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Can you take advantage of any symetry in the model? If the model is symetric you can reduce the size of the computational domain and apply symetry to its boundaries. I believe there is a tutorial that uses symetry that explains how to use it.
To check if your mesh is too small you can show the mesh from the results section in the floworks model tree. Visually inspect the mesh and see if you have too many cells in areas that are not very important to your analysis. If this is the case then you can reduce the initial mesh settings by right clicking on "Input Data" in the model tree and selecting "Initial Mesh...". A screen should popup showing different mesh setttings. Near the bottom you can uncheck the automatic settings to allow you more control over your mesh. If you decrese the number of cells per x,y, and z then you will have a corser mesh that should not take as long to calculate. I believe that the initial mesh settings are based on the boundary conditions. So if your boundary conditions are very small compared to the computational area then your mesh could be much finer than you need.
This could be detrimental to the accuracy of your analysis. To help the accuracy you can add mesh controls and increase the partial cell refinement. Also, for Floworks 2007, make sure that "Optimize thin walls resolution" is selected.
Changing mesh setting can increase the amount of time and resources required to mesh the model but it can help speed up the calculation process.
Thank you both for your advice, it was all very useful!