### Abstract

An approximate—locally analytic in the time variable and globally analytic in the space variable—solution is developed for the one-dimensional Stefan problem with time-dependent boundary conditions. Because of local analyticity in time, the solution is accurate over time intervals that are much larger than the step size permitted by most numerical schemes. The solution is developed by reducing the governing partial differential equation (PDE) to two ordinary differential equations (OOE), and then simultaneously solving them along with the ODE for the moving-boundary interface condition. The resulting scheme requires the solution of only a single transcendental (algebraic) equation at each time interval for the time-step-averaged temperature gradient at the moving boundary. The position of the moving boundary and the temperature distribution at the end of the time interval are then simply evaluated using approximate analytical expressions. Good agreement with reference solutions is obtained.

Original language | English (US) |
---|---|

Pages (from-to) | 269-285 |

Number of pages | 17 |

Journal | Numerical Heat Transfer, Part B: Fundamentals |

Volume | 33 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1998 |

### ASJC Scopus subject areas

- Numerical Analysis
- Modeling and Simulation
- Condensed Matter Physics
- Mechanics of Materials
- Computer Science Applications