PART II: THE CIP NUMERICAL MODELING SYSTEM 

 Numerical Modeling 



4. Before details of the CIP modeling system are presented, a brief in- 

 troduction to certain aspects of numerical models is in order. Generally, the 

 physical variables of practical interest such as surface elevation, velocity, 

 wave height, and sediment transport rate vary continuously in space and time. 

 On the basis of the physics of the particular process, the variables are de- 

 scribed by differential equations. In numerical modeling, the differential 

 equations are replaced by difference equations involving finite differences in 

 space and time. Thus, a numerical model considers values of the variables at 

 discrete points in space and time and solves for the values of the variables 

 by numerical techniques. 



5. Numerical models are classified on the basis of variation of the 

 dependent variables in space and time. If the dependent variable is a func- 

 tion only of one coordinate, then we have a one-dimensional model. For exam- 

 ple, the average velocity in a river cross section may be a function only of 

 distance along the river, and we can describe the flow using a one-dimensional 

 model. If the dependent variable is a function of two coordinates, then we 

 have a two-dimensional model. For instance, tidal elevations and currents in 

 a shallow bay may be a function only of the two horizontal coordinates, and 

 the tidal hydrodynamics can be described by a vertically averaged two- 

 dimensional model. If the dependent variable is independent of time, a steady 

 model Is applicable; whereas if the variable varies with time, an unsteady 

 model is needed. 



6. It should be recognized that numerical models are only as good as 

 the physics that goes into them and are in general approximations to physical 

 reality. In recent years, numerical models have become standard tools to 

 answer questions connected with engineering projects and have replaced tradi- 

 tional physical hydraulic models for studies involving tidal hydraulics, wave 

 transformation, etc. They are the only feasible tools available for analyzing 

 certain phenomena such as sediment transport under the combined action of 

 tides and waves, wind-generated flows, etc. They have the following advan- 

 tage. Once a numerical model has been calibrated and verified for a given 

 project area for a given set of conditions, it can predict, within a 



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