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Application of infinite elements to phase change situations on deforming meshes
Author(s) -
Sullivan John M.,
O'Neill Kevin
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620330907
Subject(s) - polygon mesh , quadrilateral , finite element method , quadratic equation , quadrature (astronomy) , galerkin method , mathematics , boundary (topology) , gaussian quadrature , basis function , transformation (genetics) , boundary value problem , geometry , mathematical analysis , physics , structural engineering , engineering , nyström method , optics , biochemistry , chemistry , gene
In recent years progress has been made in applying moving and deforming mesh systems to phase change problems. This allows the numerical attention where it is needed, near the migrating phase change zone. In spatially unbounded problems one hopes that numerically finite outer boundaries either escape significant activity or are automatically pushed further away as activity nears. Not infrequently this approach fails. Temperature activity often spreads more rapidly than phase change, thereby reaching far boundaries; stretching of the mesh by movement of far boundaries can challenge mesh control and cause ill‐conditioning. In this paper the advantages of time dependent mesh adaption are enhanced by the joining of a new formulation for infinite elements to far boundaries. This is accomplished through a co‐ordinate transformation within the framework of conventional 2‐D quadratic, biquadratic, and linear–quadratic elements. Standard 2 by 2 Gauss–Legendre quadrature suffices throughout and normal Galerkin finite element features are undisturbed, including strict conservation of energy. The formulation is independent of global co‐ordinates, entails no restrictions on the unknown function and should be applicable to other problem types. All test cases on quadrilateral and triangular grids show very significant improvements with infinite elements relative to comparable solution systems using strictly finite grids.