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Understanding the sonicFoam tutorial energy equation

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September 13, 2019, 06:01	Understanding the sonicFoam tutorial energy equation	#1
metalfox New Member Join Date: Dec 2015 Posts: 24 Rep Power: 10	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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