Record Details

Kinetic Theory Based Numerical Schemes for Incompressible Flows

Electronic Theses of Indian Institute of Science

View Archive Info
 
 
Field Value
 
Title Kinetic Theory Based Numerical Schemes for Incompressible Flows
 
Creator Ruhi, Ankit
 
Subject Turbulence Modeling
Incompressible Flows
Large Eddy Simulation (LES)
Numerical Schemes
Turbulence Model
Lattice Boltzmann Relaxation Scheme (LBRS)
Burgers Turbulence
Implicit Large Eddy Simulation (ILES)
Turbulence Kinetic Theory
Turbulence
Mathematics
 
Description Turbulence 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.
 
Contributor Raghurama Rao, S V
Sekhar, M
 
Date 2018-02-07T12:43:14Z
2018-02-07T12:43:14Z
2018-02-07
2016
 
Type Thesis
 
Identifier http://hdl.handle.net/2005/3072
http://etd.ncsi.iisc.ernet.in/abstracts/3937/G28253-Abs.pdf
 
Language en_US
 
Relation G28253