The stability of the axisymmetric incompressible Newtonian flow in an annular pipe suddenly expanding radially inward is investigated. The axisymmetric steady basic flow is discretized using primitive variables and second-order finite volumes on a staggered grid. The resulting algebraic equations are solved by Newton–Raphson iteration. A three-dimensional global linear stability analysis is performed. The solutions to the linear stability problem are represented by normal modes. The generalized eigenvalue problem is solved using an implicitly restarted Arnoldi algorithm which is provided by the ARPACK library and a Cayley transformation. Stability boundaries have been computed for a range of parameters varying the outlet radius ratio. The physical instability mechanisms are studied by a an posteriori analysis of the kinetic energy transferred between the basic state and the critical mode. Neutral curves and critical modes are presented and the instability mechanisms are discussed.

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