# Rhie & Chow interpolation

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 January 17, 2003, 07:41 Rhie & Chow interpolation #1 Barry Guest   Posts: n/a My CFD friends... Can someone explain to me in plain and simple English what the idea behind Rhie and Chow interpolation is? I know that its purpose is to couple pressure and velocity on co-located meshes, but how does it work? How do I calculate the pressure gradient (face pressure) before I solve the momentum equation? Do we use linear interpolation for the pressure or some other scheme? And what about the pressure correction equation? Where does it fit in? Thank you. Looking forward to your replies! Barry

 January 17, 2003, 07:57 Re: Rhie & Chow interpolation #2 Angela Guest   Posts: n/a i am also a fresh in CFD.And does your Rhie and Chow mean some similarity as ROE?

 January 17, 2003, 13:18 Re: Rhie & Chow interpolation #3 frederic felten Guest   Posts: n/a Hi there, Here is my understanding of the Rhie & Chow interpolation procedure and some of the issues associated with it. The Cartesian velocity components u_i (or u, v, w) are stored with the pressure, p, at the cell center. In addition, contravariant volume fluxes, F_i ( i= 1, 2, 3), are defined at the cell face in a manner analogous to the staggered-mesh system. The volume fluxes are not solution variables, but rather are determined through interpolation of the cell-centered u_i values plus a projection operation that guarantees exact conservation of mass. Use of the mass-conserving volume fluxes results in a pressure equation identical to that in the staggered-mesh system and thus also leads to fully-coupled velocity and pressure fields. While the pressure field determined in this manner leads to mass conserving volume fluxes, it leaves the primary solution variables, u_i, only approximately divergence free. As pointed out by Morinishi et al.(J Comput. Phys., 143, 1998, pp 90-124), this defect leads to one source of kinetic energy conservation error. In my case, the pressure gradient on the face, is obtain just by differentiating the pressure values on both side of the face. In 1D, you then only need 3 points (i-1,i,i+1) to write the laplace operator. Now as far as the correction step for the cartesian cell center velocities is concern, this step will allow you to reduce the divergence level of the primary variables u_i. I did some testing involving this correction step and whether I did it or not, the code (turbulent channel flow) was still running fine, providing good results in both cases. Still, when the correction step was performed, the level of divergence came back half the non-corrected one. My advice to you is: do perform this correction step so that you'll avoid any kind of funky behavior that could eventually lead to instability. Hope this helps. Sincerely, Frederic Felten.

 January 20, 2003, 10:11 Re: Rhie & Chow interpolation #4 Barry Guest   Posts: n/a Dear Frderic Thank you for the explanation. It goes a long way in improving my understanding of the matter! Regards Barry

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