Accuracy, efficiency and scalability of explicit and implicit FR/CPR schemes in large eddy simulation

Abstract

The accuracy, efficiency and scalability of explicit and implicit temporal schemes associated with FR/CPR spatial schemes are studied in the context of large eddy simulation. One low pressure turbine and one high pressure turbine blade cases with different Mach numbers and Reynolds numbers are employed in this study. The 3 stage SSP Runge–Kutta (RK) scheme is compared with implicit backward difference formulas (BDF) of first and second order accuracy with a non-linear LU-SGS solver in the present evaluation. Various factors such as inner convergence tolerance, the frequency of the implicit operator update, and the order of time accuracy are investigated for large eddy simulation. The implicit BDF2-LUSGS algorithm can achieve good time accuracy, and is more efficient than the 3rd order explicit RK scheme, but not as scalable on a small cluster. At a very low Mach number, the explicit scheme is clearly not adequate, suggesting the need for pre-conditioning and/or an implicit scheme.