2026-09-18T22:58:04Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/392182022-01-13T07:54:53Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Anthony T. Patera.
Garlapati, Revanth Reddy
Massachusetts Institute of Technology. Computation for Design and Optimization Program.
Massachusetts Institute of Technology. Computation for Design and Optimization Program
2007-10-19T20:32:33Z
2007-10-19T20:32:33Z
2006
2006
http://hdl.handle.net/1721.1/39218
85844342
Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006.
Includes bibliographical references (p. 103-106).
The main aim of the project is to solve the BGK model of the Knudsen parameterized Boltzmann equation which is 1-d with respect to both space and velocity. In order to solve the Boltzmann equation, we first transform the original differential equation by replacing the dependent variable with another variable, weighted with function t(y); next we obtain a Petrov Galerkin weak form of this new transformed equation. To obtain a stable and accurate solution of this weak form, we perform a transformation of the velocity variable y, such that the semi-infinite domain is mapped into a finite domain; we choose the weighting function t(y), to balance contributions at infinity. Once we obtain an accurate and well defined finite element solution of the problem. The next step is to perform the reduced basis analysis of the equation using these accurate finite element solutions. We conclude the project by verifying that the orthonormal reduced Basis method based on the greedy algorithm converges rapidly over the chosen test space.
by Revanth Reddy Garlapati.
S.M.
106 p.
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Computation for Design and Optimization Program.
Reduced basis method for Boltzmann equation
Thesis
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<Abstract>The main aim of the project is to solve the BGK model of the Knudsen parameterized Boltzmann equation which is 1-d with respect to both space and velocity. In order to solve the Boltzmann equation, we first transform the original differential equation by replacing the dependent variable with another variable, weighted with function t(y); next we obtain a Petrov Galerkin weak form of this new transformed equation. To obtain a stable and accurate solution of this weak form, we perform a transformation of the velocity variable y, such that the semi-infinite domain is mapped into a finite domain; we choose the weighting function t(y), to balance contributions at infinity. Once we obtain an accurate and well defined finite element solution of the problem. The next step is to perform the reduced basis analysis of the equation using these accurate finite element solutions. We conclude the project by verifying that the orthonormal reduced Basis method based on the greedy algorithm converges rapidly over the chosen test space.</Abstract>
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