Functions/Subroutines
subroutine	solve_elliptic_system (x, pv, nx, ny, deltax, deltay, F1, F2)
	Solves the elliptic system that arises when inverting potential vorticity. More...

Function/Subroutine Documentation

◆ solve_elliptic_system()

subroutine solve_elliptic_system	(	real(kind=kind_real), dimension(nx,ny,2), intent(out)	x,
		real(kind=kind_real), dimension(nx,ny,2), intent(in)	pv,
		integer, intent(in)	nx,
		integer, intent(in)	ny,
		real(kind=kind_real), intent(in)	deltax,
		real(kind=kind_real), intent(in)	deltay,
		real(kind=kind_real), intent(in)	F1,
		real(kind=kind_real), intent(in)	F2
	)

Solves the elliptic system that arises when inverting potential vorticity.

Here, we are solving the coupled system:

\begin{eqnarray} \nabla^2 \psi_1 - F_1 (\psi_1 -\psi_2 ) &=& p_1 \\\\ \nabla^2 \psi_2 - F_2 (\psi_2 -\psi_1 ) &=& p_2 \nonumber \end{eqnarray}

where the subscript refers to model level, and \( \nabla^2 \) is the 5-point finite-difference two-dimensional Laplacian.

We reduce this to a 2D problem, which we solve for \( \nabla^2 \psi_1 \):

\[ \nabla^2 \left(\nabla^2 \psi_1 \right) - (F_1 + F_2 ) \nabla^2 \psi_1 = \nabla^2 p_1 - F_2 p_1 - F_1 p_2 \]

Having found \( \nabla^2 \psi_1 \), we invert the Laplacian to determine \( \psi_1 \), and then get \( \psi_2 \) by substitution in equation 1 above.

Parameters

[in]	nx	Zonal grid dimension
[in]	ny	Meridional grid dimension
[out]	x	Streamfunction
[in]	pv	Right hand side
[in]	deltax	Zonal grid spacing (non-dimensional)
[in]	deltay	Meridional grid spacing (non-dimensional)
[in]	f1	Coefficient in the PV operator
[in]	f2	Coefficient in the PV operator

Definition at line 31 of file solve_elliptic_system.f90.

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