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An Extension of Energy Stable Flux Reconstruction to Unsteady, Non-linear, Viscous Problems on Mixed Grids
, 2011
"... 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 ..."
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Cited by 5 (3 self)
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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. I.
Optimized explicit Runge-Kutta schemes for the spectral difference method applied to wave propagation problems
- SIAM J. Sci. Comput
, 2013
"... Explicit Runge–Kutta schemes with large stable step sizes are developed for integration of high order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard expli ..."
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Explicit Runge–Kutta schemes with large stable step sizes are developed for integration of high order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge–Kutta schemes available in literature. Furthermore, they have a small principal error norm and admit a low-storage implementation. The advantages of the new schemes are demonstrated through application to the Euler equations and the linearized Euler equations. 1
Accepted by. High Order Hybrid Discontinuous Galerkin Regional Ocean
, 2014
"... A c............................................. ..."
Contents lists available at ScienceDirect Journal of Computational Physics
"... journal homepage: www.elsevier.com/locate/jcp Insights from von Neumann analysis of high-order flux ..."
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journal homepage: www.elsevier.com/locate/jcp Insights from von Neumann analysis of high-order flux
Seventh International Conference on Computational Fluid Dynamics (ICCFD7),
"... spectral difference schemes ..."
Toward structural LES modeling with high-order spectral difference schemes
, 2012
"... The combination of the high-order unstructured spectral difference spatial discretization scheme with sub-grid scale modeling for large-eddy simulation was investigated with particular focus on the consistent implementation of a structural mixed model based on the scale similarity hypothesis. The di ..."
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The combination of the high-order unstructured spectral difference spatial discretization scheme with sub-grid scale modeling for large-eddy simulation was 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 for the discrete filter within hexahedral elements of arbitrary order led to the development of anewclassofthree-dimensionalconstraineddiscretefilters. Resultsfromcomputations of turbulent channel flow at Re τ =180and 395 and flow past a confined circular cylinder at ReD =2580were compared against direct numerical simulation and particle image velocimetry measurements, respectively. The numerical experiments suggest that the results are sensitive to the use of an sub-grid scale closure, even when a high-order numerical scheme is used, especially when the grid resolution is kept relatively low. The use of the similarity mixed formulation proved to be particularly accurate in reproducing sub-grid scale interactions, confirming that its well-known potential can be realized in conjunction with state-of-the-art high-order numerical schemes. I.
The
"... generation of arbitrary order curved meshes for 3D finite element analysis ..."
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generation of arbitrary order curved meshes for 3D finite element analysis
Available online at www.sciencedirect.com
, 2014
"... www.elsevier.com/locate/cma An isoparametric approach to high-order curvilinear boundary-layer meshing ..."
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www.elsevier.com/locate/cma An isoparametric approach to high-order curvilinear boundary-layer meshing
Stabilization of High-Order Methods for Unstructured Grids with Local Fourier Spectral Filtering: high-Re Simulations in Coarse
"... One of the main barriers to wide adoption of high-order numerical methods in industrial applications is the schemes ’ low robustness relative to low-order methods. HiFiLES, an open-source, high-order, Navier-Stokes solver for unstructured grids is not impervious to this problem. Its stability is gen ..."
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One of the main barriers to wide adoption of high-order numerical methods in industrial applications is the schemes ’ low robustness relative to low-order methods. HiFiLES, an open-source, high-order, Navier-Stokes solver for unstructured grids is not impervious to this problem. Its stability is generally highly dependent on the quality of the grid. This paper describes the implementation of the Local Fourier-spectral (LFS) filters, developed by Asthana and the authors, in HiFiLES, and shows the results of high-Re simulations in coarse, unstructured 2D meshes. The simulations demonstrate the potential for LFS filters to stabilize high-order simulations under extreme conditions: very coarse grids, high-Re, high-Ma, and very low-Ma. We present a formulation of the LFS filters for a general high-order polygon (2D) or polyhedron (3D). LFS filters are uniquely suited to implementation in highly-parallelizable numerical schemes like Flux Reconstruction (FR) because they operate element-wise, use interface information that is already used by the element to advance the solution, and maintain the operational complexity of the underlying scheme –the filtering operation is two element-local matrix multiplications. I.
Efficient Finite Element Assembly of High Order Whitney Forms
"... This paper presents an efficient method for the finite element assembly of high or-der Whitney elements. We start by reviewing the classical assembly technique and by highlighting the most time consuming part. Then, we show how this classical approach can be reformulated into a computationally effic ..."
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This paper presents an efficient method for the finite element assembly of high or-der Whitney elements. We start by reviewing the classical assembly technique and by highlighting the most time consuming part. Then, we show how this classical approach can be reformulated into a computationally efficient matrix-matrix product. We also ad-dress the global orientation problem of the vector valued basis functions. We conclude by presenting numerical results for a three dimensional wave propagation problem. 1
