division into inner and outer zone

resolution requirements DNS (lecture 5)

$$t_{CPU,DNS}\propto Re^{9/4} = Re^{2.75}$$

observation: resolution requirements typically not homogeneous for flows with boundary layers

idea I: refined resolution estimate based on division into inner and outer region

idea II: reduce computational cost by modelling of inner region

LES with wall-functions

concept of wall-functions

1. employ default LES over entire domain
2. correct wall shear stress $\tau_w$ based on
   simplified laws (e.g., logarithmic law)

$\rightarrow \tau_w$ main source of error

some (rough) guidelines for meshing

• $30 < y^+ < 200$, $x^+\approx z^+ < 100$
• cell expansion ratio less than $10\%$

detached eddy simulation

some DES variants

• zonal DES (ZDES):
  user-defined division intro LES/RANS zones
• automated ZDES (ZDES):
  user-defined division intro LES/RANS zones simplified by precursor RANS simulation
• DES97:
  originally proposed DES; automatic division at runtime

even more variants

• delayed DES (DDES):
  DES without grid-induced separation (GIS)
• improved DDES (IDDES):
  possible switching between DDES and wall-modelled LES; improves log-layer mismatch

some (rough) guidelines for meshing

• $30 < y^+ < 200$ for (RANS) wall-functions
• $y^+ < 1$ without wall-functions
• no restrictions on $x^+$, $z^+$
• cell expansion ratio less than $10\%$

summary

• modelling of inner region reduces computational costs significantly
• WMLES: combination of LES and wall model
• DES: hybrid method with RANS region near the wall and LES for separated flow
• $t_{LES} > t_{WMLES} > t_{DES}$