TY - JOUR
T1 - A Straightforward $hp$-Adaptivity Strategy for Shock-Capturing with High-Order Discontinuous Galerkin Methods
AU - Lu , Hongqiang
AU - Sun , Qiang
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 135
EP - 144
PY - 2014
DA - 2014/06
SN - 6
DO - http://doi.org/10.4208/aamm.2013.m-s1
UR - https://global-sci.org/intro/article_detail/aamm/9.html
KW - $hp$-adaptivity, shock capturing, discontinuous Galerkin.
AB - <p style="text-align: justify;">In 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 straightforward $hp$-adaptivity strategy is introduced, which is based on the high-order contribution
calculated using hierarchical basis. Numerical results indicate that the $hp$-adaptivity
method is easy to implement and better shock resolution can be obtained with smaller
local mesh size and higher local order.</p>