Numerical simulation of shear layer instability using a scheme with ninth-order multioperator approximations

Double shear layer evolution on the non-uniform computational mesh

“…For the parameters defining the initial velocity field, the following values are set: n = 6 (harmonics with the maximum growth rate). Following [37] the calculation of the flow is carried out at Reynolds number Re = 4 × 10 5 , determined by the characteristic size of the computational domain.…”

“…Basing on the dimensionless wavenumber α = 4πn/r, one can determine dimensionless growth rate γ versus D shown in (figure 19) along with results of [36,37] reconstructed from from the graphs. Within one series, the change in γ relative to the initial value on a uniform grid is (γ − γ D2.0 )/γ D2.0 = 2.69 × 10 −2 (256 2 ), 6.4 × 10 −3 (512 2 ), 4.18 × 10 −3 (1024), 4 × 10 4 (2048 2 ), where the values of growth rate at the maximum D = 2.0are, respectively, γ = 0.37199 (256 2 ), 0.368 31 (512 2 ), 0.367 22 (1024 2 ), 0.366 58 (2048 2 ).…”

“…The dispersion curve is a continuous function, however, due to the limitations of the periodicity, we are dealing only with a discrete set of modes. The growth rate of discrete harmonics n = 1 − 12 were obtained in [37] using a high-order accuracy method. The harmonics n = 6 is closest to the maximum point of the dispersion curve, thus, in the paper it is designated as the fastest growing mode.…”