| John C. Chien
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May 8, 2001 12:40 |
Re: SIMPLE for transient NS.
(1). For compressible flows, the methods used are normally the so-called density-based, where the continuity equation will provide one equation for the transient density calculation. (2). For incompressible flows, there is no density transient term in the continuity equation. The normal approach is to use stream function (2-D), and vorticity-velocity (3-D) formulation, where the pressure is de-coupled from the governing equations (one does not need to solve the pressure in order to solve the velocity field). (3). The pressure-based formulation like "SIMPLE" try to retain the form of primitive variable in the governing equation (instead of the derived stream function and vorticity), and solve the unknown pressure terms (in the momentum eqautions ) iteratively through another external pressure-guessing(updating) loop. And hoping that both pressure and the velocity fields will converge to the true solutions. (4). As you can see, for the transient flows, it is easier to use the compressible, density-based approach. (both explicit-marching in time, or using implicit method in time) (5). The so-called pressure-based method for transient flows will have a lot of "guessing" (iteration) to do in looking for the solution.(both the pressure and the velocity iteratively at any time)
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