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Basic Equations in Eulerian Continuum Mechanics

In: Numerical Methods and Software Tools in Industrial Mathematics

Author

Listed:
  • Einar Haug

    (SINTEF)

  • Hans Petter Langtangen

    (University of Oslo, Dept. of Math.)

Abstract

We present a general framework applicable to several mathematical models in continuum mechanics. Particularly, we demonstrate that mass, momentum and energy balancing along with appropriate constitutive laws, form the basis of a broad class of boundary value problems for macroscopic motion of a solid, fluid, gas and mixture of several media. We also point out the similarities in the final governing equations and the resulting advantage of this when constructing numerical solution methods. Finally, we derive closed mathematical models that cover the following fields: heat transfer, solute transport, potential fluid flow (including water surface waves), turbulence, elastic and viscoplastic deformations and multiphase porous media flow. We believe that a unified view like the one presented here enhances the fundamental understanding and supports the development of generic solution methods and software for continuum mechanical problems.

Suggested Citation

  • Einar Haug & Hans Petter Langtangen, 1997. "Basic Equations in Eulerian Continuum Mechanics," Springer Books, in: Morten Dæhlen & Aslak Tveito (ed.), Numerical Methods and Software Tools in Industrial Mathematics, chapter 6, pages 121-156, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-1984-2_6
    DOI: 10.1007/978-1-4612-1984-2_6
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