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    Entropy stable h/p-nonconforming discretization with the summation-by-parts property for the compressible Euler and Navier–Stokes equations

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    hp_entropy_sn_revision.pdf
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    Description:
    Accepted Manuscript
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    Type
    Article
    Authors
    Fernández, David C. Del Rey
    Carpenter, Mark H.
    Dalcin, Lisandro
    Zampini, Stefano cc
    Parsani, Matteo cc
    KAUST Department
    Extreme Computing Research Center
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2020-03-16
    Preprint Posting Date
    2019-10-04
    Online Publication Date
    2020-03-16
    Print Publication Date
    2020-04
    Submitted Date
    2019-10-04
    Permanent link to this record
    http://hdl.handle.net/10754/662193
    
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    Abstract
    In this paper, the entropy conservative/stable algorithms presented by Del Rey Fernandez and coauthors [18,16,17] for the compressible Euler and Navier-Stokes equations on nonconforming p-refined/coarsened curvilinear grids is extended to h/p refinement/coarsening. The main difficulty in developing nonconforming algorithms is the construction of appropriate coupling procedures across nonconforming interfaces. Here, a computationally simple and efficient approach based upon using decoupled interpolation operators is utilized. The resulting scheme is entropy conservative/stable and element-wise conservative. Numerical simulations of the isentropic vortex and viscous shock propagation confirm the entropy conservation/stability and accuracy properties of the method (achieving ~ p + 1 convergence) which are comparable to those of the original conforming scheme [4,35]. Simulations of the Taylor-Green vortex at Re = 1,600 and turbulent flow past a sphere at Re = 2,000 show the robustness and stability properties of the overall spatial discretization for unstructured grids. Finally, to demonstrate the entropy conservation property of a fully-discrete explicit entropy stable algorithm with h/p refinement/coarsening, we present the time evolution of the entropy function obtained by simulating the propagation of the isentropic vortex using a relaxation Runge-Kutta scheme.
    Citation
    Fernández, D. C. D. R., Carpenter, M. H., Dalcin, L., Zampini, S., & Parsani, M. (2020). Entropy stable h/p-nonconforming discretization with the summation-by-parts property for the compressible Euler and Navier–Stokes equations. SN Partial Differential Equations and Applications, 1(2). doi:10.1007/s42985-020-00009-z
    Sponsors
    The research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST). We are thankful for the computing resources of the Supercomputing Laboratory and the Extreme Computing Research Center at KAUST. Special thanks are extended to Dr. Mujeeb R. Malik for supporting this work as part of NASA’s “Transformational Tools and Technologies” (T3) project.
    Publisher
    Springer Nature
    Journal
    SN Partial Differential Equations and Applications
    DOI
    10.1007/s42985-020-00009-z
    arXiv
    1910.02110
    Additional Links
    http://link.springer.com/10.1007/s42985-020-00009-z
    ae974a485f413a2113503eed53cd6c53
    10.1007/s42985-020-00009-z
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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