IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v413y2022ics0096300321006962.html
   My bibliography  Save this article

Evaluation of an effective and robust implicit time-integration numerical scheme for Navier-Stokes equations in a CFD solver for compressible flows

Author

Listed:
  • Maia, A.A.G.
  • Cavalca, D.F.
  • Tomita, J.T.
  • Costa, F.P.
  • Bringhenti, C.

Abstract

The present work describes the implementation of an implicit time-integration numerical scheme to solve viscous flows in an in-house CFD solver. The scheme is developed to calculate engineering problems involving compressible flows. This work extends the defect-correction technique for the 3D flow calculations, and all mathematical formulations are described. The CFD solver is based on the finite-volume method (FVM) to calculate the three-dimensional flow and can be applied to solve unstructured meshes. The current implementation uses the Flux-Difference Splitting method (FDS) developed by Roe combined with the MUSCL method and the Venkatakrishnan flux limiters to provide better accuracy of the numerical solutions. The implicit time-integration scheme was linearized applying the backward Euler method on the left-hand side (LHS) and a Newton-type linearization on the right-hand side (RHS) of the governing equations. The Jacobian matrix was computed analytically for the inviscid fluxes using the Roe fluxes, and for the viscous fluxes differentiating the conservative vector. Earlier work by Cavalca et al. (2018) showed the robustness and accuracy of this implicit solver to predict inviscid flows over the airfoil and into the supersonic nozzle. Finally, the Gauss-Seidel (GS) iterative method was applied to solve the resultant sparse and large system of equations. These numerical schemes and methods were applied to solve the laminar flow over a flat plate. Afterwards, the numerical solution was validated and verified with the exact Blasius solution. From the results, the numerical simulations exhibited superior robustness of the implicit-defect correction scheme when compared with the explicit scheme for compressible flows. All numerical particularities and their implementations are detailed in this paper.

Suggested Citation

  • Maia, A.A.G. & Cavalca, D.F. & Tomita, J.T. & Costa, F.P. & Bringhenti, C., 2022. "Evaluation of an effective and robust implicit time-integration numerical scheme for Navier-Stokes equations in a CFD solver for compressible flows," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    • Handle: RePEc:eee:apmaco:v:413:y:2022:i:c:s0096300321006962
    DOI: 10.1016/j.amc.2021.126612
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321006962
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126612?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zhao, Jingjun & Zhao, Wenjiao & Xu, Yang, 2021. "Lagrange nodal discontinuous Galerkin method for fractional Navier-Stokes equations," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    2. Rubino, Samuele, 2019. "An efficient time-splitting approximation of the Navier–Stokes equations with LPS modeling," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 318-337.
    3. Huang, Zheng-Ge & Wang, Li-Gong & Xu, Zhong & Cui, Jing-Jing, 2020. "An efficient preconditioned variant of the PSS preconditioner for generalized saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    4. Vorozhtsov, Evgenii V. & Shapeev, Vasily P., 2019. "On the efficiency of combining different methods for acceleration of iterations at the solution of PDEs by the method of collocations and least residuals," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cheng, Yong & Song, Fukai & Fu, Lei & Dai, Saishuai & Zhiming Yuan, & Incecik, Atilla, 2024. "Experimental investigation of a dual-pontoon WEC-type breakwater with a hydraulic-pneumatic complementary power take-off system," Energy, Elsevier, vol. 286(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Semisalov, Boris & Belyaev, Vasily & Bryndin, Luka & Gorynin, Arsenii & Blokhin, Alexander & Golushko, Sergey & Shapeev, Vasily, 2022. "Verified simulation of the stationary polymer fluid flows in the channel with elliptical cross-section," Applied Mathematics and Computation, Elsevier, vol. 430(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:413:y:2022:i:c:s0096300321006962. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.