Patrice Castonguay

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The Flux Reconstruction (FR) approach unifies several well-known high-order schemes for unstructured grids, including a collocation-based nodal discontinuous Galerkin (DG) method and all types of Spectral Difference (SD) methods, at least for linear problems. The FR approach also allows for the formulation of new families of schemes. Of particular interest(More)
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)
Keywords: High-order methods Flux reconstruction Nodal discontinuous Galerkin method Spectral difference method Dispersion Dissipation a b s t r a c t The flux reconstruction (FR) approach unifies various high-order schemes, including collo-cation based nodal discontinuous Galerkin methods, and all spectral difference methods (at least for a linear flux(More)
The flux reconstruction approach to high-order methods is robust, efficient, simple to implement, and allows various high-order schemes, such as the nodal discontinu-ous 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 one-dimensional(More)
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)
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)
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)
SUMMARY 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(More)
This work discusses the development of a three-dimensional, high-order, compressible viscous flow solver for mixed unstructured grids that can run on multiple GPUs. The solver utilizes a range of so-called Vincent-Castonguay-Jameson-Huynh (VCJH) flux reconstruction schemes in both tensor-product and simplex elements. Such schemes are linearly stable for all(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)