Lagrange

This algorithm solves the conservation of momentum stated in EquationsToSolve. \begin{align} \mathbf{\tilde{v}}_{i}^{n+1}-\frac{\Delta t}{\rho }\sum\limits_{j}{c_{ij}^{{{\nabla }^{T}}\left( \hat{\eta} \nabla \right)}}\cdot \mathbf{\tilde{v}}_{j}^{n+1}+\Delta t\cdot \beta \cdot \mathbf{\tilde{v}}_{i}^{n+1}=\mathbf{v}_{i}^{n}-\frac{\Delta t}{\rho }\left( \nabla \tilde{p}_{hyd}^{n+1} \right)_{i}-\frac{\Delta t}{\rho }\left( \nabla \tilde{p}_{dyn}^{n} \right)_{i}+\Delta t\cdot \mathbf{\hat{g}}_{i}^{n}\end{align}