COMPUTATIONAL METHODS FOR PROPAGATING PHASE BOUNDARIES
       Xiaoguang Zhong
       Thomas Y.Hou
       Philippe G.LeFloch  

RAPPORT NUMERO 316 


This paper considers numerical methods for computing 
propagating phase boundaries in solids described  by the physical model introduced by  
Abeyaratne and  Knowles. The model  
under consideration consists of a set of conservation laws supplemented with 
a kinetic relation and a nucleation criterion. 
Discontinuities between two different phases 
are undercompressive crossing waves
in the general terminology of non-strictly hyperbolic
systems of conservation laws. 
This paper studies numerical methods designed for the
computation of such crossing waves.  
We propose a Godunov-type method combining front tracking 
with a capturing method; we also consider Glimm's random choice scheme.  
Both methods share the property that the phase boundaries
are sharply computed in the sense that 
there are no numerical interior points 
for the description of a phase boundary.  
This property is well-known for the Glimm's scheme; 
on the other hand, our front tracking algorithm is designed so that 
it tracks phase boundaries but captures shock waves. 
Phase boundaries are sensitive to 
numerical dissipation effects, so the above property 
is essential to ensure convergence 
toward the correct entropy weak solution. 
Convergence of the Godunov-type method is demonstrated numerically. 
Extensive numerical  
experiments show the practical interest of both approaches 
for computations of undercompressive crossing waves. 

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