Acta mathematica scientia, Series B >
AN EMBEDDED BOUNDARY METHOD FOR ELLIPTIC AND PARABOLIC PROBLEMS WITH INTERFACES AND APPLICATION TO MULTI-MATERIAL SYSTEMS WITH PHASE TRANSITIONS
Received date: 2009-12-01
Online published: 2010-03-20
Supported by
This research is supported by the U.S. Department of Energy under Contract No. DE-AC02-98CH10886 and by the State of New York.
The embedded boundary method for solving elliptic and parabolic problems in geometrically complex domains using Cartesian meshes by Johansen and Colella (1998, J. Comput. Phys. 147, 60) has been extended for elliptic and parabolic problems with interior boundaries or interfaces of discontinuities of material properties or solutions. Second order accuracy is achieved in space and time for both stationary and moving interface problems. The method is conservative for elliptic and parabolic problems with fixed interfaces. Based on this method, a front tracking algorithm for the Stefan problem has been developed. The accuracy of the method is measured through comparison with exact solution to a two-dimensional Stefan problem. The algorithm has been used for the study of melting and solidification problems.
Shuqiang Wang , Roman Samulyak , Tongfei Guo . AN EMBEDDED BOUNDARY METHOD FOR ELLIPTIC AND PARABOLIC PROBLEMS WITH INTERFACES AND APPLICATION TO MULTI-MATERIAL SYSTEMS WITH PHASE TRANSITIONS[J]. Acta mathematica scientia, Series B, 2010 , 30(2) : 499 -521 . DOI: 10.1016/S0252-9602(10)60059-8
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