Open AccessThe Higher-Order CESE Method for Two-dimensional Shallow Water Magnetohydrodynamics Equations
Author(s) -
Sidrah Ahmed,
Saqib Zia
Publication year - 2019
Publication title -
european journal of pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.245
H-Index - 5
ISSN - 1307-5543
DOI - 10.29020/nybg.ejpam.v12i4.3538
Subject(s) - mathematics , finite volume method , finite element method , total variation diminishing , robustness (evolution) , magnetohydrodynamics , taylor series , degenerate energy levels , conservation law , finite difference , projection method , shallow water equations , mathematical analysis , mathematical optimization , mechanics , physics , magnetic field , biochemistry , chemistry , quantum mechanics , gene , dykstra's projection algorithm , thermodynamics
The numerical solution of two-dimensional shallow water magnetohydrodynamics model is obtained using the $4^{th}$-order conservation element solution element method (CESE). The method is based on unified treatment of spatial and temporal dimensions contrary to the finite difference and finite volume methods. The higher-order CESE scheme is constructed using same definitions of conservation and solution elements that are used for $2^{nd}$-order CESE scheme formulation. Hence it is more convenient to increase accuracy of CESE methods as compared to the finite difference and finite volume methods. Moreover the scheme is developed using the conservative formulation and do not require change in the source term for treating the degenerate hyperbolic nature of shallow water magnetohydrodynamics system due to divergence constraint. The spatial and temporal derivatives have been obtained by incorporating $4^{th}$-order Taylor expansion and the projection method is used to handle the divergence constraint. The accuracy and robustness of the extended method is tested by performing a benchmark numerical test taken from the literature. Numerical experiment revealed the accuracy and computational efficiency of the scheme.