Application of the improved discontinuous Galerkin method in shock tubes

被引：0

作者：

Hou P. ^{[1
]}

Zhang W.-P. ^{[1
]}

Ming P.-J. ^{[1
]}

Na W. ^{[1
]}

Shi F. ^{[1
]}

机构：

[1] College of Power and Energy Engineering, Harbin Engineering University

来源：

Harbin Gongcheng Daxue Xuebao/Journal of Harbin Engineering University | 2010年 / 31卷 / 02期

关键词：

Discontinuous Galerkin method; Distinguish rate; Shock wave; Upwind format;

D O I：

10.3969/j.issn.1006-7043.2010.02.010

中图分类号：

O24 [计算数学];

学科分类号：

070102 ;

摘要：

In recent years, the discontinuous Galerkin (DG) method emerged to produce excellent results in fluid computations. However, the DG method can be improved in two areas. One area allows the main part to correct the assistant part. The improved DG method with upwind format can lock shock waves within a small number of grids, sometimes locking them into one grid. Left or right upwind format can distinguish mini type shock waves, and the dual lateral upwind format can provide a better fit, and thus a more precise solution. Results of numerical simulations showed that the DG method has many helpful characteristics, such as good convergence, small numerical dissipation and good shock wave capturing ability. If you select an m-basis function, the DG method can achieve m+1 order accuracy. When calculating the interface flux function we need no additional nodal information and accuracy is improved. In addition, it is very easy to achieve high-order accuracy.

引用

页码：188 / 194

页数：6

共 10 条

[1] Su M., Zhang J., Application of RKDG in solution of N-S equation, Chinese Journal of Computational Physics, 16, 2, pp. 168-176, (1999)
[2] Cockburn B., Lin S.Y., Shu C.W., TVB Runge-Kutta method local projection discontinuous Galerkin finite element method for conservation laws III: One dimensional systems, Comput Phys, 84, 5, pp. 90-113, (1989)
[3] Cockburn B., Shu C.W., TVB Runge-Kutta method local projection-discontinuous, Galerkin finite element method for Conservation laws, Mathematics of Computation, 52, 8, pp. 411-435, (1989)
[4] Cockburn B., Shu C.W., The Runge-Kutta method local projection p1-discontinuous Galerkin method for scalar conservation law, Computers and Fluids, 34, 4, pp. 491-506, (2005)
[5] Cockburn B., Houand S., Shu C.W., The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: The multidimensional case, Math Comput, 54, 9, pp. 545-581, (1990)
[6] pp. 130-151, (1998)
[7] Cockburn B., Shu C.W., The Runge-Kutta discontinuous Galerkin method for conservation laws V: Multidimensional systems, Comput Phys, 53, 11, pp. 141-199, (1998)
[8] Cockburn B., Shu C.W., Runge-Kutta discontinuous Galerkin method for convection-dominated problems, Sci Comput, 19, 7, pp. 173-261, (2001)
[9] pp. 463-467, (2001)
[10] Cockburn B., Shu C.W., The local discontinuous Galerkin for time dependent convection-diffusion systems, SIAM Journal of Numerical Analysis, 17, 3, pp. 2440-2463, (1998)

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