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Understanding the sonicFoam tutorial energy equation

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Old   September 13, 2019, 06:01
Default Understanding the sonicFoam tutorial energy equation
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In the supersonic flow over a forward-facing step tutorial (https://www.openfoam.com/documentati...utorialse6.php), the energy equation is stated to be:
\frac{\partial\rho e}{\partial t}+\nabla\cdot(\rho\mathbf{U}e)-\nabla\cdot\frac{k}{C_{v}}\nabla e=p\nabla\cdot\mathbf{U}

I have doubts regarding the p\nabla\cdot\mathbf{U} term. It appears in the right hand side of this equation. However, in the general energy equation (https://cfd.direct/openfoam/energy-equation/), there is a term \nabla\cdot(\mathbf{U}p), which appears in the left hand side.

If I'm not mistaken, \nabla\cdot(\mathbf{U}p) expands to p\nabla\cdot\mathbf{U}+\mathbf{U}\cdot\nabla p.

Why \mathbf{U}\cdot\nabla p vanishes in the above equation?

Isn't there a missing minus sign for the p\nabla\cdot\mathbf{U} term?
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