Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Low-dissipative high-order shock-capturing methods using characteristic-based filters
Journal of Computational Physics
Journal of Computational Physics
The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems
SIAM Journal on Scientific Computing
Discretisation of diffusive fluxes on hybrid grids
Journal of Computational Physics
Journal of Computational Physics
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The present work details the Elastoplast (this name is a translation from the French ''sparadrap'', a concept first applied by Yves Morchoisne for Spectral methods [1]) Discontinuous Galerkin (EDG) method to solve the compressible Navier-Stokes equations. This method was first presented in 2009 at the ICOSAHOM congress with some Cartesian grid applications. We focus here on unstructured grid applications for which the EDG method seems very attractive. As in the Recovery method presented by van Leer and Nomura in 2005 for diffusion, jumps across element boundaries are locally eliminated by recovering the solution on an overlapping cell. In the case of Recovery, this cell is the union of the two neighboring cells and the Galerkin basis is twice as large as the basis used for one element. In our proposed method the solution is rebuilt through an L^2 projection of the discontinuous interface solution on a small rectangular overlapping interface element, named Elastoplast, with an orthogonal basis of the same order as the one in the neighboring cells. Comparisons on 1D and 2D scalar diffusion problems in terms of accuracy and stability with other viscous DG schemes are first given. Then, 2D results on acoustic problems, vortex problems and boundary layer problems both on Cartesian or unstructured triangular grids illustrate stability, precision and versatility of this method.