III.2 Initial/Boundary Conditions

There is one major issue that we have ignored so far, namely initial and boundary conditions. The initial condition for a problem is the state of p and u- at all points in the flow. As mentioned before, most fluid flow problems are parabolic or hyperbolic, and so the solution at any time t depends in part on the initial conditions in the region of interest. Thus to start our calculation we will need to specify these initial conditions, typically either by specifying known values for p and u- or making a sensible guess (for instance, specifying u- = 0- at all points in the domain). Steady viscous flows are elliptic, and so should not be dependent on the initial conditions, however the SIMPLE algorithm has to start with some initial values for p and u-, and in extreme cases specifying sensible initial conditions may make the difference between the solution converging or not.

Boundary conditions also need to be specified, and these largely determine what the solution will be. There are 3 types of boundaries to be considered : walls, inlets and outlets. For a laminar flow they are as follows

Inlets and outlets are best thought of in terms of the information flow. Fluid at an inlet has just come from outside, so you must specify a great deal of information about its state, in the form of the velocity. Fluid about to leave the domain is taking its information out of the domain, so much less information actually needs to be supplied, and only the pressure outside the domain needs to be specified. Note that if the boundary conditions for a problem are incorrectly specified, the problem becomes ill posed and no solution may be possible. In this case the CFD code may fail to produce a solution, or worse, produce one which is incorrect.