A High-Order Modified Finite Volume WENO Method on 3D Cartesian Grids (Communications in Computational Physics, 2019)
The modified dimension-by-dimension finite volume (FV) WENO methodon 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 Cartesiangrids. It is shown that the resulting modified FV WENO method is efficient and high-order accurate when applied to smooth nonlinear multidimensional problems, and isrobust for calculating non-smooth nonlinear problems with strong shocks.