Open AccessCombined DG scheme that maintains increased accuracy in areas of shock waves
Author(s) -
M. E. Ladonkina,
M. E. Ladonkina,
O. A. Nekliudova,
O. A. Nekliudova,
В. В. Остапенко,
Vladimir Victorovich Ostapenko,
В. Ф. Тишкин,
В. Ф. Тишкин
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-56524892119-124
Subject(s) - smoothness , monotonic function , scheme (mathematics) , nonlinear system , shock wave , shock (circulatory) , galerkin method , mathematics , mathematical analysis , physics , mechanics , quantum mechanics , medicine
A combined scheme of the discontinuous Galerkin method is proposed. This scheme monotonously localizes the fronts of shock waves and simultaneously maintains increased accuracy in the regions of smoothness of the calculated solutions. In this scheme, a non-monotonic version of the third-order DG method is used as the baseline and a monotonic version of this method is used as the internal one, in which a nonlinear correction of numerical flows is used. Tests demonstrating the advantages of the new scheme compared to the standard monotonized variants of the DG method are provided.