Deshpande, SM and Anil, N and Arora, K and Malagi, K and Varma, M (2004) Some Fascinating New Developments in Kinetic Schemes. In: Workshop on Modeling & Simulation in Life Sciences, Materials and Technology, December 78, 2004, I.I.T. Madras, pp. 4363.

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Abstract
Least Squares Kinetic Upwind Method (LSKUM) which is a grid free or meshless method is a subject of intense R&D activity in ARDB CFD Centre. The LSKUM requires point distribution (or a cloud of points) and a connectivity preprocessor to generate connectivity for each node in the computational domain. These clouds of points have been classified into simple clouds, chimera clouds and multiple chimera clouds. A simple cloud is a cloud of points generated by a simple grid generator such as elliptic grid generator in a geometrically simple block or by a triangular grid generator for simple shapes. A chimera cloud is a cloud of points obtained by overlapping two simple grids. For example, for a 2 D cascade we may obtain chimera cloud by overlapping two Ogrids around each aerofoil in the cascade. A multiple chimera cloud is obtained by overlapping of several simple clouds. Central to the application of LSKUM is therefore generation of connectivity for all types of clouds.Various methods have been developed for the same. FAME cloud consists of several overlapping simple clouds with a high degree of clustering near sharp geometric features. Connectivity is called nearly degenerate when the least squares matrix becomes singular or very nearly singular. This is just one example of bad connectivity which causes code divergence or "blowing up"  a term commonly used by code developers. Other examples of bad connectivity are : highly anisotropic distribution of points, nearly empty quadrants, etc. Large inaccuracy in computation of derivatives on such connectivity sets gives very inaccurate results and in extreme cases causes code divergence. Highly clustered grids are necessary for resolution of fine scales in flow and these in turn lead to highly anisotropic connectivity. There is thus a need for the development of robust solver. Improvements in solution algorithm are required in many directions. One direction of research is a robust solver and better connectivity. Yet another direction is low dissipation flux splitting and further introduce rotational invariance, ie. develop upwinding without symmetry breaking. Another line of research is a new method of point generation without use of grid generator.
Item Type:  Conference Paper 

Keywords:  LSKUM;Low Dissipation;BGK;mkfvs;Eigenvector basis;WLSKUM;LSKUMARI;Rotational Invariance;Symmetry breaking;Fourier Series;Quadtree;Octree;Point generation;Adaptive;Connectivity 
Department/Centre:  Division of Mechanical Sciences > Aerospace Engineering (Formerly, Aeronautical Engineering) 
Date Deposited:  05 Feb 2007 
Last Modified:  19 Sep 2010 04:20 
URI:  http://eprints.iisc.ernet.in/id/eprint/3828 
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