dc.contributor.advisor Kulkarni, P S dc.contributor.author Malagi, Keshav Shrinivas dc.date.accessioned 2009-03-11T06:55:01Z dc.date.accessioned 2018-07-31T05:17:05Z dc.date.available 2009-03-11T06:55:01Z dc.date.available 2018-07-31T05:17:05Z dc.date.issued 2009-03-11T06:55:01Z dc.date.submitted 2006 dc.identifier.uri https://etd.iisc.ac.in/handle/2005/419 dc.description.abstract 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. en dc.language.iso en_US en dc.relation.ispartofseries G20358 en dc.subject Kinetics en dc.subject Aeronautics en dc.subject Airflow en dc.subject Least Squares Kinetic Upwind Method (LSKUM) en dc.subject Rotational InVariance en dc.subject Upwinding en dc.subject Kinetic Upwind Method Avec Rotational InVariance (KUMARI) en dc.subject Kinetic Flux Vector Splitting en dc.subject Flux Vector Splitting Method en dc.subject Kinetic Upwind Method en dc.subject.classification Aeronautics en dc.title Rotationally Invariant Kinetic Upwind Method (KUMARI) en dc.type Thesis en dc.degree.name MSc Engg en dc.degree.level Masters en dc.degree.discipline Faculty of Engineering en
﻿