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Higher-order compact scheme for high-performance computing of stratified rotating flows. (English) Zbl 1410.76278
Summary: 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 \(128 \times 568 \times 568\) in radial, axial and azimuthal directions.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
76D50 Stratification effects in viscous fluids
76U05 General theory of rotating fluids
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