COMPUTATIONAL GEOMECHANICS GeoEE 557 Fall 2006 Instructor Derek Elsworth w 865 2225 elsworth psu edu Content Modeling deformation flow and transport using finite element finite difference and boundary element methods Coupled processes of flow deformation and heat mass and reactive transport Objectives To gain an appreciation of numerical methods through exposure to finite element finite difference and boundary element codes The course is designed for potential users and developers of domain and integral numerical methods that are ubiquitously applied in hydrology and atmospheric sciences mining civil mechanical and petroleum engineering and the geologic and materials sciences Prerequisites Matrix algebra elementary calculus elementary programming in MatLab Location T Th 4 40 5 30 25 Deike 3 credits 1 Overview of Coupled Processes 1 1 Uncoupled systems 1 2 Coupled processes Thermo Hydro Mechanical Chemical T H M C 1 3 Balances of Mass Momentum and Energy 1 4 Interaction and Onsager Processes 1 5 Building representative systems incorporating couplings 1 6 Preliminary examples of THM processes 1 7 Key couplings 1 8 Dependent variables their selection and modes of coupling 2 Mechanical Behavior M Deformation 2 1 Conservation of momentum and Hooke s law 2 1 1 Principle of virtual work 2 2 Finite element representation 2 2 1 1 dimensional elements 2 2 2 2 dimensional behavior 2 2 2 1 CST elements 2 2 2 2 Isoparametric elements 2 3 Variational procedures 3 Hydraulic Behavior H Flow 3 1 Conservation of mass and Darcy s law 3 2 Steady behavior 3 2 1 1 dimensional elements 3 2 2 2 dimensional behavior 2 D triangular and 2 D isoparametric elements 3 3 Transient behavior 3 3 1 Time stepping methods 3 4 Dual porosity flows 4 Hydro Mechanical Coupling H M 4 1 Stiffness and conductance terms 4 2 Coupling terms and symmetry 4 3 Time stepping 4 4 1 dimensional examples 4 5 Dual porosity behavior 5 Mass Chemical Transport C 5 1 Conservation of mass and Fick s law 5 2 Steady behavior 5 3 Transient behavior 5 4 Considerations of local equilibrium 6 Hydro Mechanical Chemical Coupling H M C 6 1 Stiffness conductance and advective terms 6 2 Coupling terms and symmetries 7 Thermal Transport T 7 1 Conservation of Energy and Fourier s law 7 2 Steady behavior 7 3 Transient behavior 8 Thermo Hydro Mechanical Coupling T H M 8 1 Stiffness conductance and advective terms 8 2 Coupling terms and symmetry 8 3 Time stepping 8 4 1 dimensional examples 9 Thermo Hydro Mechanical Chemical Coupling T H M C 9 1 Stiffness conductance and advective terms 9 2 Coupling terms and symmetries 10 Summary Behaviors 11 Boundary Element Methods Introduction 11 1 Indirect method General principles 11 1 1 Groundwater mechanics 11 1 2 Elasticity 11 2 Direct Method General principles 11 2 1 Groundwater mechanics 11 2 2 Elasticity 11 3 Coupled FEM BEM analysis 12 Overview and Summary Transport Transport Selected texts on reserve in the EMS library Lecture Overheads and Course Notes available online Grading 40 60 Mid term exam Final project Academic Conduct Penn State s policy on academic integrity applies to all aspects of course deliverables Students are encouraged to work together in groups but to submit independent work Further details are available at http www ems psu edu students integrity index html