High order finite volume schemes on unstructured grids using Moving Least Squares reconstruction. Application to shallow water dynamics
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High order finite volume schemes on unstructured grids using Moving Least Squares reconstruction. Application to shallow water dynamicsDate
2005Abstract
[Abstract] 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
succesive derivatives can be accurately reconstructed using this meshfree technique in a general
nodal arrangement. The methodology proposed is used in the construction of low-dissipative highorder
high-resolution schemes for the shallow water equations. In particular, second and third-orderreconstruction
upwind schemes for unstructured grids based on Roe’s flux difference splitting are
developed and applied to inviscid and viscous flows. This class of meshfree reconstruction techniques
provide 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.
Keywords
Shallow water dynamics
Finite volume method
High-resolution schemes
Meshfree methods
Moving least-squares
Unstructured grids
Finite volume method
High-resolution schemes
Meshfree methods
Moving least-squares
Unstructured grids
Description
Aceptado para su publicación en International journal for numerical methods in engineering, el 08/06/2005
Editor version
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This is a preprint of an
article accepted for publication in "International journal for numerical methods in engineering" © copyright 2005 John Wiley & Sons