Simulate with complex geometries and complex physics
ComputationOfPSI
how to numerically compute the source term that goes with the viscous forces
From DerivePoissonEquationForPressure we have a formulation for \( \Phi(\mathbf{v})\), which is
\begin{align}
\Psi \left( \mathbf{v} \right)\equiv \nabla ^{T}\left( \frac{1}{\rho }\nabla \mathbf{S}_{v}\left( \mathbf{v} \right) \right)
\end{align}
In the same fashion as in ComputationOfPHI , we have the classical and the derived differential operators for the divergence operation needed for \( \Psi\).
Therefore, numerically, we have the two choices
- Variant 1: compute \( \Psi \left( \mathbf{v} \right) = \nabla ^{T}\left( ... \right)\) with the classical differential operators
- Variant 2: compute \( \Psi \left( \mathbf{v} \right) = \nabla ^{T}\left( ... \right)\) with the derived differential operators