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

Journal Article · Fri Mar 08 00:00:00 EST 2019 · Computers and Fluids

DOI:https://doi.org/10.1016/j.compfluid.2019.03.010· OSTI ID:1515763

Li, Mao ^[1]; Qiu, Zihua ^[2]; Liang, Chunlei ^[1]; Sprague, Michael A. ^[3]; Xu, Min ^[2]; Garris, Charles A. ^[1]

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

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.

• Research Organization: National Renewable Energy Laboratory (NREL), Golden, CO (United States)
• Sponsoring Organization: USDOE Office of Energy Efficiency and Renewable Energy (EERE), Renewable Power Office. Wind Energy Technologies Office; USDOE Office of Energy Efficiency and Renewable Energy (EERE), Wind and Water Technologies Office (EE-4W)
• Grant/Contract Number: AC36-08GO28308
• OSTI ID: 1515763
• Alternate ID(s): OSTI ID: 1547658
• Report Number(s): NREL/JA--5000-73472
• Journal Information: Computers and Fluids, Journal Name: Computers and Fluids Journal Issue: C Vol. 184; ISSN 0045-7930
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

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