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On splitting‐based mass and total energy conserving arbitrary order shallow‐water schemes
Author(s) -
Skiba Yuri N.,
Filatov Denis M.
Publication year - 2007
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20196
Subject(s) - discretization , mathematics , partial derivative , partial differential equation , cartesian coordinate system , simple (philosophy) , finite difference , numerical analysis , finite difference method , shallow water equations , space (punctuation) , order (exchange) , method of lines , scheme (mathematics) , order of accuracy , mathematical optimization , mathematical analysis , differential equation , numerical partial differential equations , ordinary differential equation , geometry , computer science , differential algebraic equation , philosophy , epistemology , finance , economics , operating system
A new method for numerical solution to the shallow‐water equations is suggested. The method allows constructing a family of finite difference schemes of different approximation order that conserve the mass and the total energy. Our approach is based on the method of splitting, and unlike others it permits to derive conservative numerical schemes after discretizing all the partial derivatives, both spatial and temporal. The schemes thus appear to be fully discrete, both in time and in space. Besides, due to a simple structure of the matrices appeared therewith, the method provides essential benefits in the computational cost of solution and is easy‐to‐implement in the Cartesian and spherical geometries. Numerical results confirm functionality and efficiency of the developed method. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007