r7.01.10 Modelings THHM. General information and algorithms

Summary

Modules THMsont those that deal with the equations of the mechanics of continuous media using the theory of possibly unsaturated porous media and considering that mechanical, thermal and hydraulic phenomena are completely coupled. Here we present the equilibrium equations, or conservation equations, solved by these modules. We give a definition of generalized constraints and generalized deformations, making it possible to define in a fairly general way what a THM law of behavior is - at least what the modules considered consider as such - and making it possible to treat the nonlinear equations shown in the framework of the algorithms of the operator STAT_NON_LINE.

• 1. Introduction
• 2. Presentation of the problem: hypotheses, notations
  • 2.1. Description of the porous medium
  • 2.2. Ratings
  • 2.3. Particle derivatives, volume and mass densities
• 3. Continuous equations
  • 3.1. Mechanics: conservation of momentum
  • 3.2. Hydraulics: mass conservation
  • 3.3. Energy equation
• 4. Variational writing of equilibrium equations
  • 4.1. Mechanics
  • 4.2. Hydraulics
  • 4.3. Thermal
• 5. Discretization in time
  • 5.1. Mechanics
  • 5.2. Hydraulics
  • 5.3. Thermal
• 6. Principle of virtual work, generalized deformations and constraints, laws of behavior
  • 6.1. Generalized stresses and deformations
  • 6.2. Principle of virtual work
  • 6.3. Laws of behavior
• 7. Resolution algorithm
  • 7.1. Nonlinear algorithm for solving balance equations
  • 7.2. Transition from nodal values to values at Gauss points
  • 7.3. Vectors and matrices according to the options
  • 7.4. Global algorithm
• 8. Option FORC_NODA
• 9. Spatial discretization
• 10. Bibliography