Application of High-Order Compact Difference Scheme in the Computation of Incompressible Wall-Bounded Turbulent Flows
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 fo...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2018-04-01
|
| Series: | Computation |
| Subjects: | |
| Online Access: | http://www.mdpi.com/2079-3197/6/2/31 |
| _version_ | 1819232265973006336 |
|---|---|
| author | Ruifeng Hu Limin Wang Ping Wang Yan Wang Xiaojing Zheng |
| author_facet | Ruifeng Hu Limin Wang Ping Wang Yan Wang Xiaojing Zheng |
| author_sort | Ruifeng Hu |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-23T11:58:07Z |
| format | Article |
| id | doaj.art-b7153765b74d4a989ddcf08100205c34 |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-12-23T11:58:07Z |
| publishDate | 2018-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj.art-b7153765b74d4a989ddcf08100205c342022-12-21T17:48:02ZengMDPI AGComputation2079-31972018-04-01623110.3390/computation6020031computation6020031Application of High-Order Compact Difference Scheme in the Computation of Incompressible Wall-Bounded Turbulent FlowsRuifeng Hu0Limin Wang1Ping Wang2Yan Wang3Xiaojing Zheng4Research Center for Applied Mechanics, School of Mechano-Electronic Engineering, Xidian University, Xi’an 710071, ChinaKey Laboratory of Mechanics on Disaster and Environment in Western China (Lanzhou University), Ministry of Education, Lanzhou 730000, ChinaKey Laboratory of Mechanics on Disaster and Environment in Western China (Lanzhou University), Ministry of Education, Lanzhou 730000, ChinaKey Laboratory of Mechanics on Disaster and Environment in Western China (Lanzhou University), Ministry of Education, Lanzhou 730000, ChinaResearch Center for Applied Mechanics, School of Mechano-Electronic Engineering, Xidian University, Xi’an 710071, ChinaIn 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.http://www.mdpi.com/2079-3197/6/2/31incompressible Navier–Stokes equationscompact difference schemesemi-implicit time advancementstaggered gridwall-bounded turbulent flows |
| spellingShingle | Ruifeng Hu Limin Wang Ping Wang Yan Wang Xiaojing Zheng Application of High-Order Compact Difference Scheme in the Computation of Incompressible Wall-Bounded Turbulent Flows Computation incompressible Navier–Stokes equations compact difference scheme semi-implicit time advancement staggered grid wall-bounded turbulent flows |
| title | Application of High-Order Compact Difference Scheme in the Computation of Incompressible Wall-Bounded Turbulent Flows |
| title_full | Application of High-Order Compact Difference Scheme in the Computation of Incompressible Wall-Bounded Turbulent Flows |
| title_fullStr | Application of High-Order Compact Difference Scheme in the Computation of Incompressible Wall-Bounded Turbulent Flows |
| title_full_unstemmed | Application of High-Order Compact Difference Scheme in the Computation of Incompressible Wall-Bounded Turbulent Flows |
| title_short | Application of High-Order Compact Difference Scheme in the Computation of Incompressible Wall-Bounded Turbulent Flows |
| title_sort | application of high order compact difference scheme in the computation of incompressible wall bounded turbulent flows |
| topic | incompressible Navier–Stokes equations compact difference scheme semi-implicit time advancement staggered grid wall-bounded turbulent flows |
| url | http://www.mdpi.com/2079-3197/6/2/31 |
| work_keys_str_mv | AT ruifenghu applicationofhighordercompactdifferenceschemeinthecomputationofincompressiblewallboundedturbulentflows AT liminwang applicationofhighordercompactdifferenceschemeinthecomputationofincompressiblewallboundedturbulentflows AT pingwang applicationofhighordercompactdifferenceschemeinthecomputationofincompressiblewallboundedturbulentflows AT yanwang applicationofhighordercompactdifferenceschemeinthecomputationofincompressiblewallboundedturbulentflows AT xiaojingzheng applicationofhighordercompactdifferenceschemeinthecomputationofincompressiblewallboundedturbulentflows |