Comparison of finite element techniques for solidification problems
article
For various fixed-grid finite element techniques the accuracies of the computed temperatures of a liquid in a
corner region under isothermal freezing conditions are compared using the analytical solution for this problem as a reference. Different time discretization schemes are examined: the implicit, two- time- level Euler-backward scheme and two three-time-level methods - a Dupont algorithm and the Lees algorithm, both non- iterative. In the enthalpy formulation of the problem the evaluation of the effective heat capacity c'=dH/dT is achieved by averaging techniques suggested by Lemmon and by Del Giudice to handle the evolution of latent heat. Since linear elements are used, lumping of the heat capacity matrix in the finite element formulation is allowed, resulting in a diagonal mass matrix instead of the consistent banded matrix. In the calculations both matrices are applied, showing the lumped matrix to lead to reduced computation times and enhanced accuracy.
corner region under isothermal freezing conditions are compared using the analytical solution for this problem as a reference. Different time discretization schemes are examined: the implicit, two- time- level Euler-backward scheme and two three-time-level methods - a Dupont algorithm and the Lees algorithm, both non- iterative. In the enthalpy formulation of the problem the evaluation of the effective heat capacity c'=dH/dT is achieved by averaging techniques suggested by Lemmon and by Del Giudice to handle the evolution of latent heat. Since linear elements are used, lumping of the heat capacity matrix in the finite element formulation is allowed, resulting in a diagonal mass matrix instead of the consistent banded matrix. In the calculations both matrices are applied, showing the lumped matrix to lead to reduced computation times and enhanced accuracy.
TNO Identifier
246394
Source
Numerical methods in thermal problems, VI(1), pp. 300-308.
Collation
9 p.
Pages
300-308
Files
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