Numerical Simulation of Transitional Flow Past a Wing Using Flux Reconstruction Method

Abstract

In this paper, the capabilities of a high-order flux reconstruction scheme for the implicit large-eddy simulations of a transitional flow at a low Reynolds number of 60,000 around the SD7003 wing are examined. This is the case posed in the First and Second International Workshops on the high-order computational fluid dynamics method held in 2012 and 2013. The correction function used in the flux reconstruction scheme is the Radau polynomial, which is equivalent to the discontinuous Galerkin scheme. A time-accurate implicit lower/upper symmetric Gauss–Seidel solution algorithm for the application of the flux reconstruction scheme to complex unsteady flows is developed, and it is found to be able to produce comparable results to the explicit Runge–Kutta scheme while achieving better computational efficiency. Simulations are carried out at and 8 deg with polynomials of degree , 2, and 3 resulting in second-, third-, and fourth-order-accurate flux reconstruction schemes, respectively. Two structured hexahedral O-grid domains that differ in the grid resolution in a circumferential direction on the upper surface of the wing are considered, with a maximum of 2,000,000 degrees of freedom for the fourth-order () simulations on the finer domain. The results are validated by comparison with many reference data obtained from various high-order schemes using time-accurate explicit/implicit methods. The results agree reasonably well. The developed method with the flux reconstruction scheme can be a reliable tool of implicit large-eddy simulations for low-Reynolds-number flows.