Geodesic
Unsteady high order accuracy DG method for turbulent flow modeling
Matematičeskoe modelirovanie, Tome 30 (2018) no. 5, pp. 37-56

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The paper provides a brief description of TsAGI code based on the high order of accuracy Discontinuous Galerkin method. Reconstruction of the functions is carried out for the conservative variables. Gradients of variables are calculated using the method of Bassi–Rebay 2. For integration, Gauss quadrature rules are used. Coordinate transformations are done by serendipity elements. In calculations with schemes of order higher than second, curvature of the mesh lines is taken into account. In the paper, a comparison with finite volume methods is performed, including WENO method with linear weights and a single quadrature point on a cell side. The classical tests are used such as subsonic flow around a circular cylinder in an ideal gas, diagonal convection of two-dimensional isentropic vortex, and decay of the Taylor–Green vortex.
Keywords: Discontinuous Galerkin method (DG), Finite Volume method (FV), high order of accuracy, Taylor–Green vortex. 
@article{MM_2018_30_5_a3,
     author = {S. M. Bosnyakov and S. V. Mikhaylov and V. Yu. Podaruev and A. I. Troshin},
     title = {Unsteady high order accuracy {DG} method for turbulent flow modeling},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {37--56},
     publisher = {mathdoc},
     volume = {30},
     number = {5},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2018_30_5_a3/}
}
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S. M. Bosnyakov; S. V. Mikhaylov; V. Yu. Podaruev; A. I. Troshin. Unsteady high order accuracy DG method for turbulent flow modeling. Matematičeskoe modelirovanie, Tome 30 (2018) no. 5, pp. 37-56. http://geodesic.mathdoc.fr/item/MM_2018_30_5_a3/