An efficient parallel high-order compact scheme for the 3D incompressible Navier–Stokes equations

Abide, Stéphane; Binous, M. S.; Zeghmati, Belkacem

doi:10.1080/10618562.2017.1326592

Cited by 15 publications

(22 citation statements)

References 29 publications

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“…These nodes are distributed in M subdomains, and̂and ′′ are calculated by using Equations (23) and (24), respectively. The implementation of the DCOM scheme is related to the number of nodes in the subdomain, data swapping and averaging between neighbouring subdomains, and analytical expressions for̂and ′′ are therefore hard to obtain.…”

Section: Fourier Analysismentioning

confidence: 99%

“…To analyse its spectral property, the numerical approximations of the first and second derivatives of (x) (ie,̃′ and̃′ ′ ), with ranging from 0 to , are calculated by specific schemes in a 1-D domain x ∈ [0, 2 ] discretised with N nodes. These nodes are distributed in M subdomains, and̂and ′′ are calculated by using Equations (23) and (24), respectively. The analysis of mean values for̂and ′′ , averaged on all nodes, and the values of̂and ′′ on the interface node are conducted.…”

Section: Fourier Analysismentioning

confidence: 99%

“…The first group focuses on the method of solving a linear system in parallel, using either pipeline methods, 19,20 alternating direction methods, 21 parallel diagonal dominant algorithms, 22,23 or line-relaxation methods. In general, there are two categories of methods for dealing with a parallel compact scheme.…”

Section: Introductionmentioning

confidence: 99%

“…In general, there are two categories of methods for dealing with a parallel compact scheme. The first group focuses on the method of solving a linear system in parallel, using either pipeline methods, 19,20 alternating direction methods, 21 parallel diagonal dominant algorithms, 22,23 or line-relaxation methods. 24 The second group essentially decouples compact schemes to enable them to be solved independently on each processor.…”

Section: Introductionmentioning

confidence: 99%

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An improved parallel compact scheme for domain‐decoupled simulation of turbulence

Fang

Gao

Moulinec

et al. 2019

Numerical Methods in Fluids

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Summary An improved domain‐decoupled compact scheme for first and second spatial derivatives is proposed for domain‐decomposition‐based parallel computational fluid dynamics. The method improves the accuracy of previously developed decoupled schemes and preserves the accuracy and bandwidth properties of fully coupled compact schemes, even for a very large degree of parallelism, and enables the Navier‐Stokes equations to be solved independently on each processor. The scheme is analysed using Fourier analysis and error analysis, and tested on one‐dimensional wave‐packet propagation, a two‐dimensional vortex convection problem, and in the direct numerical simulation of the three‐dimensional Taylor‐Green vortex problem and turbulent channel flow. Our results demonstrate the scheme's effectiveness in performing direct numerical simulation of turbulence in terms of accuracy and scalability.

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Section: Fourier Analysismentioning

confidence: 99%

Section: Fourier Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An improved parallel compact scheme for domain‐decoupled simulation of turbulence

Fang

Gao

Moulinec

et al. 2019

Numerical Methods in Fluids

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“…In the present study, a higher-order compact scheme solver [10] is tailored for solving complex rotating stratified flows in annular domains to take advantage of modern generation computing hardware. Our goal is to reduce the huge total time due to the very long transient stage resulting from the thermal stratification associated with the rotation.…”

Section: Introductionmentioning

confidence: 99%

Higher-order compact scheme for high-performance computing of stratified rotating flows

et al. 2018

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To take advantage of modern generation computing hardware, a scalable numerical method, based on higher-order compact scheme, is described to solve rotating stratified flows in cylindrical annular domains. An original approach combining 2d-pencil decomposition and reduced Parallel Diagonal Dominant is proposed to improve the parallelization performance during the computation of Poisson/Helmholtz solvers and time explicit terms. The developed technique is validated with respect to analytical solutions, using the method of manufactured solutions, and available data for two specific configurations. The purpose is to demonstrate its ability to correctly capture the flow characteristics in strato-rotational instability and in baroclinic instability with associated small-scale features. Moreover, this code is found to drastically reduce the huge execution times often preventing detailed numerical investigations of these complex phenomena. Strong scaling test is carried out to assess the performance for up to 1024 cores using grid up to 128 × 568 × 568 in radial, axial and azimuthal directions.

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Compact High Order Accurate Schemes for the Three Dimensional Wave Equation

2019

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An efficient parallel high-order compact scheme for the 3D incompressible Navier–Stokes equations

Cited by 15 publications

References 29 publications

An improved parallel compact scheme for domain‐decoupled simulation of turbulence

An improved parallel compact scheme for domain‐decoupled simulation of turbulence

Higher-order compact scheme for high-performance computing of stratified rotating flows

Compact High Order Accurate Schemes for the Three Dimensional Wave Equation

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