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Computation 2018, 6(2), 31; https://doi.org/10.3390/computation6020031

Application of High-Order Compact Difference Scheme in the Computation of Incompressible Wall-Bounded Turbulent Flows

1
Research Center for Applied Mechanics, School of Mechano-Electronic Engineering, Xidian University, Xi’an 710071, China
2
Key Laboratory of Mechanics on Disaster and Environment in Western China (Lanzhou University), Ministry of Education, Lanzhou 730000, China
*
Author to whom correspondence should be addressed.
Received: 6 March 2018 / Revised: 29 March 2018 / Accepted: 4 April 2018 / Published: 11 April 2018
(This article belongs to the Section Computational Engineering)
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Abstract

In the present work, a highly efficient incompressible flow solver with a semi-implicit time advancement on a fully staggered grid using a high-order compact difference scheme is developed firstly in the framework of approximate factorization. The fourth-order compact difference scheme is adopted for approximations of derivatives and interpolations in the incompressible Navier–Stokes equations. The pressure Poisson equation is efficiently solved by the fast Fourier transform (FFT). The framework of approximate factorization significantly simplifies the implementation of the semi-implicit time advancing with a high-order compact scheme. Benchmark tests demonstrate the high accuracy of the proposed numerical method. Secondly, by applying the proposed numerical method, we compute turbulent channel flows at low and moderate Reynolds numbers by direct numerical simulation (DNS) and large eddy simulation (LES). It is found that the predictions of turbulence statistics and especially energy spectra can be obviously improved by adopting the high-order scheme rather than the traditional second-order central difference scheme. View Full-Text
Keywords: incompressible Navier–Stokes equations; compact difference scheme; semi-implicit time advancement; staggered grid; wall-bounded turbulent flows incompressible Navier–Stokes equations; compact difference scheme; semi-implicit time advancement; staggered grid; wall-bounded turbulent flows
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Hu, R.; Wang, L.; Wang, P.; Wang, Y.; Zheng, X. Application of High-Order Compact Difference Scheme in the Computation of Incompressible Wall-Bounded Turbulent Flows. Computation 2018, 6, 31.

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