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Rotationally Invariant Kinetic Upwind Method (KUMARI)

Electronic Theses of Indian Institute of Science

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Title Rotationally Invariant Kinetic Upwind Method (KUMARI)
 
Creator Malagi, Keshav Shrinivas
 
Subject Kinetics
Aeronautics
Airflow
Least Squares Kinetic Upwind Method (LSKUM)
Rotational InVariance
Upwinding
Kinetic Upwind Method Avec Rotational InVariance (KUMARI)
Kinetic Flux Vector Splitting
Flux Vector Splitting Method
Kinetic Upwind Method
Aeronautics
 
Description In the quest for a high fidelity numerical scheme for CFD it is necessary to satisfy demands on accuracy, conservation, positivity and upwinding. Recently the requirement of rotational invariance has been added to this list. In the present work we are mainly interested in upwinding and rotational invariance of Least Squares Kinetic Upwind Method (LSKUM). The standard LSKUM achieves upwinding by stencil division along co-ordinate axes which is referred to as co-ordinate splitting method. This leads to symmetry breaking and rotational invariance is lost. Thus the numerical solution becomes co-ordinate frame dependent. To overcome this undesirable feature of existing numerical schemes, a new algorithm called KUMARI (Kinetic Upwind Method Avec Rotational Invariance, 'Avec' in French means 'with') has been developed. The interesting mathematical relation between directional derivative, Fourier series and divergence operator has been used effectively to achieve upwinding as well as rotational invariance and hence making the scheme truly or genuinely multidimensional upwind scheme. The KUMARI has been applied to the test case of standard 2D shock reflection problem, flow past airfoils, then to 2D blast wave problem and lastly to 2D Riemann problem (Lax's 3rd test case). The results show that either KUMARI is comparable to or in some cases better than the usual LSKUM.
 
Contributor Kulkarni, P S
 
Date 2009-03-11T06:55:01Z
2009-03-11T06:55:01Z
2009-03-11T06:55:01Z
2006-07
 
Type Thesis
 
Identifier http://hdl.handle.net/2005/419
 
Language en_US
 
Relation G20358