Book contents
- Frontmatter
- Contents
- Acknowledgements
- Introduction
- 1 The continuity equation
- 2 Density and gravity
- 3 Numerical solutions of partial differential equations
- 4 Stress and strain
- 5 The momentum equation
- 6 Viscous rheology of rocks
- 7 Numerical solutions of the momentum and continuity equations
- 8 The advection equation and marker-in-cell method
- 9 The heat conservation equation
- 10 Numerical solution of the heat conservation equation
- 11 2D thermomechanical code structure
- 12 Elasticity and plasticity
- 13 2D implementation of visco-elasto-plastic rheology
- 14 The multigrid method
- 15 Programming of 3D problems
- 16 Numerical benchmarks
- 17 Design of 2D numerical geodynamic models
- Epilogue: outlook
- Appendix: MATLAB program examples
- References
- Index
11 - 2D thermomechanical code structure
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Acknowledgements
- Introduction
- 1 The continuity equation
- 2 Density and gravity
- 3 Numerical solutions of partial differential equations
- 4 Stress and strain
- 5 The momentum equation
- 6 Viscous rheology of rocks
- 7 Numerical solutions of the momentum and continuity equations
- 8 The advection equation and marker-in-cell method
- 9 The heat conservation equation
- 10 Numerical solution of the heat conservation equation
- 11 2D thermomechanical code structure
- 12 Elasticity and plasticity
- 13 2D implementation of visco-elasto-plastic rheology
- 14 The multigrid method
- 15 Programming of 3D problems
- 16 Numerical benchmarks
- 17 Design of 2D numerical geodynamic models
- Epilogue: outlook
- Appendix: MATLAB program examples
- References
- Index
Summary
Theory: Principal steps of a coupled thermomechanical solution with finite-differences and marker-in-cell techniques. Organisation of a thermomechanical code for the case of viscous, multi-component flows. Adding self-gravity. Handling free planetary surfaces with a weak layer approach.
Exercises: Building a 2D thermomechanical code.
What do we expect from geodynamic codes?
Before describing possible structures for thermomechanical codes, let us discuss what we actually expect from a state-of-the-art, numerical geodynamic modelling tool. Today, as numerical modelling of geodynamic and planetary processes is in the ‘new millennium’ (although it is only around 40 years old, see Introduction), geoscientists are targeting modelling of realistic situations in lithospheric, mantle and planetary dynamics (e.g. Gerya and Yuen, 2007; Moresi et al., 2008; Zhong et al., 2007; Tackley, 2008). The rheology of crustal and mantle rocks depends strongly on the temperature, strain-rate, volatile content, grain size and the fluid pressure. Physical and dynamical circumstances imposed by the sharply varying viscosity represent a major challenge for solving the momentum equation in geodynamics, unlike those found in the oceanographic or atmospheric sciences. Another complication is due to the variable thermal conductivity in the heat conservation equation. The thermal conductivity of various crustal and mantle rocks is notably different and is also a strong function of temperature, pressure and mineralogy which causes numerical difficulties compared to the constant thermal conductivity situation. Finally, all physical (transport) properties of rocks, including viscosity and conductivity, vary strongly with chemical composition and/or mineralogy.
- Type
- Chapter
- Information
- Introduction to Numerical Geodynamic Modelling , pp. 149 - 164Publisher: Cambridge University PressPrint publication year: 2009