Email this article Combined DG Scheme That Maintains Increased Accuracy in Shock Wave Areas
- Authors: Ladonkina M.E.1,2, Nekliudova O.A.1,2, Ostapenko V.V.2,3, Tishkin V.F.1,2
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Affiliations:
- Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences
- Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences
- Novosibirsk State University
- Issue: Vol 100, No 3 (2019)
- Pages: 519-523
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225735
- DOI: https://doi.org/10.1134/S106456241906005X
- ID: 225735
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Abstract
A combined scheme for the discontinuous Galerkin (DG) method is proposed. This scheme monotonically localizes the fronts of shock waves and simultaneously maintains increased accuracy in the regions of smoothness of the computed weak solutions. In this scheme, a nonmonotone version of the third-order DG method is used as a baseline scheme and a monotone version of this method is used as an internal scheme, in which a nonlinear correction of numerical fluxes is used. Tests demonstrate the advantages of the new scheme as compared to standard monotonized variants of the DG method.
About the authors
M. E. Ladonkina
Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences; Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences
Email: ostapenko_vv@ngs.ru
Russian Federation, Moscow, 125047; Novosibirsk, 630090
O. A. Nekliudova
Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences; Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences
Email: ostapenko_vv@ngs.ru
Russian Federation, Moscow, 125047; Novosibirsk, 630090
V. V. Ostapenko
Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences; Novosibirsk State University
Author for correspondence.
Email: ostapenko_vv@ngs.ru
Russian Federation, Novosibirsk, 630090; Novosibirsk, 630090
V. F. Tishkin
Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences; Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences
Email: ostapenko_vv@ngs.ru
Russian Federation, Moscow, 125047; Novosibirsk, 630090
