Natural grid stretching for DNS of compressible wall-bounded flows

Abstract

We propose a physics-driven stretching function for direct numerical simulation (DNS) of compressible turbulent wall-bounded flows, which blends uniform near-wall spacing with uniform resolution in terms of semi-local Kolmogorov units in the outer wall layer. Given target Mach number, Reynolds number and wall temperature, our procedure yields a well-defined prescription for the number of grid points and their distribution which guarantee at the same time numerical accuracy and judicious exploitation of computational resources. DNS of high-speed turbulent boundary layers are used to evaluate the quality of the proposed stretching function, which show that one can achieve identical results as with general-purpose stretching functions, however with substantially higher efficiency. A Python script is provided to facilitate implementation of the proposed grid stretching.