Efficiency and accuracy of time-accurate turbulent Navier-Stokes computations

Abstract

The accuracy and efficiency of two types of subiterations in both explicit and implicit Navier-Stokes codes are explored for unsteady laminar circular-cylinder flow and unsteady turbulent flow over an 18-percent-thick circular-arc (biconvex) airfoil. Grid and time-step studies are used to assess the numerical accuracy of the methods. Nonsubiterative time-stepping schemes and schemes with physical time subiterations are subject to time-step limitations in practice that are removed by pseudo time subiterations. Computations for the circular-arc airfoil indicate that a one-equation turbulence model predicts the unsteady separated flow better than an algebraic turbulence model; also, the hysteresis with Mach number of the self-excited unsteadiness due to shock and boundary-layer separation is well predicted.ations to advance the equations of motion in a time-accurate manner. Two approaches to performing sub-code CFL3D % are both used in conjunction with subiter-*Senior Member AIAA. ?Associate Fellow AIAA.

Numerical investigation of the compressible flow past an aerofoil

“…McDevitt et al 1976;Levy 1978;Marvin et al 1980). Since the frequency is greatly sensitive to the grid resolution and time step (Rumsey et al 1996), the agreement between the numerical result and the previous experimental data also verifies the reliability of the present simulation as described above. The location of shock wave motion along the surface is shown in figure 9(a), where t * represents the fractional cyclic time during one period, and t * = 0 is taken as the Mach number ahead of shock wave, where the solid line and the symbol respectively represent computational result and experimental data (Marvin et al 1980).…”

“…type A, B and C. Previous experimental studies of transonic flow over an 18 % thick circular-arc aerofoil at zero incidence have indicated that upstream-propagating shock waves occur alternately on the upper and lower surfaces for a certain range of the free-stream Mach number (McDevitt, Levy & Deiwert 1976;Levy 1978;McDevitt 1979;Marvin, Levy & Seegmiller 1980), which belongs to type C. Moreover, some numerical simulations have been performed using the time-dependent twodimensional Reynolds-averaged Navier-Stokes (RANS) equations with turbulence models (e.g. Marvin et al 1980;Rumsey et al 1996;Xiao, Tsai & Liu 2003). A zonal detached-eddy simulation (DES) method has also been used to predict the buffet phenomenon on a supercritical aerofoil (Deck 2005).…”

Numerical Study of Transonic Buffet on a Supercritical Airfoil

“…When marching in pseudotime, this method permits the use of acceleration techniques such as local time step and multigrid to speed up the steady flows calculations. The application of dual-time stepping method of self-excited flow includes Rumsey et al 3 and Oliver et al 5 for the 18% circular-arc airfoil.…”

Detached Eddy Simulation of Base Flow in Supersonic Mainstream

“…대류 플럭스항은 일반 좌표계에서 Roe FDS 기법을 사용하여 차분하였으며, 5차 MUSCL-TVD 기법 [13,14]을 이용하여 고차의 공 간차분 정확도를 유지하였다. 비정상 문제의 고 차 시간 정확도 해석 수행을 위하여 2차 정확도 의 Euler 후방 차분 및 이중 시간 부반복 (dual time sub-iteration)을 이용한 완전 내재적 기법을 물리적 시간에 적용하였다 [15].…”