A finite element solution for freezing problems using a continuously deforming coordinate system
Abstract
In a significant class of thermal problems, important quantities vary rapidly or are discontinuous in the vicinity of 'transition zones' whose locations or extents change as the solution evolves. Examples of such zones are areas of phase change or unusually high heat flux. Solution of such problems is facilitated by methods in which the numerical resolution evolves in response to the solution itself. In this chapter, a general method for finite element simulation of these problems is presented, incorporating mesh evolution. Unlike other methods which rely on periodic generation of new finite element meshes during the simulation, the present method is based upon the continuous deformation and/or translation of a single initially specified mesh. The effects of arbitrary mesh motion are included directly in the governing equations. The method is applied to onedimensional problems involving heat conduction with and without phase change, and is shown to be attractive with respect to stability, accuracy, and economy. Hermite basis functions appear to offer some benefits in the types of problems considered, and a preliminary comparison is made with simple linear elements.
 Publication:

Numerical Methods in Heat Transfer
 Pub Date:
 1981
 Bibcode:
 1981nmht.book..215O
 Keywords:

 Computerized Simulation;
 Finite Element Method;
 Freezing;
 Galerkin Method;
 Heat Flux;
 Error Analysis;
 Numerical Stability;
 Phase Transformations;
 Radiative Heat Transfer;
 Solidification;
 StefanBoltzmann Law;
 Temperature Distribution;
 Fluid Mechanics and Heat Transfer