@Article{NMTMA-1-435,
author = {Jianxian Qiu},
title = {Development and Comparison of Numerical Fluxes for LWDG Methods},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2008},
volume = {1},
number = {4},
pages = {435--459},
abstract = {<p style="text-align: justify;">The discontinuous Galerkin (DG) or local discontinuous Galerkin (LDG)
method is a spatial discretization procedure for convection-diffusion equations, which
employs useful features from high resolution finite volume schemes, such as the exact
or approximate Riemann solvers serving as numerical fluxes and limiters. The Lax-Wendroff time discretization procedure is an alternative method for time discretization
to the popular total variation diminishing (TVD) Runge-Kutta time discretizations. In
this paper, we develop fluxes for the method of DG with Lax-Wendroff time discretization procedure (LWDG) based on different numerical fluxes for finite volume or finite
difference schemes, including the first-order monotone fluxes such as the Lax-Friedrichs
flux, Godunov flux, the Engquist-Osher flux etc. and the second-order TVD fluxes. We
systematically investigate the performance of the LWDG methods based on these different numerical fluxes for convection terms with the objective of obtaining better performance by choosing suitable numerical fluxes. The detailed numerical study is mainly
performed for the one-dimensional system case, addressing the issues of CPU cost, accuracy, non-oscillatory property, and resolution of discontinuities. Numerical tests are
also performed for two dimensional systems.</p>},
issn = {2079-7338},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/nmtma/6058.html}
}