A High-Order Modified Finite Volume WENO Method on 3D Cartesian Grids
This work provides an incremental improvement to numerical methods for solving hyperbolic conservation laws on Cartesian grids.
The paper derives sixth-order accurate conversion formulas for a modified finite volume WENO method on 3D Cartesian grids, demonstrating efficiency and high-order accuracy for smooth problems and robustness for problems with strong shocks.
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..