A New High-Order Spectral Difference Method for Simulating Viscous Flows on Unstructured Grids with Mixed-Element Meshes

Mao Li, Zihua Qiu, Chunlei Liang, Michael Sprague, Min Xu, Charles A. Garris

Research output: Contribution to journalArticlepeer-review

5 Scopus Citations

Abstract

In the present study, a spectral difference (SD) method is developed for viscous flows on meshes with a mixture of triangular and quadrilateral elements. The standard SD method for triangular elements, which employs Lagrangian interpolating functions for fluxes, is not stable when the designed accuracy of spatial discretization is third order or higher. Unlike the standard SD method, the method examined here uses vector interpolating functions in the Raviart-Thomas (RT) spaces to construct continuous flux functions on reference elements. The spectral-difference Raviart-Thomas (SDRT) method was originally proposed by Balan et al. [1] and implemented on triangular-element meshes for invisid flow only. Our present results demonstrated that the SDRT method is stable and high-order accurate in two dimensions (2D) for a number of test problems by using triangular-, quadrilateral-, and mixed-element meshes for both inviscid and viscous flows. A stability analysis is also performed for mixed elements. We found our current SDRT scheme is stable for fourth-order accurate spatial discretizations. However, a stable fifth-order SDRT scheme remains to be identified.

Original languageAmerican English
Pages (from-to)187-198
Number of pages12
JournalComputers and Fluids
Volume184
DOIs
StatePublished - 30 Apr 2019

Bibliographical note

Publisher Copyright:
© 2019

NREL Publication Number

  • NREL/JA-5000-73472

Keywords

  • Mixed elements
  • Navier-Stokes equations
  • Raviart-Thomas space
  • Spectral difference method

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