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The role of pressure for incompressible flows

Posted July 1, 2013 at 10:34 by sbaffini (NuTBox)
Updated December 21, 2016 at 10:11 by sbaffini

If we consider the continuity and momentum equations for a general compressible fluid:

\frac{\partial \rho}{\partial t} +
\frac{\partial}{\partial x_j}\left[ \rho u_j \right] = 0

\frac{\partial}{\partial t}\left( \rho u_i \right) +
\frac{\partial}{\partial x_j}
\left[ \rho u_i u_j + p \delta_{ij} - \tau_{ji} \right] = 0

taking the time derivative of the first one and the divergence of the second one:
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