@Article{IJNAM-2-2,
author = {Tu, S. and S., Aliabadi},
title = {A Slope Limiting Procedure in Discontinuous Galerkin Finite Element Method for Gasdynamics Applications},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2005},
volume = {2},
number = {2},
pages = {163--178},
abstract = {<p style="text-align: justify;">In this paper we demonstrate the performance of a slope
limiting procedure combined with a discontinuous Galerkin (DG) finite
element solver for 2D compressible Euler equations. The slope limiter
can be categorized into van Albada type and is differentiable. This
slope limiter is modified from a similar limiter used in finite volume
solvers to suit the needs of the DC solver. The gradient in an element
is limited using the weighted average of the face gradients. The face
gradients are obtained from the area-weighted average of the gradient on
both sides of the faces. The slope limiting process is very suitable for
meshes discretized by triangle elements. The HLLC (Harten, Lax and van
Leer) or the local Lax-Friedrich (LLF) flux functions is used to compute
the interface fluxes in the DG formulation. The second order TVD
Runge-Kutta scheme is employed for the time integration. The numerical
examples including transonic, supersonic and hypersonic flows show that
the current slope limiting process together with the DG solver is able
to remove overshoots and undershoots around high gradient regions while
preserving the high accuracy of the DC method. The convergence histories
of all examples demonstrate that the limiting process does not stall
convergence to steady state as many other slope limiters do.</p>},
issn = {2617-8710},
doi = {https://doi.org/2005-IJNAM-927},
url = {https://global-sci.com/article/83853/a-slope-limiting-procedure-in-discontinuous-galerkin-finite-element-method-for-gasdynamics-applications}
}