TITLE:
A Simple Strategy for Capturing the Unstable Steady Solution of an Unsteady Flow
AUTHORS:
Weiwei Zhang, Yilang Liu, Jing Li
KEYWORDS:
Unstable Steady Solution, Real Time Step, Modeling, Unsteady Flows
JOURNAL NAME:
Open Journal of Fluid Dynamics,
Vol.5 No.2,
June
24,
2015
ABSTRACT: A simple strategy for capturing unstable steady solution is proposed in this paper. By enlarging the real time step, the unstable high frequency modes of the unsteady flow can be effectively suppressed because of the damping action on the real time level. The steady component will not be changed during real time marching. When the unsteady flow solution converges to a steady state, the partial derivatives of real time in unsteady governing equations will disappear automatically. The steady solution is the exacted unstable steady solution. The method is validated by the laminar flow past a circular cylinder and a transonic buffet of NACA0012 airfoil. This approach can acquire high-precision unstable steady solutions quickly and effectively without reducing the spatial discretization accuracy. This work provides the basis for unstable flow modeling and analysis.