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A numerical method for solving the two‐dimensional unsteady solidification problem with the motion of melt by using the boundary‐fitted co‐ordinate system
Author(s) -
Saitou Masatoshi,
Hirata Akira
Publication year - 1993
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.1620360304
Subject(s) - motion (physics) , ordinate , boundary (topology) , mathematics , boundary value problem , vorticity , symmetry (geometry) , mathematical analysis , stream function , interface (matter) , equations of motion , function (biology) , numerical analysis , geometry , mechanics , classical mechanics , physics , vortex , bubble , maximum bubble pressure method , evolutionary biology , biology
Abstract A numerical method for solving the two‐dimensional unsteady solidification problem with the motion of melt is proposed. The boundary‐fitted co‐ordinate system is applied to a treatment for the moving solid‐liquid interface in cylindrical co‐ordinates with a symmetry axis. An alternating‐direction‐implicit (ADI) method is used to solve the transformed equations of motion and energy, which are expressed in terms of the vorticity and stream function. Several examples are displayed.