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Performance study of the multiwavelet discontinuous Galerkin approach for solving the Green‐Naghdi equations
Author(s) -
Sharifian Mohammad Kazem,
Hassanzadeh Yousef,
Kesserwani Georges,
Shaw James
Publication year - 2019
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.4732
Subject(s) - solver , discontinuous galerkin method , grid , mathematics , benchmark (surveying) , transformation (genetics) , galerkin method , nonlinear system , multiresolution analysis , sparse grid , mathematical optimization , algorithm , mathematical analysis , computer science , geometry , wavelet , finite element method , artificial intelligence , chemistry , wavelet transform , biochemistry , geodesy , quantum mechanics , thermodynamics , discrete wavelet transform , physics , gene , geography
Summary This paper presents a multiresolution discontinuous Galerkin (DG) scheme for the adaptive solution of Boussinesq‐type equations. The model combines multiwavelet (MW)–based grid adaptation with a DG solver based on the system of fully nonlinear and weakly dispersive Green‐Naghdi (GN) equations. The key feature of the adaptation procedure is to conduct a multiresolution analysis using MWs on a hierarchy of nested grids to improve the efficiency of the reference DG scheme on a uniform grid by computing on a locally refined adapted grid. This way, the local resolution level will be determined by manipulating MW coefficients controlled by a single user‐defined threshold value. The proposed adaptive multiwavelet DG solver for GN equations is assessed using several benchmark problems related to wave propagation and transformation in nearshore areas. The numerical results demonstrate that the proposed scheme retains the accuracy of the reference scheme, while significantly reducing the computational cost.