TY - JOUR
T1 - A Study on CFL Conditions for the DG Solution of Conservation Laws on Adaptive Moving Meshes
AU - Zhang , Min
AU - Huang , Weizhang
AU - Qiu , Jianxian
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 111
EP - 139
PY - 2023
DA - 2023/01
SN - 16
DO - http://doi.org/10.4208/nmtma.OA-2021-0169
UR - https://global-sci.org/intro/article_detail/nmtma/21345.html
KW - Discontinuous Galerkin method, adaptive mesh, moving mesh, CFL condition, stability.
AB - <p style="text-align: justify;">The selection of time step plays a crucial role in improving stability and efficiency in the Discontinuous Galerkin (DG) solution of hyperbolic conservation laws
on adaptive moving meshes that typically employs explicit stepping. A commonly
used selection of time step is a direct extension based on Courant-Friedrichs-Levy
(CFL) conditions established for fixed and uniform meshes. In this work, we provide
a mathematical justification for those time step selection strategies used in practical
adaptive DG computations. A stability analysis is presented for a moving mesh DG
method for linear scalar conservation laws. Based on the analysis, a new selection
strategy of the time step is proposed, which takes into consideration the coupling
of the $α$-function (that is related to the eigenvalues of the Jacobian matrix of the
flux and the mesh movement velocity) and the heights of the mesh elements. The
analysis also suggests several stable combinations of the choices of the $α$-function
in the numerical scheme and in the time step selection. Numerical results obtained
with a moving mesh DG method for Burgers&#39; and Euler equations are presented. For
comparison purpose, numerical results obtained with an error-based time step-size
selection strategy are also given.</p>