@Article{NMTMA-17-1074,
author = {Zhao , XiaolongYu , XijunSong , ShicangZou , Shijun and Qing , Fang},
title = {A Lagrangian Discontinuous Galerkin Scheme for the Compressible Euler Equations on Unstructured Triangular Meshes},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2024},
volume = {17},
number = {4},
pages = {1074--1099},
abstract = {<p style="text-align: justify;">The numerical simulation of fluid dynamics problems plays an important role in the studies of laser inertial confinement fusion (ICF) and magnetic confinement fusion (MCF). Due to the complexity of physical processes and the large
deformations of flow field, the numerical simulation of these problems has considerable difficulty. Taking the advantages of the discontinuous Galerkin (DG) method
and the Lagrangian scheme, a second-order Lagrangian type scheme for solving the
compressible Euler equations is developed on unstructured triangular meshes and
implemented by the Runge-Kutta (RK) DG method in this paper. The solver of node
velocity in the scheme has good adaptability for many problems. Without considering the material derivatives of basis functions and the Jacobian matrix associated
with the map between Lagrangian space and Eulerian space, our scheme is relatively
succinct. A HWENO reconstruction is used to eliminate the false oscillations whose
stencils involve only the von Neumann neighborhood so that the scheme keeps compact within the DG method. Finally, some numerical examples are presented to
illustrate the accuracy, resolution, and robustness of our scheme.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2024-0042 },
url = {http://global-sci.org/intro/article_detail/nmtma/23652.html}
}