Numerical calculations topography

The composition of this chapter is based on a well-known and well-understood model of the electrical double layer and therefore does not pretend to enhance overall understanding. It does, however, aim to answer the question of whether a useful mathematical technique exists that may allow for a numerical, if not analytical, description of the double layer for a surface of arbitrary shape and topography. It is fair to say that the colloid scientist ultimately seeks a quantitative description of the electrical double layer for whatever reason. The task then now faced is to uncover the most appropriate theoretical method of calculating the electrical double layer properties for a given nonideal situation. Here we suggest a few methods that may help in this respect. 

The use of local theories, incorporating parameters such as the eddy viscosity Km and eddy thermal conductivity Ke, has given reasonable descriptions of numerous important flow phenomena, notably large scale atmospheric circulations with small variations in topography and slowly varying surface temperatures. The main reason for this success is that the system dynamics are dominated primarily by inertial effects. In these circumstances it is not necessary that the model precisely describe the role of turbulent momentum and heat transport. By comparison, problems concerned with urban meso-meteorology will be much more sensitive to the assumed mode of the turbulent transport mechanism. The main features of interest for mesoscale calculations involve abrupt... 

Numerical models have been developed for calculating the probable maximum seiche in the form of the amplitude of oscillation as a function of time at any point within a bay of arbitrary shape. These models usually require as input a specification of the overall geometry (bathymetry and coastal topography) and of the forcing wave system. They also require as input the time dependence of the excitation (tsunami wave, surge wave, wind wave etc.) at the open boundary or source location. The amplitude time history of the seiches for the location of the plant should then be calculated. Hydraulic model studies and/or field results should be used to validate the calculation model selected. 

This, plus the vertical thickness of the uniformly thick layers (1 ft) and the number of layers (again, four), completely defines the stratigraphy. More general topographies require detailed I/O procedures, which are avoided in this book. Next, pressure constrain Well 1 at 1,000 psi, and flow rate constrain Well 2 at 50 cu ft r. Also, model a liquid with a viscosity of 1 cp, and assume that the six sides of the computational box are solid no-flow walls in order to provide a severe test for mass conservation. The steady numerical scheme, in order to conserve mass, must determine a flow rate at Well 1 that is exactly the negative of the assumed rate at Well 2. Can this be achieved Calculated results follow. 

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