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

2018/09/25 by Yulong Du, Li Yuan, Du, Yulong +3
Engineering · Mathematics · #65M08 #65M12 #65M20 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1809.09355

openalex publication_date 2018/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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..

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