@Article{NMTMA-9-87,
author = {Jianming Liu, Jianxian Qiu, Mikhail Goman, Xinkai Li and Meilin Liu},
title = {Positivity-Preserving Runge-Kutta Discontinuous Galerkin Method on Adaptive Cartesian Grid for Strong Moving Shock},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2016},
volume = {9},
number = {1},
pages = {87--110},
abstract = {<p style="text-align: justify;">In order to suppress the failure of preserving positivity of density or pressure,
a positivity-preserving limiter technique coupled with $h$-adaptive Runge-Kutta
discontinuous Galerkin (RKDG) method is developed in this paper. Such a method is
implemented to simulate flows with the large Mach number, strong shock/obstacle
interactions and shock diffractions. The Cartesian grid with ghost cell immersed
boundary method for arbitrarily complex geometries is also presented. This approach
directly uses the cell solution polynomial of DG finite element space as the
interpolation formula. The method is validated by the well documented test examples
involving unsteady compressible flows through complex bodies over a large
Mach numbers. The numerical results demonstrate the robustness and the versatility
of the proposed approach.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2015.m1416},
url = {http://global-sci.org/intro/article_detail/nmtma/12368.html}
}