2.13. Grid Size and Computational Cost

Try these first

1. 1.

   Define Reynolds shear stress.

   Hint

   Think about its relationship to average velocities.

2. 2.

   What is the significance of Kolmogorov length scale in turbulence?

   Hint

   Consider its relation to grid size.

3. 3.

   What does Reynolds shear stress represent in fluid dynamics?

   • A. Viscous forces
   • B. Turbulent effects on mean flow
   • C. Gravitational forces
   • D. None of the above

   Hint

   Focus on its definition in turbulence modeling.

4. 4.

   True or False: The Kolmogorov length scale is the largest scale of turbulence.

   • True
   • False

   Hint

   Recall the definition of Kolmogorov scale.

5. 5.

   Given a turbulent flow with a Reynolds number of 10^5, calculate how many grid points would be required based on the relation derived (Re^9/4). Discuss feasibility in terms of computational power.

   Hint

   Consider the implications of needing such a large number of grid points.

6. 6.

   Develop a method for optimizing grid size in a DNS simulation of a turbulent flow where computational resources are limited. Outline your strategy.

   Hint

   Think about adapting grid sizes based on observed turbulence characteristics.