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A numerical model for the investigation of hydrodynamic stability of viscous incompressible shear flows in pipes of constant elliptic cross-section is proposed. The model is supplied with efficient algorithms for computing various hydrodynamic stability characteristics including the maximum possible amplification of the average kinetic energy density of disturbances and the so-called optimal disturbances. An efficient spectral reduction is also implemented, which allows one to eliminate spurious disturbances due to spatial approximation errors. The results of computing the maximum possible amplification of the average kinetic energy density of disturbances for pipes with different cross-sectional aspect ratios are presented.

Numerical model for the investigation of hydrodynamic stability of shear flows in pipes of elliptic cross-section