Application of Wave-Propagation Algorithm to Two-Dimensional Thermoelastic Wave Propagation in Inhomogeneous Media

  • A. Berezovski
  • G. A. Maugin


The system of equations for thermoelastic wave propagation in an inho-mogeneous medium is not in the conservation form. Nevertheless, a modification of the wave propagation algorithm for conservation laws is successfully used for the numerical simulation. The modification is made in two ways. First, the algorithm is represented in terms of contact quantities to provide the satisfaction of the thermodynamic consistency conditions between adjacent cells. As usual, the finite volume Godunov scheme is improved by introducing correction terms to obtain high resolution results. Secondly, a composite scheme is obtained by application of the Godunov step after each three second-order Lax-Wendroff steps. The multidimensional motion is accomplished by including into consideration the transverse fluctuations. At last, the elimination of source terms is made following the method of balancing source terms after independent solution of the heat conduction equation. Results of computation for certain test problems show the efficiency and physical consistency of the algorithm.


Discrete System Heat Conduction Equation Contact Temperature Godunov Method Composite Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Germain P (1973). Cours de Mécanique des Milieux Continus, v. 1, Masson.MATHGoogle Scholar
  2. Nowacki W (1986). Thermoelasticity. Pergamon-PWN.MATHGoogle Scholar
  3. LeVeque R J (1990). Numerical Methods for Conservation Laws. Birkhäuser Verlag.MATHGoogle Scholar
  4. Godlewski E and Raviart P A (1996). Numerical Approximation of Hyperbolic Systems of Conservation Laws. Springer.MATHGoogle Scholar
  5. Godunov S K (1959). A Finite Difference Method for the Computation of Discontinuous Solutions of the Equations of Fluid Dynamics. Mat. Sb. 47, pp 271–306.MathSciNetGoogle Scholar
  6. LeVeque R J (1997). Wave Propagation Algorithms for Multidimensional Hyperbolic Systems. J. Comput. Phys. 131, pp 327–353.MATHCrossRefGoogle Scholar
  7. Liska R and Wendroff B (1998). Composite Schemes for Conservation Laws. SIAM J. Numer. Anal. 35, pp 2250–2271.MathSciNetMATHCrossRefGoogle Scholar
  8. Muschik W (1993). Fundamentals of Non-Equilibrium Thermodynamics. Non-Equilibrium Thermodynamics with Application to Solids, pp 1–63. Muschik W (Editor). Springer.Google Scholar
  9. Berezovski A (1997). Continuous Cellular Automata for Simulation of Thermoelasticity, Proc. Estonian Acad. Sci. Phys. Mat. 46, pp 5–13.MATHGoogle Scholar
  10. Berezovski A and Rosenblum V (1996). Thermodynamic Modelling of Heat Conduction, Proc. Estonian Acad. Sci. Engin. 2, pp 196–208.Google Scholar
  11. LeVeque R J (1998). Balancing Source Terms and Flux Gradients in High-resolution Godunov Methods: the Quasi-steady Wave-propagation Algorithm, J. Comput. Phys. 148, pp 346–365.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • A. Berezovski
    • 1
  • G. A. Maugin
    • 2
  1. 1.Department of Mechanics and Applied MathematicsInstitute of Cybernetics at Tallinn Technical UniversityTallinnEstonia
  2. 2.Université Pierre et Marie CurieLaboratoire de Modélisation en Mécanique, UMR 7607Paris Cédex 05France

Personalised recommendations