IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v266y2015icp316-327.html
   My bibliography  Save this article

High-order finite volume shallow water model on the cubed-sphere: 1D reconstruction scheme

Author

Listed:
  • Katta, Kiran K.
  • Nair, Ramachandran D.
  • Kumar, Vinod

Abstract

A central-upwind finite-volume (CUFV) scheme for shallow-water model on a nonorthogonal equiangular cubed-sphere grid is developed, consequently extending the 1D reconstruction CUFV transport scheme developed by us. High-order spatial discretization based on weighted essentially non-oscillatory (WENO) is considered for this effort. The CUFV method combines the alluring features of classical upwind and central schemes. This approach is particularly useful for complex computational domain such as the cubed-sphere. The continuous flux-form spherical shallow water equations in nonorthogonal curvilinear coordinates are utilized. Fluxes along the element boundaries are approximated by a Kurganov–Noelle–Petrova scheme. A fourth-order strong stability preserving Runge–Kutta time stepping scheme for time integration is employed in the present work. The numerical scheme is evaluated with standard shallow water test suite, which accentuate accuracy and conservation properties. In addition, an efficient yet inexpensive bound preserving filter with an optional positivity filter is used to remove spurious oscillations and to achieve strictly positive definite numerical solution. To tackle the discontinuities that arise at the edges of the cubed-sphere grid, we utilize a high-order 1D interpolation procedure combining cubic and quadratic interpolations.The results with the high-order scheme is compared with the results for the same tests for various schemes available in literature. Since, the scheme presented here uses local-cell information, it is expected to be scalable to high number of processors count in a distributed node high-performance computer.

Suggested Citation

  • Katta, Kiran K. & Nair, Ramachandran D. & Kumar, Vinod, 2015. "High-order finite volume shallow water model on the cubed-sphere: 1D reconstruction scheme," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 316-327.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:316-327
    DOI: 10.1016/j.amc.2015.04.053
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315005111
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.04.053?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. Feng, Hui & Huang, Cong & Wang, Rong, 2014. "An improved mapped weighted essentially non-oscillatory scheme," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 453-468.
    Full references (including those not matched with items on IDEAS)

    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. Hajipour, Mojtaba & Jajarmi, Amin & Malek, Alaeddin & Baleanu, Dumitru, 2018. "Positivity-preserving sixth-order implicit finite difference weighted essentially non-oscillatory scheme for the nonlinear heat equation," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 146-158.
    2. Huang, Cong & Chen, Li Li, 2021. "A simple WENO-AO method for solving hyperbolic conservation laws," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    3. Tang, Shujiang & Feng, Yujie & Li, Mingjun, 2022. "Novel weighted essentially non-oscillatory schemes with adaptive weights," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    4. Zhang, Xin & Huang, Lintao & Qin, Xueyu & Qu, Feng & Yan, Chao, 2023. "An efficient finite difference IFWENO-THINC hybrid scheme for capturing discontinuities," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    5. Huang, Cong, 2016. "WENO scheme with new smoothness indicator for Hamilton–Jacobi equation," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 21-32.
    6. Ruo Li & Wei Zhong, 2022. "An Improved Component-Wise WENO-NIP Scheme for Euler System," Mathematics, MDPI, vol. 10(20), pages 1-21, October.
    7. Li, Ruo & Zhong, Wei, 2023. "A robust and efficient component-wise WENO scheme for Euler equations," Applied Mathematics and Computation, Elsevier, vol. 438(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:266:y:2015:i:c:p:316-327. 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.