Groundwater Modeling: Numerical Methods EENG 7742

Upon successful completion, the student will be able to:

• Explain the following basic properties and their significance to aquifers:
• Water: Mass density, weight density, viscosity, dynamic viscosity, compressibility, thermal expansion.
• Conservation of mass in flow, nature of stress as a flow phenomenon.
• Aquifers: Permeability, conductivity, soil compressibility, porosity.
• Fundamental dimensions: Mass, Length and Time.
• Hydraulic gradients.
• Carry out the following computer applications:
• Initiate a CAD drawing.
• Edit existing aquifer modeling data files.
• Create new aquifer modeling data files.
• Explain the nature of aquifer properties and water flows in them with respect to or employing:
• Darcy's equation.
• Bernoulli's equation.
• Derive La Place flow equation.
• Accurately describe flow and equipotential lines and their relationships to each other.
• Describe the nature of the stream function.
• Describe the nature of boundary values.
• Describe the nature of residuals.
• Use a simple finite difference model, with the software provided, to show relationship between boundary values and the flow net.
• Discuss, in simple detail, finite difference models:
• Explain the nature of a residual.
• Explain the mathematical foundation of relaxation.
• Show how Taylor's theorem leads to relaxation.
• Explain some of the relevant calculus of relaxation.
• Discuss, in detail, the nature of an aquifer with emphasis on:
• Internal aquifer relaxation.
• Boundary relaxation.
• How finite difference can be applied in relaxation to simple boundary conditions such as well extractions in horizontal confined aquifers.
• Use CAD and supplied software to experiment with concepts of 6.3.
• Explain the nature of finite element analysis in aquifer modeling:
• Explain the nature of the grid in geographical terms.
• Explain the difference between infinitesimal models and finite models.
• Discuss the nature of continuity and its importance in FE models.
• Illustrate the simplicity of concepts from mechanics of particles and solids and their aquifer analogues.
• Explain necessary aspects of the use of algebra of stiffness matrices.
• Discuss minimization of Potential Energy for stress analysis versus minimization of A Functional in the case of aquifers.
• Describe the nature of the interpolation function with calculated examples of its application.
• Derive the gradient function for a triangular element.
• Use CAD and supplied software to experiment with concepts of 7.7 and section 7 in general.
• Construct and employ triangular FE nets:
• Describe the nature and mathematics of the triangular element in detail.
• Describe the global stiffness matrix assembly process.
• Discuss and compare the finite difference and finite element methods.
• Use supplied software to practice flow net construction.
• Explain, discuss or answer questions on the use of the FE analysis of aquifers:
• Describe transmissivity in horizontal aquifers in contrast to permeability.
• Show how a single element stiffness is formulated.
• Describe the physical nature of variables that are used in the formulation of the stiffness of a single element.
• Define the 'load' being the flow in the simple application of the method, as opposed to the 'head.'
• Define the nature of the boundary values.

Effective as of Fall 2003