pressure velocity decoupling
I know of two methods for eliminating pressure velocity decoupling. One is a staggered grid. The other is Rhie and Chow's method of essentially adding a fourth derivative of pressure to the continuity equation as a smoothing term. Are there any other methods?

Re: pressure velocity decoupling
By using the curloperation on the momentum equation, you can get rid of the pressure gradient terms because curl of gradient of p is zero. The resultant equation is the vorticity equation. The density variation can be considered as the source term which disappears completely at the incompressible flow limit ( constant density ). This approach can be used safely for subsonic flow without shock waves. The equation of state can also be used in the calculation. For viscous flow, the use of vorticity is more attractive, even the old and popular BaldwinLomax turbulence model is based on the vorticity.

Re: pressure velocity decoupling
Another method is Peric's method. See Ferziger&Peric's book for details.

Re: pressure velocity decoupling
which is basically a more detailed derivation of Rhie & Chow. If I'm not mistaken, Peric developed roughly the same approach independently of, but later than, Rhie & Chow.

Re: pressure velocity decoupling
Another possibilities are: 1. Conforming piecewise linear P1 finite elements and the pair of spaces V_h, V_h/2 for the pressure and velocity, respectively (i.e, use triangular meshes consisting of triangles with six nodes each). The BabuskaBrezzi condition is satisfied by this pair of spaces. 2. P1 FE and the Chorin method (adapted for compressible flows, if necessary). Essentially an L2 method for pressure equation. See, e.g., Prohl's book on projection methods. 3. Masson, Saabas and Baligas's method: not as elgant as 2), roughly speaking, it is a discrete version of 2)  see Int. J. Numer. Meth. Fluids 18, 126 (1994).

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