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**An enthalpy method for convection/diffusion phase change.**
*(English)*
Zbl 0609.76104

An enthalpy formulation for convection/diffusion phase change is developed. The essential feature of this formulation is that latent heat effects are isolated in a source term. This formulation is applicable to a general convection/diffusion phase change, i.e. it is valid in the cases of evolution of latent heat either at an isothermal temperature or over a temperature range. Before implementation of the enthalpy formulation, a technique is required to ensure that velocities predicted to be in a solid region actually take the value zero. Three alternative schemes for achieving this are presented.

The enthalpy formulation and velocity correction schemes are independent of the numerical technique. As an example of how the method can be implemented a control volume numerical discretization is chosen. This implementation is applied to two test problems: a solidification phase change in a cavity under conduction and the same phase change under conduction and natural convection. The natural convection problem is used to compare the performances of the various velocity correction schemes. The results of the problems are in good agreement with available analytical solutions and previous numerical solutions.

The enthalpy formulation and velocity correction schemes are independent of the numerical technique. As an example of how the method can be implemented a control volume numerical discretization is chosen. This implementation is applied to two test problems: a solidification phase change in a cavity under conduction and the same phase change under conduction and natural convection. The natural convection problem is used to compare the performances of the various velocity correction schemes. The results of the problems are in good agreement with available analytical solutions and previous numerical solutions.

### MSC:

76T99 | Multiphase and multicomponent flows |

76R50 | Diffusion |

76M99 | Basic methods in fluid mechanics |

76R10 | Free convection |

### Keywords:

enthalpy formulation; convection/diffusion phase change; latent heat effects; velocity correction schemes; numerical technique; control volume numerical discretization; solidification phase change; cavity under conduction; natural convection; analytical solutions; numerical solutions
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\textit{V. R. Voller} et al., Int. J. Numer. Methods Eng. 24, 271--284 (1987; Zbl 0609.76104)

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### References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.