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Numerical simulation of flows at low Mach numbers with heat sources
In the thesis, a class of preconditioning techniques was used to extend the validity of a density based flow solver into the low Mach number regime. The behavior of the preconditioned schemes with respect to the class parameters was analyzed and thus the regime of suitable parameters could be narrowed down. For the remaining schemes, a stability analysis was performed. A von Neumann stability analysis showed that the stability region of the corresponding explicit scheme gets smaller with M2, as M tends to zero, thus rendering the explicit scheme unapplicable. Thus, implicit time integration methods have to be used in this context. The method was then applied to problems with gravitation. There, the incorporation of the gravitational source term posed special difficulties. It was shown that a first order discretization needs an unacceptable fine grid in this context and that higher order discretizations have to be used. Finally, in addition to gravitation, a heat source term was included in the model to simulate tunnel fires. Several test cases demonstrate the feasibility of the method. The thesis focused on properties of the discretization. It turned out in the test problems that the solution algorithm for the appearing linear equation systems is unsatisfactory slow. Further work is thus required for the development of a fast solution algorithm. A better linear preconditioner for these problems might improve the speed dramatically. Once this is achieved, further test cases on longer time scales can be computed to compare with results obtained in experiments or by other authors.
Numerical simulation of flows at low Mach numbers with heat sources
In the thesis, a class of preconditioning techniques was used to extend the validity of a density based flow solver into the low Mach number regime. The behavior of the preconditioned schemes with respect to the class parameters was analyzed and thus the regime of suitable parameters could be narrowed down. For the remaining schemes, a stability analysis was performed. A von Neumann stability analysis showed that the stability region of the corresponding explicit scheme gets smaller with M2, as M tends to zero, thus rendering the explicit scheme unapplicable. Thus, implicit time integration methods have to be used in this context. The method was then applied to problems with gravitation. There, the incorporation of the gravitational source term posed special difficulties. It was shown that a first order discretization needs an unacceptable fine grid in this context and that higher order discretizations have to be used. Finally, in addition to gravitation, a heat source term was included in the model to simulate tunnel fires. Several test cases demonstrate the feasibility of the method. The thesis focused on properties of the discretization. It turned out in the test problems that the solution algorithm for the appearing linear equation systems is unsatisfactory slow. Further work is thus required for the development of a fast solution algorithm. A better linear preconditioner for these problems might improve the speed dramatically. Once this is achieved, further test cases on longer time scales can be computed to compare with results obtained in experiments or by other authors.
Numerical simulation of flows at low Mach numbers with heat sources
Numerische Simulation von Strömungen bei niedrigen Mach-Zahlen mit Wärmequellen
Birken, Philipp (author)
Berichte aus der Mathematik ; 1-97
2006
97 Seiten, Bilder, Tabellen, 72 Quellen
Theses
English
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