Analysis and design of substation earthing involves computing the equivalent resistance of grounding systems, as well as distribution of potentials on the earth surface due to fault currents [1,2]. While very crude approximations were available in the sixties, several methods have been proposed in the last two decades, most of them on the basis of intuitive ideas such as superposition of punctual current sources and error averaging [3,4]. Although these techniques represented a signicant improvement in the area of earthing analysis, a number of problems have been reported; namely: large computational requirements, unrealistic results when segmentation of conductors is increased, and uncertainty in the margin of error [4].A Boundary Element approach for the numerical computation of substation grounding systems is presented in this paper. Several widespread intuitive methods (such as the Average Potential Method) can be identi ed in this general formulation as the result of suitable assumptions introduced in the BEM formulation to reduce computational cost for speci c choices of the test and trial functions. On the other hand, this general approach allows the use of linear and parabolic leakage current elements to increase accuracy. E orts have been particularly made in getting a drastic reduction in computing time by means of new completely analytical integration techniques, while semi-iterative methods have proven to be specially efcient for solving the involved system of linear equations. This BEM formulation has been implemented in a speci c Computer Aided Design system for grounding analysis developed within the last years. The feasibility of this approach is nally demonstrated by means of its application to two real problems.

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This paper introduces the use of Moving Least-Squares (MLS) approximations for the development of high order upwind schemes on unstructured grids, applied to the numerical solution of the compressible Navier-Stokes equations. This meshfree interpolation technique is designed to reproduce arbitrary functions and their succesive derivatives from scattered, pointwise data, which is precisely the case of unstructured-grid finite volume discretizations. The Navier-Stokes solver presented in this study follows the ideas of the generalized Godunov scheme, using Roe's approximate Riemann solver for the inviscid fluxes. Linear, quadratic and cubic polynomial reconstructions are developed using MLS to compute high order derivatives of the field variables. The diffusive fluxes are computed using MLS as a global reconstruction procedure. Various examples of inviscid and viscous flow are presented and discussed.

SUMMARYThis 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. Copyright