# Jacobian of NS equation

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 May 18, 2013, 18:57 Jacobian of NS equation #1 New Member   Mojtaba Moshiri Join Date: May 2013 Posts: 2 Rep Power: 0 Dear SU2 developers My question is about the projected Jacobian of NS equation as is calculated in function "CNumerics::GetViscProjJacs" I derived the very same expressions except from the length of edge vector in the denominator of all elements of Jacobian matrix. Could you please explain where this term came from? I wonder if it is possible to have some more detailed references about the formulation used in different parts of the code other than what is cited in the website and the paper AIAA 2013-0287.

May 27, 2013, 21:28
#2
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Francisco Palacios
Join Date: Jan 2013
Location: Long Beach, CA
Posts: 342
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Quote:
 Originally Posted by Mojtaba M Dear SU2 developers My question is about the projected Jacobian of NS equation as is calculated in function "CNumerics::GetViscProjJacs" I derived the very same expressions except from the length of edge vector in the denominator of all elements of Jacobian matrix. Could you please explain where this term came from? I wonder if it is possible to have some more detailed references about the formulation used in different parts of the code other than what is cited in the website and the paper AIAA 2013-0287.
Hi,

The length of the edge is a key element that you obtain when you estimate the normal gradient as $\partial_n U = (U_i - U_j) / (x_i - x_j)$. This simplification is used to evaluate the first order Jacobian (instead of Green-Gauss or LS).

Cheers,
Francisco

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