Entrainment and boundary-layer separation: a modeling history

Abstract

For many decades since Prandtl's presentation of the boundary-layer equations, all attempts to calculate separated boundary layers ended up in a break-down of the numerical algorithm. It was not until the late 1970s that the first successful calculations were reported. The paper describes the history and philosophy of the steps that led to understanding where the break-down originates and how to circumvent it. Especially, the role of Head's entrainment will be highlighted.

Quasi-simultaneous coupling methods for partitioned problems in computational hemodynamics

“…At locations where the flow in the boundary layer separates from the airfoil surface, the operator M 2 becomes singular [95,98,101]. As a result, one or more eigenvalues of the iteration operator M −1 2 M 1 , and hence the (equivalence of the) added-mass ratio, move towards infinity: the 'added-mass ratio' may even change sign.…”