An extension of energy stable flux reconstruction to unsteady, non-linear, viscous problems on mixed grids

David M. Williams, Patrice Castonguay, Peter E. Vincent, Antony Jameson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

Abstract

This paper extends the high-order Flux Reconstruction (FR) approach to the treatment of non-linear diffusive fluxes on triangles. The FR approach for solving diffusion problems is reviewed on quadrilaterals and extended for triangles, allowing the treatment of mixed grids. In particular, this paper examines a subset of FR schemes, referred to as Vincent- Castonguay-Jameson-Huynh (VCJH) schemes, which are provably stable across all orders of accuracy for linear fluxes in first order systems. The correction fields of the VCJH schemes are shown to represent a family of lifting operators which are used to enforce inter-element continuity of the solution and the diffusive flux. For diffusion problems, the lifting operators of nodal DG schemes are shown to be a subset of this family. Finally, numerical results are used to show the effectiveness of VCJH schemes for a range of problems, including the model diffusion equation and the compressible Navier-Stokes equations. Optimal orders of accuracy are obtained on unstructured mixed meshes of triangular and quadrilateral elements.

Original languageEnglish (US)
Title of host publication20th AIAA Computational Fluid Dynamics Conference 2011
StatePublished - Dec 1 2011
Event20th AIAA Computational Fluid Dynamics Conference 2011 - Honolulu, HI, United States
Duration: Jun 27 2011Jun 30 2011

Publication series

Name20th AIAA Computational Fluid Dynamics Conference 2011

Other

Other20th AIAA Computational Fluid Dynamics Conference 2011
CountryUnited States
CityHonolulu, HI
Period6/27/116/30/11

Fingerprint

Fluxes
Navier Stokes equations

All Science Journal Classification (ASJC) codes

  • Fluid Flow and Transfer Processes
  • Energy Engineering and Power Technology
  • Aerospace Engineering
  • Mechanical Engineering

Cite this

Williams, D. M., Castonguay, P., Vincent, P. E., & Jameson, A. (2011). An extension of energy stable flux reconstruction to unsteady, non-linear, viscous problems on mixed grids. In 20th AIAA Computational Fluid Dynamics Conference 2011 (20th AIAA Computational Fluid Dynamics Conference 2011).
Williams, David M. ; Castonguay, Patrice ; Vincent, Peter E. ; Jameson, Antony. / An extension of energy stable flux reconstruction to unsteady, non-linear, viscous problems on mixed grids. 20th AIAA Computational Fluid Dynamics Conference 2011. 2011. (20th AIAA Computational Fluid Dynamics Conference 2011).
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Williams, DM, Castonguay, P, Vincent, PE & Jameson, A 2011, An extension of energy stable flux reconstruction to unsteady, non-linear, viscous problems on mixed grids. in 20th AIAA Computational Fluid Dynamics Conference 2011. 20th AIAA Computational Fluid Dynamics Conference 2011, 20th AIAA Computational Fluid Dynamics Conference 2011, Honolulu, HI, United States, 6/27/11.

An extension of energy stable flux reconstruction to unsteady, non-linear, viscous problems on mixed grids. / Williams, David M.; Castonguay, Patrice; Vincent, Peter E.; Jameson, Antony.

20th AIAA Computational Fluid Dynamics Conference 2011. 2011. (20th AIAA Computational Fluid Dynamics Conference 2011).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Williams DM, Castonguay P, Vincent PE, Jameson A. An extension of energy stable flux reconstruction to unsteady, non-linear, viscous problems on mixed grids. In 20th AIAA Computational Fluid Dynamics Conference 2011. 2011. (20th AIAA Computational Fluid Dynamics Conference 2011).