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Weighted Least Squares Kinetic Upwind Method using Eigenvector Basis

Arora, Konark and Deshpande, SM (2004) Weighted Least Squares Kinetic Upwind Method using Eigenvector Basis. 2004 FM 17.


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The least squares grid-free method, though having the ability to work effectively on any distribution of points is limited by the requirement of a good connectivity around a node. This report deals with a fundamental improvement over the usual least squares grid-free method to overcome this limitation of the least squares grid-free methods. The new approach involves the use of the weights to diagonalize the least squares matrix A such that the x and y directions become the eigen directions along which the higher dimensional least squares formulae reduce to the one dimensional formulae. A very important advantage of this approach (apart from improving the convergence characteristics of the grid-free solver) is that it helps in tackling the problems of code divergence due to the degenerate and other cases of bad connectivity. Appropriate methods of finding suitable weights to diagonalize the two and three dimensional least squares matrix have been discussed in this report. Finally, some two dimensional results have been given in support of our claim.

Item Type: Departmental Technical Report
Keywords: Weighted Least Squares;LSKUM;Eigenvector Basis
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited: 24 Oct 2004
Last Modified: 19 Sep 2010 04:16
URI: http://eprints.iisc.ac.in/id/eprint/2171

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