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The modified dimension-by-dimension finite volume (FV) WENO method onCartesian grids proposed by Buchm\"{u}ller and Helzel can retain the full orderof accuracy of the one-dimensional WENO reconstruction and requires only oneflux computation per interface. The high-order accurate conversion betweenface-averaged values and face-center point values is the main ingredient ofthis method. In this paper, we derive sixth-order accurate conversion formulason three-dimensional Cartesian grids. It is shown that the resulting modifiedFV WENO method is efficient and high-order accurate when applied to smoothnonlinear multidimensional problems, and is robust for calculating non-smoothnonlinear problems with strong shocks..

A High-Order Modified Finite Volume WENO Method on 3D Cartesian Grids