Numerical methods for incompressible flows in vorticity formulation with application of combustion
This dissertation contains three parts. In the first part, we present local vorticity boundary conditions for incompressible flows in an open boundary. In the second part, we present a method for solving incompressible flows in cylindrical geometry. In the third part, which is perhaps the most signi...
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| Format: | Dissertation |
| Language: | English |
| Published: |
ProQuest Dissertations & Theses
01-01-2000
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| Online Access: | Get full text |
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| Summary: | This dissertation contains three parts. In the first part, we present local vorticity boundary conditions for incompressible flows in an open boundary. In the second part, we present a method for solving incompressible flows in cylindrical geometry. In the third part, which is perhaps the most significant part of the thesis, we develop a method for zero Mach number combustion using procedures developed in the first part with applications to direct simulations of flame/vortex interactions. In particular, we introduce a method to treat the baroclinic generation of vorticity. The design of finite difference schemes for unsteady viscous incompressible flows using vorticity formulation dates back to 1930s when Thom's formula [28] was derived. The point of view that was heavily favored in the 80s and early 90s is that vorticity boundary conditions have to be global [2, 20, 24, 23]. Numerical schemes using vorticity formulation of incompressible flows have been unnecessarily complicated and inefficient because of this theory. Weinan E and Jian-Guo Liu [5] showed that many of the complicated schemes using global conditions could be written as schemes with local formulas. They also showed that center difference coupled with any high order explicit Runge-Kutta method have no cell Reynolds number constraints. For high Reynolds number flows, these schemes are stable under the CFL condition given only by the convective terms. We have extended this strategy to study a variety of problems in incompressible flows and related problems in combustion. Local conditions for open flow boundaries are introduced with applications to flows in a split channel. A solver for axisymmetric incompressible flows is presented with application to the study of centrifugal instability. Several schemes are developed for solving the system of equations describing combustion processes at a low Mach number either with or without the baroclinic torque in both 2 and 3-dimensions. |
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| ISBN: | 0599759631 9780599759633 |