The primitive Orr-Sommerfeld equation and finite elements
(2021)Abstract
We consider solving the Orr–Sommerfeld equation of linear hydrodynamic stability theory by reverting to the linearized Navier–Stokes equation in velocity and pressure. This second order system can be discretized with simple Mini finite elements rather than the Hermite elements required for the classical fourth-order equation. On computing both solutions using scikit-fem, the primitive-Mini approach is revealed as simple, clear, well-conditioned, and very accurate.