TY - JOUR T1 - A High-Order Modified Finite Volume WENO Method on 3D Cartesian Grids AU - Yulong Du, Li Yuan & Yahui Wang 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 -

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.