Cueto-Felgueroso Landeira, LuisColominas, IgnasiNavarrina, FermínCasteleiro, Manuel2005-12-052005-12-052005http://hdl.handle.net/2183/338Aceptado para su publicación en International journal for numerical methods in engineering, el 08/06/2005[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.application/pdftext/plainengThis is a preprint of an article accepted for publication in "International journal for numerical methods in engineering" © copyright 2005 John Wiley & SonsShallow water dynamicsFinite volume methodHigh resolution schemesMeshfree methodsMoving least squaresUnstructured gridspreprintopen access