Spreadsheet Object Refinement

The result will nominally be a type box that defines our system as if it were a single object (Section 6.6, Spreadsheet — Object Refinement, on page 288). Like all types, the... 

Separate concerns into different objects (and abstract objects see Section 6.6, Spreadsheet Object Refinement). Compose those objects together to provide the overall behavior. In general, prefer composition and black-box reuse over subclassing. 

Focusing on the system we re interested in refining (the spreadsheet rather than the user), we may decide, as we did in this example, to use a different set of objects in the actual design. We have already seen how to use abstraction functions to relate the design model to the specification. 

We refine the actions down from the highest-level business abstractions but not down to individual keystrokes or electrical pulses. We refine actions to the point where they make sense as individual actions on the objects we have chosen for our design—if you like, to the same conceptual layer as our design. Make a spreadsheet is too abstract for our design click mouse at (x,y) is too detailed but setNumber(n) makes sense as a message to one of our cells. 

For the systems that we have considered so far, the solutions behave smoothly in time and space. Often one can simply inspect the solution and decide if the mesh is sufficiently fine to represent it accurately. Refining mesh sizes and time steps is another simple method to assure oneself that a particular discretization was sufficient. Later we will be much more concerned about numerical accuracy and stability, especially when complex chemistry is considered. For now we take a somewhat cavalier approach, with the objective being mainly to explore the general numerical approaches to solving the conservation equations describing fluid flow. For relatively simple problems we can implement usable solutions with relative ease, for example, in a spreadsheet. 

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