Performance study of the multiwavelet discontinuous Galerkin approach for solving the Green‐Naghdi equations. (2nd May 2019)

• Record Type: Journal Article
• Authors: Sharifian, Mohammad Kazem; Hassanzadeh, Yousef; Kesserwani, Georges; Shaw, James
• Is Part Of: International journal for numerical methods in fluids. Volume 90:Number 10(2019)
• Page Start: 501
• Page End: 521
• Publication Date: 2019-05-02
• Subjects: Boussinesq‐type equations -- discontinuous Galerkin -- Green‐Naghdi equations -- multiresolution analysis -- multiwavelets -- nearshore wave processes; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4732
• Languages: English
• ISSNs: 0271-2091

Abstract

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. Abstract : In this paper, we report a multiresolution grid adaption technique for solving the fully nonlinear and weakly dispersive Green‐Naghdi equations, based on combining multiwavelets with the discontinuous Galerkin approach. The main motivation is to use multiwavelets as a mechanism for transforming the single resolution information into multiresolution information and deploy this feature to create an adaptive grid. The resulting framework is robust and straightforward and provides accessing, upscaling, and downscaling data across various spectrum of resolutions involved in the adaptive grid.