AN ADAPTIVE FINITE-ELEMENT METHOD FOR 2-PHASE STEFAN-PROBLEMS IN 2 SPACE DIMENSIONS .2. IMPLEMENTATION AND NUMERICAL EXPERIMENTS

被引:45
作者
NOCHETTO, RH
PAOLINI, M
VERDI, C
机构
[1] CNR,IST ANALISI NUMER,I-27100 PAVIA,ITALY
[2] UNIV PAVIA,CNR,IST ANALISI NUMER,DIPARTIMENTO MECCAN STRUTT,I-27100 PAVIA,ITALY
来源
SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING | 1991年 / 12卷 / 05期
关键词
FREE BOUNDARIES; FINITE ELEMENTS; ADAPTIVITY; MESH GENERATION; QUADTREES; COMPUTATIONAL COMPLEXITY;
D O I
10.1137/0912065
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
An adaptive local mesh refinement strategy for two-phase Stefan problems is discussed in light of its efficiency and computational complexity. Three local parameters are used to equidistribute interpolation errors in maximum norm for temperature and a fourth one, in the event of mushy regions, to equidistribute L1-interpolation errors for enthalpy within the mush. If certain quality mesh tests fail, then the current mesh is discarded and a new one completely regenerated by an efficient mesh generator, which in turn is briefly described. A typical triangulation is strongly graded to become very fine near computed interfaces and coarse away from them. Consecutive meshes are not compatible. The use of quadtree data structures is discussed as a means to reach a nearly optimal computational complexity in various tasks to be performed, mainly in generating a mesh and interpolating. Various implementation details are given so as to derive the computational complexity of each relevant subroutine. The approximation of both solutions and interfaces is drastically improved. The proposed method is robust in that it can handle the formation of cusps and mushy regions as well as the spontaneous appearance of phases. It is also superior in terms of computing time for a desired accuracy. Several numerical experiments illustrate these facts and provide quantitative information about each task complexity.
引用
收藏
页码:1207 / 1244
页数:38
相关论文
共 23 条
[1]  
[Anonymous], 1972, DISCRETE MATH, DOI DOI 10.1016/0012-365X%2872%2990093-3
[2]  
BABUSKA I, 1986, ACCURACY ESTIMATES A
[3]   A CLASS OF DATA-STRUCTURES FOR 2-D AND 3-D ADAPTIVE MESH REFINEMENT [J].
CAREY, GF ;
SHARMA, M ;
WANG, KC .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1988, 26 (12) :2607-2622
[4]  
Ciarlet P. G., 2002, FINITE ELEMENT METHO
[5]   NUMERICAL-ANALYSIS OF 2-PHASE STEFAN PROBLEM BY METHOD OF FINITE-ELEMENTS [J].
CIAVALDINI, JF .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1975, 12 (03) :464-487
[6]   ERROR ANALYSIS OF THE ENTHALPY METHOD FOR THE STEFAN PROBLEM [J].
ELLIOTT, CM .
IMA JOURNAL OF NUMERICAL ANALYSIS, 1987, 7 (01) :61-71
[7]   DELAUNAY TRIANGULAR MESHES IN CONVEX POLYGONS [J].
JOE, B .
SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1986, 7 (02) :514-539
[8]  
Knuth DE, 1973, ART COMPUTER PROGRAM
[10]   SOME USEFUL DATA-STRUCTURES FOR THE GENERATION OF UNSTRUCTURED GRIDS [J].
LOHNER, R .
COMMUNICATIONS IN APPLIED NUMERICAL METHODS, 1988, 4 (01) :123-135