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dc.contributor.advisorRaghurama Rao, S V
dc.contributor.advisorSekhar, M
dc.contributor.authorRuhi, Ankit
dc.date.accessioned2018-02-07T12:43:14Z
dc.date.accessioned2018-07-31T06:09:14Z
dc.date.available2018-02-07T12:43:14Z
dc.date.available2018-07-31T06:09:14Z
dc.date.issued2018-02-07
dc.date.submitted2016
dc.identifier.urihttp://etd.iisc.ac.in/handle/2005/3072
dc.identifier.abstracthttp://etd.iisc.ac.in/static/etd/abstracts/3937/G28253-Abs.pdfen_US
dc.description.abstractTurbulence is an open and challenging problem for mathematical approaches, physical modeling and numerical simulations. Numerical solutions contribute significantly to the understand of the nature and effects of turbulence. The focus of this thesis is the development of appropriate numerical methods for the computer simulation of turbulent flows. Many of the existing approaches to turbulence utilize analogies from kinetic theory. Degond & Lemou (J. Math. Fluid Mech., 4, 257-284, 2002) derived a k-✏ type turbulence model completely from kinetic theoretic framework. In the first part of this thesis, a numerical method is developed for the computer simulation based on this model. The Boltzmann equation used in the model has an isotropic, relaxation collision operator. The relaxation time in the collision operator depends on the microscopic turbulent energy, making it difficult to construct an efficient numerical scheme. In order to achieve the desired numerical efficiency, an appropriate change of frame is applied. This introduces a stiff relaxation source term in the equations and the concept of asymptotic preserving schemes is then applied to tackle the stiffness. Some simple numerical tests are introduced to validate the new scheme. In the second part of this thesis, alternative approaches are sought for more efficient numerical techniques. The Lattice Boltzmann Relaxation Scheme (LBRS) is a novel method developed recently by Rohan Deshmukh and S.V. Raghuram Rao for simulating compressible flows. Two different approaches for the construction of implicit sub grid scale -like models as Implicit Large Eddy Simulation (ILES) methods, based on LBRS, are proposed and are tested for Burgers turbulence, or Burgulence. The test cases are solved over a largely varying Reynolds number, demonstrating the efficiency of this new ILES-LBRS approach. In the third part of the thesis, as an approach towards the extension of ILES-LBRS to incompressible flows, an artificial compressibility model of LBRS is proposed. The modified framework, LBRS-ACM is then tested for standard viscous incompressible flow test cases.en_US
dc.language.isoen_USen_US
dc.relation.ispartofseriesG28253en_US
dc.subjectTurbulence Modelingen_US
dc.subjectIncompressible Flowsen_US
dc.subjectLarge Eddy Simulation (LES)en_US
dc.subjectNumerical Schemesen_US
dc.subjectTurbulence Modelen_US
dc.subjectLattice Boltzmann Relaxation Scheme (LBRS)en_US
dc.subjectBurgers Turbulenceen_US
dc.subjectImplicit Large Eddy Simulation (ILES)en_US
dc.subjectTurbulence Kinetic Theoryen_US
dc.subjectTurbulenceen_US
dc.subject.classificationMathematicsen_US
dc.titleKinetic Theory Based Numerical Schemes for Incompressible Flowsen_US
dc.typeThesisen_US
dc.degree.namePhDen_US
dc.degree.levelDoctoralen_US
dc.degree.disciplineFaculty of Scienceen_US


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