Finite volume multischeme for hyperbolic conservation laws

Authors:
Ramaz Botchorishvili
Affiliations:
Faculty of Exact and Natural Sciences, Tbilisi State University, Tbilisi, Georgia
Venue:
FANDB'09 Proceedings of the 2nd WSEAS international conference on Finite differences, finite elements, finite volumes, boundary elements
Year:
2009

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Abstract

Finite volume multischeme approach is developed for numerical solution of hyperbolic conservation laws. The approach allows development of conservative adaptive mesh refinement algorithm when using different finite volume schemes for meshes of different levels of refinement. Multischeme algorithm for one dimensional in space scalar conservation laws is studied in details. Convergence to entropy solution is proved in case of monotone numerical flux functions and essentially bounded initial datum of bounded variation. Extension of the algorithm for systems of conservation laws and for several space dimensions is given.