pistol’s documentation¶
Equations of motion¶
See this Equations of motions
Install¶
We recommend conda for dependencies, see README on pistol github repository
Tutorial¶
To do …
mpirun -n 4 python analytical.py -mf -ksp_view -ksp_monitor -ksp_converged_reason
Profiling:
mpirun -n 4 python -m cProfile -o output.prof uniform.py
snakeviz output.prof
API¶
Equations of motions¶
Continuous form¶
Boussinesq, adiabatic, hydrostatic and nonlinear shallow water equations for conservation of momentum:
\[\partial_t \mathbf{u}_n(x,y) + (\zeta_n + f) \mathbf{k}\times\mathbf{u}_n = -\nabla \Big \{ M_n + \frac{1}{2} |\mathbf{u}_n|^2 + g \Pi \Big \}
+ \mathbf{H}_n + \mathbf{V}_n\]
for \(n=0,\cdots N-1\) and where \(f\) is the Coriolis frequency and \(\zeta_n = \mathbf{k}\cdot (\nabla \times \mathbf{u}_n )\) is the relative vorticity, \(M_n\) is the perturbation Montgomery potential. The latter is given by:
\[ \begin{align}\begin{aligned}z_0 &= \eta\\z_n &= z_{n-1} - h_n, n > 0\end{aligned}\end{align} \]
\[ \begin{align}\begin{aligned}M_0 &= g \eta\\M_n &= M_{n-1} + g (\rho_{n}-\rho_{n-1}) z_n, n>0\end{aligned}\end{align} \]
\[p_n(x,y,z) = M_n(x,y) - g \rho_n z\]
Thickness tendency equations:
\[\partial_t h_n(x,y) + \nabla \cdot (\mathbf{u}_n h_n ) = 0.\]
References: …