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- W2549508740 abstract "Numerical solutions for the two-dimensional Laplace equation using isosceles right triangular cell-centred and square control volumes are compared in this work. The methodology employed for the square grids is the one related to unstructured grids, while for the square volumes the discretization process is based on the structured grids methodology. For both geometries, the number of control volumes varies from 4 up to 16,777,216, with a refinement ratio of 2. In order to speed up the obtainment of the numerical results, the algebraic multigrid method was employed for the triangular grids and the geometric multigrid method for the square ones. An unexpected observation was that, for a grid with the same number of control volumes, the triangular grid has a worse performance than the square one, exhibiting a numerical error 2.3 - 2.4 greater. With the intention of reducing the discretization error, providing more accurate results, a strategy based on Richardson Extrapolations was employed, called Multiple Richardson Extrapolations (MRE). According to previous works, this methodology was successfully used in square grids, but its use is not a common practice for triangular ones. It was verified that MRE efficiently reduces the discretization error in triangular grids, although error magnitudes are considerably higher than the ones achieved for a square grid with the same number of control volumes and MRE. The main results of this work can be summarized as follows: (1) although triangular grids are more adaptable than square ones, the last ones should be used as frequent as possible due to the lower discretization errors involved; (2) MRE is efficient and can be used for the reduction of discretization errors in triangular grids; (3) for the same approximation scheme, numerical errors with MRE can not be lessening under than a limit value: there is always a dependence on the performance of the original results." @default.
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- W2549508740 date "2010-01-01" @default.
- W2549508740 modified "2023-09-27" @default.
- W2549508740 title "SOLUTIONS OF THE 2D LAPLACE EQUATION WITH TRIANGULAR GRIDS AND MULTIPLE RICHARDSON EXTRAPOLATIONS" @default.
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