On the Accuracy of Discontinuous Galerkin Method Calculating Gas-Dynamic Shock Waves

被引:2
作者
Ladonkina, M. E. [1 ,2 ]
Nekliudova, O. A. [1 ,2 ]
Ostapenko, V. V. [2 ]
Tishkin, V. F. [1 ,2 ]
机构
[1] Russian Acad Sci, Fed Res Ctr, Keldysh Inst Appl Math, Moscow, Russia
[2] Russian Acad Sci, Siberian Branch, Lavrentyev Inst Hydrodynam, Novosibirsk, Russia
基金
俄罗斯科学基金会;
关键词
gas dynamic equations; shock waves; discontinuous Galerkin method; DIFFERENCE SCHEMES;
D O I
10.1134/S1064562423700746
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The results of a numerical calculation of gas-dynamic shock waves that arise in solving the Cauchy problem with smooth periodic initial data are presented for three variants of the discontinuous Galerkin (DG) method, in which the solution is sought in the form of a piecewise linear discontinuous function. It is shown that the DG methods with the Cockburn limiter used for monotonization have approximately the same accuracy in shock influence areas, while the nonmonotone DG method (with no limiter) has a significantly higher accuracy in these areas. Accordingly, it can be used as a basic method in the construction of a combined scheme that monotonically localizes shock fronts and maintains increased accuracy in the areas of their influence.
引用
收藏
页码:120 / 125
页数:6
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