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Numerical Simulation of Heat Conduction with Melting and/or Freezing by Space-Time Conservation Element and Solution Element Method
| Title: | Numerical Simulation of Heat Conduction with Melting and/or Freezing by Space-Time Conservation Element and Solution Element Method |
| Author: | Ayasoufi, Anahita |
| Description: | Numerical simulation of the Enthalpy formulation, for the Stefan problems, is known to be limited by two difficulties: 1) non-physical waviness in the temperature distribution, as well as unwanted oscillations close to the phase interface, for isothermal phase change, and 2) convergence and stability problems, as well as inaccuracies due to overwhelming dissipation of the numerical schemes, at the limit of small Stefan numbers. The method of space-time conservation element and solution element is known for its low dissipation and dispersion errors, as well as its distinguishingly high capability of capturing discontinuities accurately. Therefore, this numerical method, mainly applied to the fluid flow problems, represents an alternative for numerical modeling of moving boundary (Stefan) problems such as solid/liquid phase change. In this dissertation, space-time CE/SE schemes are developed, for the solid/liquid phase change problems, in one-, two-, and three- spatial dimensions. A separate formulation is also presented and programmed for the axisymmetric problems. The von Neumann stability analysis is applied to the one-dimensional scheme. The results of this analysis lead to a necessary stability condition. Each scheme is then validated, numerically, using benchmark problems without and with phase change. Both analytical and experimental results are used in the validation process. The results reveal that using the space-time CE/SE method, the first problem associated with the numerical modeling of the enthalpy method is eliminated. No non-physical waviness or unwanted oscillation is detected in the results. The second problem, however, still existed. Although accurate results can be obtained for small Stefan numbers using the CE/SE method, a case-dependent adjustment in dissipation was needed. This presents the potential for a modification in the original schemes. Numerical experiments are then conducted, in order to reveal the dissipative / dispersive behavior of the numerical scheme and its variation with the Stefan number. The results of this analysis lead to the development of a CE/SE scheme that is, to a considerable degree, insensitive to the value of the Stefan number. Finally, space-time CE/SE method is established as an alternative for the numerical simulation of the enthalpy method for the Stefan problems. |
| Permanent Link: |
http://rave.ohiolink.edu/etdc/view?acc_num=toledo1103147485
http://hdl.handle.net/2374.OX/19410 |
| Date: | 2004 |
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