# 2nd order interpolation for NS solver

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 July 13, 2005, 02:11 2nd order interpolation for NS solver #1 Quarkz Guest   Posts: n/a Hi, I'm now trying to modify my cartesian grid to structured grids. My main objective is to model airfoil. I'm using 2nd order projection mtds to solve the NS eqn and hence at some pt, I need to evaluate the diffusive and convective flux. According to Peric's book on CFD, it uses linear interpolation between the 2 nodes on either side of the face to evaluate the face values. Moreover, it is stated that this is 2nd order. However, a paper by Kim & Choi (A 2nd order time accurate FVM for unsteady incompressible flow on hybrid unstructured grids) uses bilinear interpolation with 6 nodes to get the face value and it is also a 2nd order. Hence, can I just use Peric's linear interpolation or must I use Kim's bilinear interpolation to achieve 2nd order accuracy? Thanks alot

 July 13, 2005, 02:46 Re: 2nd order interpolation for NS solver #2 ramp Guest   Posts: n/a Are u modifying ur cartesian grid to structured or unstructured grid ?

 July 13, 2005, 02:48 Re: 2nd order interpolation for NS solver #3 Quarkz Guest   Posts: n/a To structured grid for airfoil (o or c grids)

 July 13, 2005, 13:03 Re: 2nd order interpolation for NS solver #4 coolblizz Guest   Posts: n/a Hi Quarkz.... The linear interpolation in Peric's book is 2nd-order only if the grids are orthogonal. If the non-orthogonality is severe, the interpolation becomes 1st-order. The interpolation by Kim and Choi will be more robust in this case since it uses more cells. Are you modifying your cartesian grid to body-fitted structured grid?

 July 13, 2005, 19:49 Re: 2nd order interpolation for NS solver #5 Quarkz Guest   Posts: n/a Hi, thanks. yes, i'll modifying my grid to body-fitted structured one for airfoils. in that case, is it recommended to use bilinear interpolation at the airfoil's leading and trailing since non-orthogonality is more pronounced at those regions?

 July 14, 2005, 14:06 Re: 2nd order interpolation for NS solver #6 coolblizz Guest   Posts: n/a Hi... Yes, sure. You will definitely want to minimize the loss of information at those regions. Just take care that if you are doing supersonic flows, the face values will have to be managed using some slope limiters for shock treatment. Just a side thought, is the name "bilinear interpolation" used in the paper by Kim and Choi? The word bilinear sounds to me it's an interpolation done on orthogonal grids.

 July 15, 2005, 21:50 Re: 2nd order interpolation for NS solver #7 Quarkz Guest   Posts: n/a yes it is written that "...and is equivalent to the bilinear interpolation in rectangular grids, ...."