Abstract
We introduce a new discontinuous Galerkin (EDG) method to solve the compressible Navier–Stokes equations where jumps across element boundaries are eliminated in the computation of the viscous fluxes using an L 2 projection of the discontinuous solution on the basis of overlapping elements (elastoplast). This method is related to the recovery method presented by Van Leer and Lo (AIAA paper, 2007-4003), and similarly it is compact and stable without introducing penalty terms. A comparison on a 1D convection-diffusion problem in terms of accuracy and stability with other viscous DG schemes is given. Finally, the first 2D results both on Cartesian and unstructured grids illustrate stability, precision and versatility of this method.
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Borrel, M., Ryan, J. (2011). A New Discontinuous Galerkin Method for the Navier–Stokes Equations. In: Hesthaven, J., Rønquist, E. (eds) Spectral and High Order Methods for Partial Differential Equations. Lecture Notes in Computational Science and Engineering, vol 76. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15337-2_35
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DOI: https://doi.org/10.1007/978-3-642-15337-2_35
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