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In imcompressible CFD code based on Chorin's projection method, the velocity is divided into 2 parts:

$\Delta u=\Delta u^*+\Delta u' $, where $\Delta u^*=\nu \nabla^2 v+f$. In classic method, pressure #p# would be solved by a Poisson equation, then the $u'$ would be calculated by its gradient.

In my code, a simple NN model is employed to predict the pressure by $u^*$, and it works approximately. However, the divergence of the velocity $\nabla \cdot \Delta u$, which should be zero in the whole flow area, could not keep zero.

I think it must be the problem of my simple NN model, and I am just wondering that can NN predict the velocity directly with the condition $\nabla \cdot \Delta u = 0$?

iElden
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Nothingts
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1 Answers1

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If your neural network does not learn to output divergence-free velocity fields, then obviously it will not do so. You could enforce the divergence free condition in the loss function of the neural network to try to achieve this.

b-fg
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