Disturbance region update method with preconditioning for steady compressible and incompressible flows

Abstract

The disturbance region update method (DRUM) was an acceleration methodology devoted to steady compressible flows. In this work, we develop DRUM for steady incompressible flows, named the disturbance region update method with preconditioning (DRUM-P). Compared with the conventional global update method (GUM), DRUM-P adopts the advective and the viscous dynamic computational domains (DCDs) updated with the time-marching process to achieve a computational speedup for compressible and incompressible flows. When DRUM is extended to incompressible flows, the stiffness of the governing equations would slow down the convergence to the steady state and thus delay the contraction of the DCDs. By employing the local preconditioning technique, DRUM-P overcomes those difficulties and exploits the full convergence potential of DRUM for incompressible flows. Besides, the operation of contracting the advective DCD is modified in subsonic flows, where the advective DCD is allowed to contract from the downstream before the upstream. A new viscous-dominated criterion of the viscous DCD based on the total pressure loss and the total enthalpy loss is proposed to improve accuracy in practical cases with complex geometric shapes and flow features. Eight test cases demonstrate the efficiency and accuracy of DRUM-P. Firstly, DRUM-P achieves remarkable convergence efficiency for solving compressible and incompressible flows, especially the compressible and incompressible mixed flows, e.g., the flow over high-lift configuration. The acceleration ability benefits from the preconditioning technique, the two high-flexible DCDs, and the modified operation of the advective DCD. Secondly, the numerical results obtained by DRUM-P are in excellent agreement with those obtained by GUM. Moreover, the numerical results verify that the proposed viscous-dominated criterion is grid-independent and more accurate in practical cases.