---
_id: '7364'
abstract:
- lang: eng
  text: We present nsCouette, a highly scalable software tool to solve the Navier–Stokes
    equations for incompressible fluid flow between differentially heated and independently
    rotating, concentric cylinders. It is based on a pseudospectral spatial discretization
    and dynamic time-stepping. It is implemented in modern Fortran with a hybrid MPI-OpenMP
    parallelization scheme and thus designed to compute turbulent flows at high Reynolds
    and Rayleigh numbers. An additional GPU implementation (C-CUDA) for intermediate
    problem sizes and a version for pipe flow (nsPipe) are also provided.
article_number: '100395'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jose M
  full_name: Lopez Alonso, Jose M
  id: 40770848-F248-11E8-B48F-1D18A9856A87
  last_name: Lopez Alonso
  orcid: 0000-0002-0384-2022
- first_name: Daniel
  full_name: Feldmann, Daniel
  last_name: Feldmann
- first_name: Markus
  full_name: Rampp, Markus
  last_name: Rampp
- first_name: Alberto
  full_name: Vela-Martín, Alberto
  last_name: Vela-Martín
- first_name: Liang
  full_name: Shi, Liang
  id: 374A3F1A-F248-11E8-B48F-1D18A9856A87
  last_name: Shi
- first_name: Marc
  full_name: Avila, Marc
  last_name: Avila
citation:
  ama: Lopez Alonso JM, Feldmann D, Rampp M, Vela-Martín A, Shi L, Avila M. nsCouette
    – A high-performance code for direct numerical simulations of turbulent Taylor–Couette
    flow. <i>SoftwareX</i>. 2020;11. doi:<a href="https://doi.org/10.1016/j.softx.2019.100395">10.1016/j.softx.2019.100395</a>
  apa: Lopez Alonso, J. M., Feldmann, D., Rampp, M., Vela-Martín, A., Shi, L., &#38;
    Avila, M. (2020). nsCouette – A high-performance code for direct numerical simulations
    of turbulent Taylor–Couette flow. <i>SoftwareX</i>. Elsevier. <a href="https://doi.org/10.1016/j.softx.2019.100395">https://doi.org/10.1016/j.softx.2019.100395</a>
  chicago: Lopez Alonso, Jose M, Daniel Feldmann, Markus Rampp, Alberto Vela-Martín,
    Liang Shi, and Marc Avila. “NsCouette – A High-Performance Code for Direct Numerical
    Simulations of Turbulent Taylor–Couette Flow.” <i>SoftwareX</i>. Elsevier, 2020.
    <a href="https://doi.org/10.1016/j.softx.2019.100395">https://doi.org/10.1016/j.softx.2019.100395</a>.
  ieee: J. M. Lopez Alonso, D. Feldmann, M. Rampp, A. Vela-Martín, L. Shi, and M.
    Avila, “nsCouette – A high-performance code for direct numerical simulations of
    turbulent Taylor–Couette flow,” <i>SoftwareX</i>, vol. 11. Elsevier, 2020.
  ista: Lopez Alonso JM, Feldmann D, Rampp M, Vela-Martín A, Shi L, Avila M. 2020.
    nsCouette – A high-performance code for direct numerical simulations of turbulent
    Taylor–Couette flow. SoftwareX. 11, 100395.
  mla: Lopez Alonso, Jose M., et al. “NsCouette – A High-Performance Code for Direct
    Numerical Simulations of Turbulent Taylor–Couette Flow.” <i>SoftwareX</i>, vol.
    11, 100395, Elsevier, 2020, doi:<a href="https://doi.org/10.1016/j.softx.2019.100395">10.1016/j.softx.2019.100395</a>.
  short: J.M. Lopez Alonso, D. Feldmann, M. Rampp, A. Vela-Martín, L. Shi, M. Avila,
    SoftwareX 11 (2020).
date_created: 2020-01-26T23:00:35Z
date_published: 2020-01-17T00:00:00Z
date_updated: 2023-08-17T14:29:59Z
day: '17'
ddc:
- '000'
department:
- _id: BjHo
doi: 10.1016/j.softx.2019.100395
external_id:
  arxiv:
  - '1908.00587'
  isi:
  - '000552271200011'
file:
- access_level: open_access
  checksum: 2af1a1a3cc33557b345145276f221668
  content_type: application/pdf
  creator: dernst
  date_created: 2020-01-27T07:32:46Z
  date_updated: 2020-07-14T12:47:56Z
  file_id: '7365'
  file_name: 2020_SoftwareX_Lopez.pdf
  file_size: 679707
  relation: main_file
file_date_updated: 2020-07-14T12:47:56Z
has_accepted_license: '1'
intvolume: '        11'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-nd/4.0/
month: '01'
oa: 1
oa_version: Published Version
publication: SoftwareX
publication_identifier:
  eissn:
  - '23527110'
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: nsCouette – A high-performance code for direct numerical simulations of turbulent
  Taylor–Couette flow
tmp:
  image: /images/cc_by_nc_nd.png
  legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
  name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
    (CC BY-NC-ND 4.0)
  short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 11
year: '2020'
...
---
_id: '1494'
abstract:
- lang: eng
  text: Turbulence is one of the most frequently encountered non-equilibrium phenomena
    in nature, yet characterizing the transition that gives rise to turbulence in
    basic shear flows has remained an elusive task. Although, in recent studies, critical
    points marking the onset of sustained turbulence have been determined for several
    such flows, the physical nature of the transition could not be fully explained.
    In extensive experimental and computational studies we show for the example of
    Couette flow that the onset of turbulence is a second-order phase transition and
    falls into the directed percolation universality class. Consequently, the complex
    laminar–turbulent patterns distinctive for the onset of turbulence in shear flows
    result from short-range interactions of turbulent domains and are characterized
    by universal critical exponents. More generally, our study demonstrates that even
    high-dimensional systems far from equilibrium such as turbulence exhibit universality
    at onset and that here the collective dynamics obeys simple rules.
acknowledgement: We thank P. Maier for providing valuable ideas and supporting us
  in the technical aspects. Discussions with D. Barkley, Y. Duguet, B. Eckhart, N.
  Goldenfeld, P. Manneville and K. Takeuchi are gratefully acknowledged. We acknowledge
  the Deutsche Forschungsgemeinschaft (Project No. FOR 1182), and the European Research
  Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC
  Grant Agreement 306589 for financial support. L.S. and B.H. acknowledge research
  funding by Deutsche Forschungsgemeinschaft (DFG) under Grant No. SFB 963/1 (project
  A8). Numerical simulations were performed thanks to the CPU time allocations of
  JUROPA in Juelich Supercomputing Center (project HGU17) and of the Max Planck Computing
  and Data Facility (Garching, Germany). Excellent technical support from M. Rampp
  on the hybrid code nsCouette is appreciated.
author:
- first_name: Grégoire M
  full_name: Lemoult, Grégoire M
  id: 4787FE80-F248-11E8-B48F-1D18A9856A87
  last_name: Lemoult
- first_name: Liang
  full_name: Shi, Liang
  id: 374A3F1A-F248-11E8-B48F-1D18A9856A87
  last_name: Shi
- first_name: Kerstin
  full_name: Avila, Kerstin
  last_name: Avila
- first_name: Shreyas V
  full_name: Jalikop, Shreyas V
  id: 44A1D772-F248-11E8-B48F-1D18A9856A87
  last_name: Jalikop
- first_name: Marc
  full_name: Avila, Marc
  last_name: Avila
- first_name: Björn
  full_name: Hof, Björn
  id: 3A374330-F248-11E8-B48F-1D18A9856A87
  last_name: Hof
  orcid: 0000-0003-2057-2754
citation:
  ama: Lemoult GM, Shi L, Avila K, Jalikop SV, Avila M, Hof B. Directed percolation
    phase transition to sustained turbulence in Couette flow. <i>Nature Physics</i>.
    2016;12(3):254-258. doi:<a href="https://doi.org/10.1038/nphys3675">10.1038/nphys3675</a>
  apa: Lemoult, G. M., Shi, L., Avila, K., Jalikop, S. V., Avila, M., &#38; Hof, B.
    (2016). Directed percolation phase transition to sustained turbulence in Couette
    flow. <i>Nature Physics</i>. Nature Publishing Group. <a href="https://doi.org/10.1038/nphys3675">https://doi.org/10.1038/nphys3675</a>
  chicago: Lemoult, Grégoire M, Liang Shi, Kerstin Avila, Shreyas V Jalikop, Marc
    Avila, and Björn Hof. “Directed Percolation Phase Transition to Sustained Turbulence
    in Couette Flow.” <i>Nature Physics</i>. Nature Publishing Group, 2016. <a href="https://doi.org/10.1038/nphys3675">https://doi.org/10.1038/nphys3675</a>.
  ieee: G. M. Lemoult, L. Shi, K. Avila, S. V. Jalikop, M. Avila, and B. Hof, “Directed
    percolation phase transition to sustained turbulence in Couette flow,” <i>Nature
    Physics</i>, vol. 12, no. 3. Nature Publishing Group, pp. 254–258, 2016.
  ista: Lemoult GM, Shi L, Avila K, Jalikop SV, Avila M, Hof B. 2016. Directed percolation
    phase transition to sustained turbulence in Couette flow. Nature Physics. 12(3),
    254–258.
  mla: Lemoult, Grégoire M., et al. “Directed Percolation Phase Transition to Sustained
    Turbulence in Couette Flow.” <i>Nature Physics</i>, vol. 12, no. 3, Nature Publishing
    Group, 2016, pp. 254–58, doi:<a href="https://doi.org/10.1038/nphys3675">10.1038/nphys3675</a>.
  short: G.M. Lemoult, L. Shi, K. Avila, S.V. Jalikop, M. Avila, B. Hof, Nature Physics
    12 (2016) 254–258.
date_created: 2018-12-11T11:52:21Z
date_published: 2016-02-15T00:00:00Z
date_updated: 2021-01-12T06:51:08Z
day: '15'
department:
- _id: BjHo
doi: 10.1038/nphys3675
ec_funded: 1
intvolume: '        12'
issue: '3'
language:
- iso: eng
month: '02'
oa_version: None
page: 254 - 258
project:
- _id: 25152F3A-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '306589'
  name: Decoding the complexity of turbulence at its origin
- _id: 2511D90C-B435-11E9-9278-68D0E5697425
  grant_number: SFB 963  TP A8
  name: Astrophysical instability of currents and turbulences
publication: Nature Physics
publication_status: published
publisher: Nature Publishing Group
publist_id: '5685'
quality_controlled: '1'
scopus_import: 1
status: public
title: Directed percolation phase transition to sustained turbulence in Couette flow
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 12
year: '2016'
...
---
_id: '2030'
abstract:
- lang: eng
  text: A hybrid-parallel direct-numerical-simulation method with application to turbulent
    Taylor-Couette flow is presented. The Navier-Stokes equations are discretized
    in cylindrical coordinates with the spectral Fourier-Galerkin method in the axial
    and azimuthal directions, and high-order finite differences in the radial direction.
    Time is advanced by a second-order, semi-implicit projection scheme, which requires
    the solution of five Helmholtz/Poisson equations, avoids staggered grids and renders
    very small slip velocities. Nonlinear terms are evaluated with the pseudospectral
    method. The code is parallelized using a hybrid MPI-OpenMP strategy, which, compared
    with a flat MPI parallelization, is simpler to implement, allows to reduce inter-node
    communications and MPI overhead that become relevant at high processor-core counts,
    and helps to contain the memory footprint. A strong scaling study shows that the
    hybrid code maintains scalability up to more than 20,000 processor cores and thus
    allows to perform simulations at higher resolutions than previously feasible.
    In particular, it opens up the possibility to simulate turbulent Taylor-Couette
    flows at Reynolds numbers up to O(105). This enables to probe hydrodynamic turbulence
    in Keplerian flows in experimentally relevant regimes.
author:
- first_name: Liang
  full_name: Shi, Liang
  id: 374A3F1A-F248-11E8-B48F-1D18A9856A87
  last_name: Shi
- first_name: Markus
  full_name: Rampp, Markus
  last_name: Rampp
- first_name: Björn
  full_name: Hof, Björn
  id: 3A374330-F248-11E8-B48F-1D18A9856A87
  last_name: Hof
  orcid: 0000-0003-2057-2754
- first_name: Marc
  full_name: Avila, Marc
  last_name: Avila
citation:
  ama: Shi L, Rampp M, Hof B, Avila M. A hybrid MPI-OpenMP parallel implementation
    for pseudospectral simulations with application to Taylor-Couette flow. <i>Computers
    and Fluids</i>. 2015;106(1):1-11. doi:<a href="https://doi.org/10.1016/j.compfluid.2014.09.021">10.1016/j.compfluid.2014.09.021</a>
  apa: Shi, L., Rampp, M., Hof, B., &#38; Avila, M. (2015). A hybrid MPI-OpenMP parallel
    implementation for pseudospectral simulations with application to Taylor-Couette
    flow. <i>Computers and Fluids</i>. Elsevier. <a href="https://doi.org/10.1016/j.compfluid.2014.09.021">https://doi.org/10.1016/j.compfluid.2014.09.021</a>
  chicago: Shi, Liang, Markus Rampp, Björn Hof, and Marc Avila. “A Hybrid MPI-OpenMP
    Parallel Implementation for Pseudospectral Simulations with Application to Taylor-Couette
    Flow.” <i>Computers and Fluids</i>. Elsevier, 2015. <a href="https://doi.org/10.1016/j.compfluid.2014.09.021">https://doi.org/10.1016/j.compfluid.2014.09.021</a>.
  ieee: L. Shi, M. Rampp, B. Hof, and M. Avila, “A hybrid MPI-OpenMP parallel implementation
    for pseudospectral simulations with application to Taylor-Couette flow,” <i>Computers
    and Fluids</i>, vol. 106, no. 1. Elsevier, pp. 1–11, 2015.
  ista: Shi L, Rampp M, Hof B, Avila M. 2015. A hybrid MPI-OpenMP parallel implementation
    for pseudospectral simulations with application to Taylor-Couette flow. Computers
    and Fluids. 106(1), 1–11.
  mla: Shi, Liang, et al. “A Hybrid MPI-OpenMP Parallel Implementation for Pseudospectral
    Simulations with Application to Taylor-Couette Flow.” <i>Computers and Fluids</i>,
    vol. 106, no. 1, Elsevier, 2015, pp. 1–11, doi:<a href="https://doi.org/10.1016/j.compfluid.2014.09.021">10.1016/j.compfluid.2014.09.021</a>.
  short: L. Shi, M. Rampp, B. Hof, M. Avila, Computers and Fluids 106 (2015) 1–11.
date_created: 2018-12-11T11:55:18Z
date_published: 2015-01-01T00:00:00Z
date_updated: 2021-01-12T06:54:51Z
day: '01'
department:
- _id: BjHo
doi: 10.1016/j.compfluid.2014.09.021
intvolume: '       106'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1311.2481
month: '01'
oa: 1
oa_version: Preprint
page: 1 - 11
publication: Computers and Fluids
publication_status: published
publisher: Elsevier
publist_id: '5042'
quality_controlled: '1'
scopus_import: 1
status: public
title: A hybrid MPI-OpenMP parallel implementation for pseudospectral simulations
  with application to Taylor-Couette flow
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 106
year: '2015'
...
---
_id: '2829'
abstract:
- lang: eng
  text: Laminar-turbulent intermittency is intrinsic to the transitional regime of
    a wide range of fluid flows including pipe, channel, boundary layer, and Couette
    flow. In the latter turbulent spots can grow and form continuous stripes, yet
    in the stripe-normal direction they remain interspersed by laminar fluid. We carry
    out direct numerical simulations in a long narrow domain and observe that individual
    turbulent stripes are transient. In agreement with recent observations in pipe
    flow, we find that turbulence becomes sustained at a distinct critical point once
    the spatial proliferation outweighs the inherent decaying process. By resolving
    the asymptotic size distributions close to criticality we can for the first time
    demonstrate scale invariance at the onset of turbulence.
article_number: '204502'
arxiv: 1
author:
- first_name: Liang
  full_name: Shi, Liang
  id: 374A3F1A-F248-11E8-B48F-1D18A9856A87
  last_name: Shi
- first_name: Marc
  full_name: Avila, Marc
  last_name: Avila
- first_name: Björn
  full_name: Hof, Björn
  id: 3A374330-F248-11E8-B48F-1D18A9856A87
  last_name: Hof
  orcid: 0000-0003-2057-2754
citation:
  ama: Shi L, Avila M, Hof B. Scale invariance at the onset of turbulence in couette
    flow. <i>Physical Review Letters</i>. 2013;110(20). doi:<a href="https://doi.org/10.1103/PhysRevLett.110.204502">10.1103/PhysRevLett.110.204502</a>
  apa: Shi, L., Avila, M., &#38; Hof, B. (2013). Scale invariance at the onset of
    turbulence in couette flow. <i>Physical Review Letters</i>. American Physical
    Society. <a href="https://doi.org/10.1103/PhysRevLett.110.204502">https://doi.org/10.1103/PhysRevLett.110.204502</a>
  chicago: Shi, Liang, Marc Avila, and Björn Hof. “Scale Invariance at the Onset of
    Turbulence in Couette Flow.” <i>Physical Review Letters</i>. American Physical
    Society, 2013. <a href="https://doi.org/10.1103/PhysRevLett.110.204502">https://doi.org/10.1103/PhysRevLett.110.204502</a>.
  ieee: L. Shi, M. Avila, and B. Hof, “Scale invariance at the onset of turbulence
    in couette flow,” <i>Physical Review Letters</i>, vol. 110, no. 20. American Physical
    Society, 2013.
  ista: Shi L, Avila M, Hof B. 2013. Scale invariance at the onset of turbulence in
    couette flow. Physical Review Letters. 110(20), 204502.
  mla: Shi, Liang, et al. “Scale Invariance at the Onset of Turbulence in Couette
    Flow.” <i>Physical Review Letters</i>, vol. 110, no. 20, 204502, American Physical
    Society, 2013, doi:<a href="https://doi.org/10.1103/PhysRevLett.110.204502">10.1103/PhysRevLett.110.204502</a>.
  short: L. Shi, M. Avila, B. Hof, Physical Review Letters 110 (2013).
date_created: 2018-12-11T11:59:49Z
date_published: 2013-05-13T00:00:00Z
date_updated: 2021-01-12T07:00:00Z
day: '13'
department:
- _id: BjHo
doi: 10.1103/PhysRevLett.110.204502
ec_funded: 1
external_id:
  arxiv:
  - '1304.5446'
intvolume: '       110'
issue: '20'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1304.5446
month: '05'
oa: 1
oa_version: Preprint
project:
- _id: 25152F3A-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '306589'
  name: Decoding the complexity of turbulence at its origin
- _id: 2511D90C-B435-11E9-9278-68D0E5697425
  grant_number: SFB 963  TP A8
  name: Astrophysical instability of currents and turbulences
publication: Physical Review Letters
publication_status: published
publisher: American Physical Society
publist_id: '3970'
quality_controlled: '1'
scopus_import: 1
status: public
title: Scale invariance at the onset of turbulence in couette flow
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 110
year: '2013'
...