TY - JOUR
T1 - A Discontinuous Galerkin Extension of the Vertex-Centered Edge-Based Finite Volume Method
JO - Communications in Computational Physics
VL - 2-4
SP - 456
EP - 468
PY - 2009
DA - 2009/02
SN - 5
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cicp/7743.html
KW - 
AB - <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>