Stabilization of explicit flow solvers using a proper orthogonal decomposition technique

A new numerical technique for the stabilization of explicit computational fluid dynamic (CFD) solvers is presented. When using CFD codes to solve practical problems, one sometimes finds the solution fails to converge due to the presence of a small number of eigenvalues of the flow solver outside the unit circle. In this paper, we use the proper orthogonal decomposition technique to estimate the unstable eigenvalues and eigenmodes of the flow solver as the solution diverges for linear problems, or exhibits limit cycle oscillations for nonlinear problems. We use the resulting eigen-information to construct a preconditioner that repositions the unstable eigenvalues from outside the unit circle to a point inside the unit close to the origin, resulting in a stable flow solver. In this work, the proposed method is applied to a nonlinear steady cascade solver. However, the technique can be easily applied to external flow solvers, and to unsteady frequency-domain (time-linearized and harmonic balance) flow solvers. Copyright © 2012 by Kivanc Ekici, Kenneth C. Hall and Huang Huang.

Duke Scholars

Author Kenneth C. Hall Thomas Lord Department of Mechanical Engineering and Materia ...

Author Jeffrey P. Thomas Thomas Lord Department of Mechanical Engineering and Materia ...