TY - JOUR
T1 - A High-Order Modified Finite Volume WENO Method on 3D Cartesian Grids
JO - Communications in Computational Physics
VL - 3
SP - 768
EP - 784
PY - 2019
DA - 2019/04
SN - 26
DO - http://doi.org/10.4208/cicp.OA-2018-0254
UR - https://global-sci.org/intro/article_detail/cicp/13146.html
KW - Finite volume method, high-order accuracy, dimension-by-dimension reconstruction,
Cartesian grid.
AB - <p style="text-align: justify;">The modified dimension-by-dimension finite volume (FV) WENO method
on Cartesian grids proposed by Buchmüller and Helzel can retain the full order of accuracy of the one-dimensional WENO reconstruction and requires only one flux computation per interface. The high-order accurate conversion between face-averaged values and face-center point values is the main ingredient of this method. In this paper,
we derive sixth-order accurate conversion formulas on three-dimensional Cartesian
grids. It is shown that the resulting modified FV WENO method is efficient and high-order accurate when applied to smooth nonlinear multidimensional problems, and is
robust for calculating non-smooth nonlinear problems with strong shocks.</p>