger number of grid points and longer computation times.

4. Why is DNS still used despite its high computational cost?

DNS is still used because it provides the most accurate results for turbulent flows. It is often used in fundamental research and for benchmarking other turbulence models. As computers become more powerful, the computational cost of DNS is becoming more manageable.

5. Are there any alternatives to DNS and k-ε turbulence modeling?

Yes, there are several other turbulence models that are less computationally expensive than DNS but more complex than k-ε. These include large eddy simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) models. These models strike a balance between accuracy and computational cost and are often used in practical engineering applications.

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