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A high‐order backward forward sweep interpolating algorithm for semi‐Lagrangian method
Author(s) -
Mortezazadeh Mohammad,
Wang Liangzhu Leon
Publication year - 2017
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4362
Subject(s) - interpolation (computer graphics) , solver , mathematics , advection , multigrid method , dissipation , mathematical optimization , algorithm , order of accuracy , linear interpolation , dispersion (optics) , computer science , mathematical analysis , numerical analysis , partial differential equation , physics , numerical stability , animation , computer graphics (images) , polynomial , optics , thermodynamics
Abstract Conventional semi‐Lagrangian methods often suffer from poor accuracy and imbalance problems of advected properties because of low‐order interpolation schemes used and/or inability to reduce both dissipation and dispersion errors even with high‐order schemes. In the current work, we propose a fourth‐order semi‐Lagrangian method to solve the advection terms at a computing cost of third‐order interpolation scheme by applying backward and forward interpolations in an alternating sweep manner. The method was demonstrated for solving 1‐D and 2‐D advection problems, and 2‐D and 3‐D lid‐driven cavity flows with a multi‐level V‐cycle multigrid solver. It shows that the proposed method can reduce both dissipation and dispersion errors in all regions, especially near sharp gradients, at a same accuracy as but less computing cost than the typical fourth‐order interpolation because of fewer grids used. The proposed method is also shown able to achieve more accurate results on coarser grids than conventional linear and other high‐order interpolation schemes in the literature. Copyright © 2017 John Wiley & Sons, Ltd.