A new high-order spectral difference method for simulating viscous flows on unstructured grids with mixed-element meshes

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

doi:10.1016/j.compfluid.2019.03.010

Title: A new high-order spectral difference method for simulating viscous flows on unstructured grids with mixed-element meshes

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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. 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. Furthermore, 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.

Authors:

Li, Mao ^[1]; Qiu, Zihua ^[2];

^[1]; Sprague, Michael A. ^[3]; Xu, Min ^[2]; Garris, Charles A. ^[1]

George Washington Univ., Washington, DC (United States)
Northwestern Polytechnical Univ., Shaanxi (China)
National Renewable Energy Lab. (NREL), Golden, CO (United States)

Publication Date:: Fri Mar 08 00:00:00 EST 2019

Research Org.:: National Renewable Energy Laboratory (NREL), Golden, CO (United States)

Sponsoring Org.:: USDOE Office of Energy Efficiency and Renewable Energy (EERE), Wind and Water Technologies Office (EE-4W); USDOE Office of Energy Efficiency and Renewable Energy (EERE), Renewable Power Office. Wind Energy Technologies Office

OSTI Identifier:: 1515763

Alternate Identifier(s):: OSTI ID: 1547658

Report Number(s):: NREL/JA-5000-73472
Journal ID: ISSN 0045-7930

Grant/Contract Number:: AC36-08GO28308

Resource Type:: Accepted Manuscript

Journal Name:: Computers and Fluids

Additional Journal Information:: Journal Volume: 184; Journal Issue: C; Journal ID: ISSN 0045-7930

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; spectral difference method; Raviart-Thomas space; Navier-Stokes equations; mixed elements

Citation Formats


                    Li, Mao, Qiu, Zihua, Liang, Chunlei, Sprague, Michael A., Xu, Min, and Garris, Charles A. A new high-order spectral difference method for simulating viscous flows on unstructured grids with mixed-element meshes.  United States: N. p., 2019. 
Web.  doi:10.1016/j.compfluid.2019.03.010.

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                    Li, Mao, Qiu, Zihua, Liang, Chunlei, Sprague, Michael A., Xu, Min, & Garris, Charles A. A new high-order spectral difference method for simulating viscous flows on unstructured grids with mixed-element meshes.  United States.  https://doi.org/10.1016/j.compfluid.2019.03.010

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                    Li, Mao, Qiu, Zihua, Liang, Chunlei, Sprague, Michael A., Xu, Min, and Garris, Charles A. Fri .  
"A new high-order spectral difference method for simulating viscous flows on unstructured grids with mixed-element meshes".  United States.  https://doi.org/10.1016/j.compfluid.2019.03.010.  https://www.osti.gov/servlets/purl/1515763.

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@article{osti_1515763,

  title        = {A new high-order spectral difference method for simulating viscous flows on unstructured grids with mixed-element meshes},

  author       = {Li, Mao and Qiu, Zihua and Liang, Chunlei and Sprague, Michael A. and Xu, Min and Garris, Charles A.},

  abstractNote = {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. 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. Furthermore, 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.},

  doi          = {10.1016/j.compfluid.2019.03.010},

  journal      = {Computers and Fluids},

  number       = C,

  volume       = 184,

  place        = {United States},

  year         = {Fri Mar 08 00:00:00 EST 2019},

  month        = {Fri Mar 08 00:00:00 EST 2019}

}

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