# Isn't the trace of gradU the continuity equation? I need a quantity for elongation

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 September 9, 2009, 03:04 Isn't the trace of gradU the continuity equation? I need a quantity for elongation #1 New Member   Alex Join Date: Jun 2009 Location: Erlangen, Germany Posts: 7 Rep Power: 9 Hi forum users, I simulated a two phase flow with interFoam and when I compute the "L" tensor (fvc::grad(U)) and take the trace of it (should be du/dx+dv/dy+dw/dz) I don't get zero. I always thought with the finite volume approximation the continuity equation is valid for each single cell?!? Or did I understand something wrong? The reason is the following. I am looking for a quantity to measure the elongation in my system. As for shear rate it is clear sqrt(2)*mag(symm(fvc::grad(U))) which is the standard definition of shear rate in 3D. But what is it for the elongation rate? I tried to look it up but I can't find a proper definition (Till now I work with sqrt(2)((du/dx)^2+(dv/dy)^2+(dw/dz)^2) I would be really happy if someone of you could help me Best regards Alex

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