A model numerical scheme for the propagation of phase transitions in solids

被引：26

作者：

Cockburn, B

Gau, HT

机构：

[1] School of Mathematics, University of Minnesota, 127 Vincent Hall, Minneapolis

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 1996年 / 17卷 / 05期

关键词：

viscosity-capillarity; phase transitions; mixed-type conservation laws;

D O I：

10.1137/S106482759426688X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we devise a simple finite difference scheme that produces approximations to the viscosity-capillarity solutions of the equations that govern the propagation of phase transitions in solids (or to the equations of van der Waals fluids) far all positive values of the dimensionless parameter that characterizes the viscosity-capillarity solution. Numerical experiments showing the convergence properties of the method are presented.

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页码：1092 / 1121

页数：30

相关论文

共 16 条

[1] KINETIC RELATIONS AND THE PROPAGATION OF PHASE BOUNDARIES IN SOLIDS [J].

ABEYARATNE, R ;

KNOWLES, JK .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1991, 114 (02) :119-154

[2] IMPLICATIONS OF VISCOSITY AND STRAIN-GRADIENT EFFECTS FOR THE KINETICS OF PROPAGATING PHASE BOUNDARIES IN SOLIDS [J].

ABEYARATNE, R ;

KNOWLES, JK .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1991, 51 (05) :1205-1221

[3]

ABYEARATNE R, 1993, IMA VOLUMES MATH ITS, P185

[4]

AFFOUF M, 1991, SIAM J APPL MATH, V4, P605

[5]

FAN H, 1993, IMA VOLUMES MATH ITS, P61

[6] THE PROPAGATION OF PHASE BOUNDARIES IN ELASTIC BARS [J].

JAMES, RD .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1980, 73 (02) :125-158

[7] NUMERICAL INTEGRATIONS OF SYSTEMS OF CONSERVATION-LAWS OF MIXED-TYPE [J].

JIN, S .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1995, 55 (06) :1536-1551

[8] VISCOELASTIC RELAXATION WITH A VAN-DER-WAALS TYPE STRESS [J].

PITMAN, EB ;

NI, YG .

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 1994, 32 (02) :327-338

[9] A NUMERICAL-METHOD FOR SYSTEMS OF CONSERVATION-LAWS OF MIXED TYPE ADMITTING HYPERBOLIC FLUX SPLITTING [J].

SHU, CW .

JOURNAL OF COMPUTATIONAL PHYSICS, 1992, 100 (02) :424-429

[10] EFFICIENT IMPLEMENTATION OF ESSENTIALLY NON-OSCILLATORY SHOCK-CAPTURING SCHEMES [J].

SHU, CW ;

OSHER, S .

JOURNAL OF COMPUTATIONAL PHYSICS, 1988, 77 (02) :439-471