Does anyone work at SIMPLE or improvement of SIMPLE in unsteady and compressibel flow? I have some problem about these.you can contact me at junl@126.com.

Dear Mr Junl

By your question, I am not certain if you are referring to the algorithm Semi-Implicit Method for Pressure-Linked Equations (SIMPLE). It has been several years since I studying this algorithm. If you are interested in a description of this algorithm (and its successor SIMPLE-Revised or SIMPLER), I suggest a textbook titled _Numerical_Heat_Transfer_and_Fluid_Flow_ by S. V. Patankar, ©1980, Hemisphere Publ., especially pp. 120-134. Hope this helps.

I am not certain that SIMPLE is appropriate for compressible flow because the method employs a staggered grid. SIMPLER assumes a pressure field and determines a correction necessary to adjust the velocity flow-field for satisfying continuity. Then the pressure field is corrected to match the revised velocity fields. The staggered grid alleviates a tendency to converg on a zig-zag pressure field (i.e., pressure value at one node differing from values at adjacent nodes, while the values at the adjacent nodes are similar to each other. At any rate, if any shocks are present, I suspect the advantage of the staggering may be lost in the scale changes needed to avoid smearing. Hence, I'm uncertain of the advantage of using SIMPLE in compressible flow, or at least where shocks might be present. In my own efforts (admittedly with very sparce grids), that when I used a relaxation coefficient for pressure greater than unity, the solution diverged.

G W Thielman