Boundary Conditions of the First Kind (Dirichlet Condition)


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1 Groundwater Modeling Boundary Conditions Boundary Conditions of the First Kind (Dirichlet Condition) Known pressure (velocity potential or total heard) head, e.g. constant or varying in time or space. Since total head, h, is known, an equation for head is not needed along the boundary. Boundary conditions of the Second Kind (Neumann Condition) Known flux or specific discharge (mass per unit volume per unit time. Express in terms of flux exiting a boundary cell. For a no flow boundary, δφ/dn = 0. Boundary conditions of the Third Kind (mixed Boundary condition or Cauchy Condition) Flux normal to a boundary can be expressed in terms of the head along the boundary and a known constant. Phreatic surface with accretion The pressure is equal to atmospheric and it is necessary to know the flux. The phreatic surface can vary if enough information on the aquifer properties are known. Can be an unconfined or confined aquifer. Surface of seepage Pressure is equal to zero so the velocity potential is a function of elevation. Boundary Between Two Porous Media The pressure or total head is equal along the boundary. Continuity must be assured along the boundary. For MODFLOW, use constanthead, inactive or variable head cells. Groundwater Modeling
2 ASTM Standard Guide for... Defining Boundary Conditions in GroundWater Flow Modeling (D ) Specific Head or Dirichlet Boundary Type GeneralSpecifiedHead Boundary  head specified as a function of position and time ConstantHead Boundary  head specified as a function of position Specific Flux or Neumann Boundary Type  flux specified as a function of position and time NoFlow Boundary  material of very low permeability Streamline Boundary  groundwater divide Head Dependent Flux or Cauchy Type Boundary  flux varies dependent on head gradient between aquifer and boundary Constant Flux Boundary  base of a confining layer after head is drawn down into confined/unconfined aquifer Head Dependent Boundary  rate of evapotranspiration specified as a function of depth to a cutoff depth FreeSurface Boundary Type 62
3  moveable boundary where the head is equal to the elevation of the boundary  water table or top flow line where the location may not be known initially SeepageFace Boundary  surface of seepage associated with a free surface boundary  location is predetermined but length is unknown  can be ignored for regional modeling Defining Initial Conditions in GroundWater Flow Modeling (D ) Defining SteadyState Initial Conditions for a TransientState Simulation of Head Distribution  field conditions that represent approximately an equilibrium condition  initial conditions might include model head adjustment to offset unknowns lack of definite information on boundary conditions, aquifer hydraulic properties and initial head values Defining TransientState Initial Condition for a TransientState Simulation of Absolute Head  the simulation boundary conditions and hydraulic properties are simulated over a long period of time so that stresses before the simulations are insignificant Defining the Initial Head for Steady or TransientState Simulation of Head Change in Response to a Stress  models only the waterlevel changes related to the application of a stress  applies the principle of superposition, if applicable 63
4 Model Calibration  Process of evaluating initial and boundary conditions and aquifer hydraulic properties to verify that the model can reproduce measured heads or fluxes  There is a package in GMS capable of performing inverse modeling, but it is not available under the present UT liscense.  Inverse modeling is the process of adjusting model inputs until the optimum set of inputs are determined for a partiticular condition.  The inputs are optimized by comparing the residuals computed using a number of pairs of predicted and measured values.  Residuals are usually computed by squaring the differences between the predicted and measured values so that positive and negative residuals do not produce a false optimum.  After a model is calibrated, then the model can be used to simulate other conditions. Conducting a Sensitivity Analysis for a GroundWater Flow Model Application (D )  used to calculate the sensitivity of a system when evaluating a model for initial and boundary conditions and for aquifer hydraulic properties  used to calculate the sensitivity with respect to a future prediction Process Identify inputs to be varied Identify variations of the inputes Perform simulations Compare predicted values with measured values Calculate residuals Determine sensitivity type (Type I, II, III, IV) Type I sensitivity occurs whtn variation of an input causes insignificant changes in the residuals as well as the model s conclusions. Type I senstitivity is of no concern because, regardless of the value of the input, the conclusion will remain the same. 64
5 Type II sensitivity occurs when variation of an input causes significant changes in the residuals but insignificant changes in the model s conclusions. Tkype II sensitivity is of no concern because, regardless of the value of the input, the conclusion will remain the same. Type III sensitivity occurs when variation of an input causes significant changes to both the residuals and the model s conclusions. Type III sensitivity is of no concern because, even though the model s conclusions change as a result of variation of the input, the parameters used in those simulations cause the model to become uncalibrated. Type IV sensitivity occurs when variation of an input causes in the residuals but significant changes in the model s conclusions. Type IV sensitivity can invalidate model results because, over the range of the that parameter in which the model can be considered calibradted, the conclusions of the model can change significantly. CHANGE IN RESIDUALS CHANGE IN CONCLUSIONS Insignificant Significant Insignificant Type I Type II Significant Type IV Type III 65
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