@Article{CiCP-5-2-4,
author = {},
title = {A Discontinuous Galerkin Extension of the Vertex-Centered Edge-Based Finite Volume Method},
journal = {Communications in Computational Physics},
year = {2009},
volume = {5},
number = {2-4},
pages = {456--468},
abstract = {<p style="text-align: justify;">The finite volume (FV) method is the dominating discretization technique
for computational fluid dynamics (CFD), particularly in the case of compressible fluids. The discontinuous Galerkin (DG) method has emerged as a promising high-accuracy alternative. The standard DG method reduces to a cell-centered FV method at
lowest order. However, many of today’s CFD codes use a vertex-centered FV method
in which the data structures are edge based. We develop a new DG method that reduces to the vertex-centered FV method at lowest order, and examine here the new
scheme for scalar hyperbolic problems. Numerically, the method shows optimal-order
accuracy for a smooth linear problem. By applying a basic hp-adaption strategy, the
method successfully handles shocks. We also discuss how to extend the FV edge-based
data structure to support the new scheme. In this way, it will in principle be possible to
extend an existing code employing the vertex-centered and edge-based FV discretization to encompass higher accuracy through the new DG method.</p>},
issn = {1991-7120},
doi = {https://doi.org/2009-CiCP-7743},
url = {https://global-sci.com/article/81095/a-discontinuous-galerkin-extension-of-the-vertex-centered-edge-based-finite-volume-method}
}