scholarly journals Chebyshev pseudospectral methods for conservation laws with source terms and applications to multiphase flow

2002 ◽  
Author(s):  
Scott Alan Sarra
Keyword(s):  
Multiphase Flow ◽  
Conservation Laws ◽  
Source Terms ◽  
Pseudospectral Methods ◽  
Chebyshev Pseudospectral

Configurational balance laws for incompatibility in stress space

2007 ◽  
Vol 463 (2081) ◽  
pp. 1379-1392 ◽  
Author(s):  
Xanthippi Markenscoff ◽  
Anurag Gupta
Keyword(s):  
Conservation Laws ◽  
Thermal Stresses ◽  
Stress Gradient ◽  
Positive Definite ◽  
Balance Laws ◽  
Source Terms ◽  
Stress Space ◽  
Lagrange Equations ◽  
Compatibility Conditions ◽  
Surface Data

Conservation laws have been recently obtained by requiring that a positive definite functional of the stress gradient (the Euler–Lagrange equations of which are the Beltrami–Michell compatibility conditions) be invariant under certain transformations. Here these laws are extended to include body forces, thermal stresses and Kröner's incompatibility tensor as source terms in the configurational balance laws, which allows for the incompatibility in the volume to be measured from surface data. An example is presented.

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