scholarly journals One-Dimensional Shock-Capturing for High-Order Discontinuous Galerkin Methods

2008 ◽  
pp. 307-325 ◽  
Author(s):  
E. Casoni ◽  
J. Peraire ◽  
A. Huerta
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
High Order ◽  
Shock Capturing ◽  
Galerkin Methods ◽  
One Dimensional

A Straightforward hp-Adaptivity Strategy for Shock-Capturing with High-Order Discontinuous Galerkin Methods

2014 ◽  
Vol 6 (01) ◽  
pp. 135-144 ◽  
Author(s):  
Hongqiang Lu ◽  
Qiang Sun
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Mesh Size ◽  
High Order ◽  
Shock Capturing ◽  
Local Order ◽  
Galerkin Methods ◽  
Numerical Tests ◽  
Dg Method ◽  
Coarse Grids

AbstractIn this paper, high-order Discontinuous Galerkin (DG) method is used to solve the two-dimensional Euler equations. A shock-capturing method based on the artificial viscosity technique is employed to handle physical discontinuities. Numerical tests show that the shocks can be captured within one element even on very coarse grids. The thickness of the shocks is dominated by the local mesh size and the local order of the basis functions. In order to obtain better shock resolution, a straightforwardhp-adaptivity strategy is introduced, which is based on the high-order contribution calculated using hierarchical basis. Numerical results indicate that thehp-adaptivity method is easy to implement and better shock resolution can be obtained with smaller local mesh size and higher local order.

scholarly journals On high-order accurate weighted essentially non-oscillatory and discontinuous Galerkin schemes for compressible turbulence simulations

2013 ◽  
Vol 371 (1982) ◽  
pp. 20120172 ◽  
Author(s):  
Chi-Wang Shu
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
High Order ◽  
Shock Capturing ◽  
Compressible Turbulence ◽  
Galerkin Methods ◽  
High Order Methods ◽  
Shock Capturing Schemes

In this article, we give a brief overview on high-order accurate shock capturing schemes with the aim of applications in compressible turbulence simulations. The emphasis is on the basic methodology and recent algorithm developments for two classes of high-order methods: the weighted essentially non-oscillatory and discontinuous Galerkin methods.

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