Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Journal of Computational Physics
On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Extension of the spectral volume method to high-order boundary representation
Journal of Computational Physics
Journal of Computational Physics
A Study of Viscous Flux Formulations for a p-Multigrid Spectral Volume Navier Stokes Solver
Journal of Scientific Computing
A New Class of High-Order Energy Stable Flux Reconstruction Schemes for Triangular Elements
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows
Journal of Computational Physics
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The local discontinuous Galerkin (LDG) viscous flux formulation was originally developed by Cockburn and Shu for the discontinuous Galerkin setting and later extended to the spectral volume setting by Wang and his collaborators. Unlike the penalty formulations like the interior penalty and the BR2 schemes, the LDG formulation requires no length based penalizing terms and is compact. However, computational results using LDG are dependant of the orientation of the faces especially for unstructured and non uniform grids. This results in lower solution accuracy and stiffer stability constraints as shown by Kannan and Wang. In this paper, we develop a variant of the LDG, which not only retains its attractive features, but also vastly reduces its unsymmetrical nature. This variant (aptly named LDG2), displayed higher accuracy than the LDG approach and has a milder stability constraint than the original LDG formulation. In general, the 1D and the 2D numerical results are very promising and indicate that the approach has a great potential for 3D flow problems.