Approximate Coordinate Transformations for Simulation of Turbulent Flows with Wall Deformation

In the present paper, approximate coordinate transformations for simulation of turbulent flows with wall deformation, significantly reducing computational cost with little degradation in numerical accuracy, are presented. The Wavier-Stokes equations are coordinate-transformed with an approximation of Tailor-series truncation. The performance is evaluated by performing numerical simulations of a channel flow at Re$\sub$$\tau$/ = 140 with active wall motions of η$\sub$m/$\^$+/ $\leq$5. The approximate transformations provide flow structures as well as turbulence statistics in good agreement with those from a complete transformation [Phys. Fluids 12, 3301 (2000) ] and allow 25-30% savings in the CPU time as compared to the complete one.