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

Michael Sprague; Mao Li; Zihua Qiu; Chunlei Liang; Min Xu

doi:10.2514/6.2017-0520

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

Michael Sprague, Mao Li, Zihua Qiu, Chunlei Liang, Min Xu

National Wind Technology Center

Research output: Contribution to conference › Paper › peer-review

1 Scopus Citations

Abstract

In the present study, a new 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. Studies have been performed for the 2D wave equation and the Euler equations. Our present results demonstrated that the spectral-difference Raviart-Thomas (SDRT) method is stable and high-order accurate for a number of test problems by using triangular-, quadrilateral-, and mixed-element meshes.

Original language	American English
Number of pages	15
DOIs	https://doi.org/10.2514/6.2017-0520 https://doi.org/10.2514/6.2017-0520
State	Published - 2017
Event	55th AIAA Aerospace Sciences Meeting - Grapevine, United States Duration: 9 Jan 2017 → 13 Jan 2017

Conference

Conference	55th AIAA Aerospace Sciences Meeting
Country/Territory	United States
City	Grapevine
Period	9/01/17 → 13/01/17

Bibliographical note

Publisher Copyright:
© 2017 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

NREL Publication Number

NREL/CP-5000-67786

Other Report Number

AIAA 2017-0520

Keywords

meshes
quadrilateral elements
spectral difference method
triangular elements

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title = "A New High-Order Spectral Difference Method for Simulating Viscous Flows on Unstructured Grids with Mixed Elements",

abstract = "In the present study, a new 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. Studies have been performed for the 2D wave equation and the Euler equations. Our present results demonstrated that the spectral-difference Raviart-Thomas (SDRT) method is stable and high-order accurate for a number of test problems by using triangular-, quadrilateral-, and mixed-element meshes.",

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author = "Michael Sprague and Mao Li and Zihua Qiu and Chunlei Liang and Min Xu",

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TY - CONF

T1 - A New High-Order Spectral Difference Method for Simulating Viscous Flows on Unstructured Grids with Mixed Elements

AU - Sprague, Michael

AU - Li, Mao

AU - Qiu, Zihua

AU - Liang, Chunlei

AU - Xu, Min

PY - 2017

Y1 - 2017

N2 - In the present study, a new 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. Studies have been performed for the 2D wave equation and the Euler equations. Our present results demonstrated that the spectral-difference Raviart-Thomas (SDRT) method is stable and high-order accurate for a number of test problems by using triangular-, quadrilateral-, and mixed-element meshes.

AB - In the present study, a new 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. Studies have been performed for the 2D wave equation and the Euler equations. Our present results demonstrated that the spectral-difference Raviart-Thomas (SDRT) method is stable and high-order accurate for a number of test problems by using triangular-, quadrilateral-, and mixed-element meshes.

KW - meshes

KW - quadrilateral elements

KW - spectral difference method

KW - triangular elements

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U2 - 10.2514/6.2017-0520

DO - 10.2514/6.2017-0520

M3 - Paper

AN - SCOPUS:85017247547

T2 - 55th AIAA Aerospace Sciences Meeting

Y2 - 9 January 2017 through 13 January 2017

ER -

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

Abstract

Conference

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Keywords

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