Recent advances in the numerical computation of environmental conservation laws with source terms

2012 ◽  
pp. 125-174
Keyword(s):  
Conservation Laws ◽  
Numerical Computation ◽  
Environmental Conservation ◽  
Source Terms ◽  
Recent Advances

scholarly journals Recent Advances in Symmetry Groups and Conservation Laws for Partial Differential Equations and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-2 ◽  
Author(s):  
Maria Gandarias ◽  
Mariano Torrisi ◽  
Maria Bruzón ◽  
Rita Tracinà ◽  
Chaudry Masood Khalique
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Symmetry Groups ◽  
Partial Differential ◽  
Recent Advances

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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