Efficient method to compute full eigenspectrum of incompressible viscous flows: Application on two-layer rectinear flow
Korea–Australia Rheology Journal, 27 (3):
177--188 (Aug 1, 2015)DOI: 10.1007/s13367-015-0018-8
Abstract
An efficient algorithm based on the matrix transformation method (Valério et al., 2007) is presented for solving the generalized eigenvalue problem (GEVP) derived from linear stability analysis of incompressible viscous flow. The proposed method uses the formulation based on primitive variables, i.e. velocity and pressure, instead of streamfunction used by typical Orr-Sommerfeld equation. A series of matrix operations removes non-physical eigenvalues at infinity and leads to a non-singular smaller size eigenvalue problem (EVP), which contains full eigenspectrum, than the original GEVP. Two different solution strategies for the transformed EVP are proposed, and their accuracies are discussed. The proposed procedure is used to solve the stability of two layer rectilinear flow. The computed eigenspectrum are compared to previously reported values.