Finite volume methods for solving hyperbolic partial differential equations on curved manifolds

The natural mathematical arena to formulate conservation laws on curve manifolds is that of differential geometry. Ricci developed this branch of mathematics from 1887 to 1896. Subsequent work in differential geometry has made it an indespensible tool for solving in mathematical physics. The idea f...

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Κύριος συγγραφέας:	Rahman, Moshiour
Μορφή:	Άρθρο
Γλώσσα:	English
Έκδοση:	BRAC University 2010
Θέματα:	Finite volume methods Curved manifolds Conservation law Wave propagation
Διαθέσιμο Online:	http://hdl.handle.net/10361/533

id	10361-533
record_format	dspace
spelling	10361-5332019-09-29T05:46:17Z Finite volume methods for solving hyperbolic partial differential equations on curved manifolds Rahman, Moshiour Finite volume methods Curved manifolds Conservation law Wave propagation The natural mathematical arena to formulate conservation laws on curve manifolds is that of differential geometry. Ricci developed this branch of mathematics from 1887 to 1896. Subsequent work in differential geometry has made it an indespensible tool for solving in mathematical physics. The idea from differential geometry is to formulate hyperbolic conservation laws of scalar field equation on curved manifolds. The finite volume method is formulated such that scalar variables are numerically conserved and vector variables have a geometric source term that is naturally incorporated into a modified Riemann solver. The orthonormalization allows one to solve Cartesian Riemann problems that are devoid of geometric terms. The new method is tested via application to the linear wave equation on a curved manifold. 2010-10-14T14:24:33Z 2010-10-14T14:24:33Z 2005 Article http://hdl.handle.net/10361/533 en BRAC University Journal, BRAC University;Vol.2, No.1,pp. 99-103 application/pdf BRAC University
institution	Brac University
collection	Institutional Repository
language	English
topic	Finite volume methods Curved manifolds Conservation law Wave propagation
spellingShingle	Finite volume methods Curved manifolds Conservation law Wave propagation Rahman, Moshiour Finite volume methods for solving hyperbolic partial differential equations on curved manifolds
description	The natural mathematical arena to formulate conservation laws on curve manifolds is that of differential geometry. Ricci developed this branch of mathematics from 1887 to 1896. Subsequent work in differential geometry has made it an indespensible tool for solving in mathematical physics. The idea from differential geometry is to formulate hyperbolic conservation laws of scalar field equation on curved manifolds. The finite volume method is formulated such that scalar variables are numerically conserved and vector variables have a geometric source term that is naturally incorporated into a modified Riemann solver. The orthonormalization allows one to solve Cartesian Riemann problems that are devoid of geometric terms. The new method is tested via application to the linear wave equation on a curved manifold.
format	Article
author	Rahman, Moshiour
author_facet	Rahman, Moshiour
author_sort	Rahman, Moshiour
title	Finite volume methods for solving hyperbolic partial differential equations on curved manifolds
title_short	Finite volume methods for solving hyperbolic partial differential equations on curved manifolds
title_full	Finite volume methods for solving hyperbolic partial differential equations on curved manifolds
title_fullStr	Finite volume methods for solving hyperbolic partial differential equations on curved manifolds
title_full_unstemmed	Finite volume methods for solving hyperbolic partial differential equations on curved manifolds
title_sort	finite volume methods for solving hyperbolic partial differential equations on curved manifolds
publisher	BRAC University
publishDate	2010
url	http://hdl.handle.net/10361/533
work_keys_str_mv	AT rahmanmoshiour finitevolumemethodsforsolvinghyperbolicpartialdifferentialequationsoncurvedmanifolds
_version_	1814307033809158144

Finite volume methods for solving hyperbolic partial differential equations on curved manifolds

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