Combined DG Scheme That Maintains Increased Accuracy
in Shock Wave Areas
M. E. Ladonkinaa,b, O. A. Nekliudovaa,b, V. V. Ostapenkob,c,*,
and Corresponding Member of the RAS V. F. Tishkina,b
a Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow,
125047 Russia
b Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
c Novosibirsk State University, Novosibirsk, 630090 Russia
Correspondence to: *e-mail: ostapenko_vv@ngs.ru
Received 27 May, 2019
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.
DOI: 10.1134/S106456241906005X