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- Peter E. Vincent, Patrice Castonguay, Antony Jameson
- J. Sci. Comput.
- 2011

The flux reconstruction approach to high-order methods is robust, efficient, simple to implement, and allows various high-order schemes, such as the nodal discontinuous Galerkin method and the spectral difference method, to be cast within a single unifying framework. Utilizing a flux reconstruction formulation, it has been proved (for onedimensional linear… (More)

- Peter E. Vincent, Patrice Castonguay, Antony Jameson
- J. Comput. Physics
- 2011

The flux reconstruction (FR) approach unifies various high-order schemes, including collocation based nodal discontinuous Galerkin methods, and all spectral difference methods (at least for a linear flux function), within a single framework. Recently, an infinite number of linearly stable FR schemes were identified, henceforth referred to as… (More)

- Antony Jameson, Peter E. Vincent, Patrice Castonguay
- J. Sci. Comput.
- 2012

The flux reconstruction (FR) approach unifies various high-order schemes, including collocation based nodal discontinuous Galerkin (DG) methods, and all spectral difference methods (at least for a linear flux function), within a single framework. Recently a new range of linearly stable FR schemes have been identified, henceforth referred to as… (More)

This work addresses the simulation of transitional flow over airfoils under low Reynolds number conditions (Rec ≤ 60000). The flow solutions are obtained by means of an Implicit Large Eddy Simulation (ILES) using a newly developed unstructured, parallel solver that employs the high-order spectral difference (SD) method for spatial discretization. The… (More)

- D. M. Williams, Patrice Castonguay, Peter E. Vincent, Antony Jameson
- J. Comput. Physics
- 2013

Article history: Received 20 December 2012 Received in revised form 15 April 2013 Accepted 7 May 2013 Available online 20 May 2013

- Patrice Castonguay, Peter E. Vincent, Antony Jameson
- J. Sci. Comput.
- 2012

The flux reconstruction (FR) approach allows various well-known high-order schemes, such as collocation based nodal discontinuous Galerkin (DG) methods and spectral difference (SD) methods, to be cast within a single unifying framework. Recently, the authors identified a new class of FR schemes for 1D conservation laws, which are simple to implement,… (More)

- Patrice Castonguay, David M. Williamsy, Peter E. Vincentz, Manuel Lopezx, Antony Jameson
- 2011

This work discusses the development of a three-dimensional, high-order, compressible viscous ow solver for mixed unstructured grids that can run on multiple GPUs. The solver utilizes a range of so-called Vincent-Castonguay-Jameson-Huynh (VCJH) ux reconstruction schemes in both tensor-product and simplex elements. Such schemes are linearly stable for all… (More)

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… (More)

The authors recently identified an infinite range of high-order energy stable flux reconstruction (FR) schemes in 1D and on triangular elements in 2D. The new flux reconstruction schemes are linearly stable for all orders of accuracy in a norm of Sobolev type. They are parameterized by a single scalar quantity, which if chosen judiciously leads to the… (More)

The combination of a high-order unstructured spectral difference (SD) spatial discretization scheme with sub-grid scale (SGS) modeling for large-eddy simulation is investigated with particular focus on the consistent implementation of a structural mixed model based on the scale similarity hypothesis. The difficult task of deriving a consistent formulation… (More)