A Conservation Element/Solution Element Method ith Discrete Ordinate Method for Ideal Gas Dynamics
Date Issued
2008
Date
2008
Author(s)
Muljadi, Bagus Putra
Abstract
ABSTRACThe dynamic theory of gases may be studied from two points of view. One may take as starting point the macroscopic equations of aerodynamics with the density, mass velocity, and temperature as independent variables and involving various coefficients, e.g., viscosity, heat conduction, etc. On the other hand, one may use a more fundamental and general microscopic formalism. The most fruitful of such formalisms available at present is that in terms of one particle distribution functions satisfying integro-differential equation of the Boltzmann type.his thesis features the usage of a novel Conservation Element/Solution Element scheme for solving gas dynamical flows. The Boltzmann equation approach is adopted and the local thermodynamic equilibrium distribution is assumed. The discrete ordinate method is first applied to remove the velocity space dependency of the distribution function which renders the model Boltzmann equation in phase space to a set of hyperbolic conservation laws. Then a two level accurate, explicit scheme called Conservation Element/Solution Element method is employed to solve those equations. The integrated results will capture the flow structure of a SOD’s shock tube and Sjögreen’s expansion problem and are to be compared to the results of Riemann’s Euler problem for the same condition.aving known that the usage of CE/SE scheme simultaneously with Discrete Ordinate Method formulation to solve equilibrium Boltzmann equation have never been done before, this study emphasizes on making a solid foundation on a more complicated computations in the future; either that be in dimensional expansion or inclusion of collision terms of Boltzmann equation.
Subjects
Computational
Fluid
Dynamics
Discrete
Ordinate
Method
Ideal
Gas
Type
thesis
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