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High‐order finite volume schemes on unstructured grids using moving least‐squares reconstruction. Application to shallow water dynamics
Author(s) -
CuetoFelgueroso L.,
Colominas I.,
Fe J.,
Navarrina F.,
Casteleiro M.
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1442
Subject(s) - finite volume method , shallow water equations , upwind scheme , quadratic equation , computation , mathematics , unstructured grid , dissipation , mathematical optimization , moving least squares , computer science , algorithm , mathematical analysis , grid , geometry , mechanics , discretization , physics , thermodynamics
This paper introduces the use of moving least‐squares (MLS) approximations for the development of high‐order finite volume discretizations on unstructured grids. The field variables and their successive derivatives can be accurately reconstructed using this mesh‐free technique in a general nodal arrangement. The methodology proposed is used in the construction of two numerical schemes for the shallow water equations on unstructured grids: a centred Lax–Wendroff method with added shock‐capturing dissipation, and a Godunov‐type upwind scheme, with linear and quadratic reconstructions. This class of mesh‐free techniques provides a robust and general approximation framework which represents an interesting alternative to the existing procedures, allowing, in addition, an accurate computation of the viscous fluxes. Copyright © 2005 John Wiley & Sons, Ltd.